diff --git a/.github/workflows/FormatCheck.yml b/.github/workflows/FormatCheck.yml index 81d18f4105e..a733cb7cc21 100644 --- a/.github/workflows/FormatCheck.yml +++ b/.github/workflows/FormatCheck.yml @@ -30,7 +30,7 @@ jobs: # format(".") run: | julia -e 'using Pkg; Pkg.add(PackageSpec(name = "JuliaFormatter"))' - julia -e 'using JuliaFormatter; format(["benchmark", "ext", "src", "test", "utils"])' + julia -e 'using JuliaFormatter; format(["benchmark", "examples", "ext", "src", "test", "utils"])' - name: Format check run: | julia -e ' diff --git a/README.md b/README.md index 673708d8b89..1d52089ae3e 100644 --- a/README.md +++ b/README.md @@ -256,31 +256,48 @@ or [create an issue](https://github.com/trixi-framework/Trixi.jl/issues/new). ## Acknowledgments -

- +

-This project has benefited from funding by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) -under Germany's Excellence Strategy EXC 2044-390685587, Mathematics Münster: -Dynamics-Geometry-Structure. - -This project has benefited from funding by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) -through the research unit FOR 5409 "Structure-Preserving Numerical Methods for Bulk- and -Interface Coupling of Heterogeneous Models (SNuBIC)" (project number 463312734). +This project has benefited from funding by the [Deutsche +Forschungsgemeinschaft](https://www.dfg.de/) (DFG, German Research Foundation) +through the following grants: +* Excellence Strategy EXC 2044-390685587, Mathematics Münster: Dynamics-Geometry-Structure. +* Research unit FOR 5409 "Structure-Preserving Numerical Methods for Bulk- and + Interface Coupling of Heterogeneous Models (SNuBIC)" (project number 463312734). +* Individual grant no. 528753982. -This project has benefited from funding from the European Research Council through the +This project has benefited from funding from the [European Research Council](https://erc.europa.eu) +through the ERC Starting Grant "An Exascale aware and Un-crashable Space-Time-Adaptive Discontinuous Spectral Element Solver for Non-Linear Conservation Laws" (Extreme), ERC grant agreement no. 714487. -This project has benefited from funding from Vetenskapsrådet (VR, Swedish Research Council), Sweden +This project has benefited from funding from [Vetenskapsrådet](https://www.vr.se) +(VR, Swedish Research Council), Sweden through the VR Starting Grant "Shallow water flows including sediment transport and morphodynamics", VR grant agreement 2020-03642 VR. -This project has benefited from funding from the United States National Science Foundation under awards +This project has benefited from funding from the United States +[National Science Foundation](https://www.nsf.gov/) (NSF) under awards DMS-1719818 and DMS-1943186. -This project has benefited from funding from the German Federal Ministry of -Education and Research through the project grant "Adaptive earth system modeling +This project has benefited from funding from the German +[Federal Ministry of Education and Research](https://www.bmbf.de) (BMBF) +through the project grant "Adaptive earth system modeling with significantly reduced computation time for exascale supercomputers (ADAPTEX)" (funding id: 16ME0668K). + +This project has benefited from funding by the +[Daimler und Benz Stiftung](https://www.daimler-benz-stiftung.de) (Daimler and Benz Foundation) +through grant no. 32-10/22. + +Trixi.jl is supported by [NumFOCUS](https://numfocus.org/) as an Affiliated Project. diff --git a/docs/literate/src/files/differentiable_programming.jl b/docs/literate/src/files/differentiable_programming.jl index 33427803afc..0960ba25d9f 100644 --- a/docs/literate/src/files/differentiable_programming.jl +++ b/docs/literate/src/files/differentiable_programming.jl @@ -43,7 +43,7 @@ scatter(real.(λ), imag.(λ), label="central flux") # As you can see here, the maximal real part is close to zero. relative_maximum = maximum(real, λ) / maximum(abs, λ) -@test 3.0e-10 < relative_maximum < 8.0e-10 #src +@test 3.0e-10 < relative_maximum < 9.0e-10 #src # Interestingly, if we add dissipation by switching to the `flux_lax_friedrichs` # at the interfaces, the maximal real part of the eigenvalues increases. @@ -87,7 +87,7 @@ scatter(real.(λ), imag.(λ), label="central flux") # Here, the maximal real part is basically zero to machine accuracy. relative_maximum = maximum(real, λ) / maximum(abs, λ) -@test 1.0e-17 < relative_maximum < 1.0e-15 #src +@test 1.0e-17 < relative_maximum < 2.0e-15 #src # Moreover, the eigenvectors are not as ill-conditioned as in 2D. diff --git a/docs/src/index.md b/docs/src/index.md index 9ffaee26c40..fd923348928 100644 --- a/docs/src/index.md +++ b/docs/src/index.md @@ -344,29 +344,58 @@ or [create an issue](https://github.com/trixi-framework/Trixi.jl/issues/new). ## Acknowledgments -![funding-logo](https://user-images.githubusercontent.com/3637659/233821022-84910be7-8649-4999-a0ff-22d5e20f0b90.jpg) - -This project has benefited from funding by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) -under Germany's Excellence Strategy EXC 2044-390685587, Mathematics Münster: -Dynamics-Geometry-Structure. +```@raw html +
+
+
+
+
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+
+
+``` -This project has benefited from funding by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) -through the research unit FOR 5409 "Structure-Preserving Numerical Methods for Bulk- and -Interface Coupling of Heterogeneous Models (SNuBIC)" (project number 463312734). +This project has benefited from funding by the [Deutsche +Forschungsgemeinschaft](https://www.dfg.de/) (DFG, German Research Foundation) +through the following grants: +* Excellence Strategy EXC 2044-390685587, Mathematics Münster: Dynamics-Geometry-Structure. +* Research unit FOR 5409 "Structure-Preserving Numerical Methods for Bulk- and + Interface Coupling of Heterogeneous Models (SNuBIC)" (project number 463312734). +* Individual grant no. 528753982. -This project has benefited from funding from the European Research Council through the +This project has benefited from funding from the [European Research Council](https://erc.europa.eu) +through the ERC Starting Grant "An Exascale aware and Un-crashable Space-Time-Adaptive Discontinuous Spectral Element Solver for Non-Linear Conservation Laws" (Extreme), ERC grant agreement no. 714487. -This project has benefited from funding from Vetenskapsrådet (VR, Swedish Research Council), Sweden +This project has benefited from funding from [Vetenskapsrådet](https://www.vr.se) +(VR, Swedish Research Council), Sweden through the VR Starting Grant "Shallow water flows including sediment transport and morphodynamics", VR grant agreement 2020-03642 VR. -This project has benefited from funding from the United States National Science Foundation under awards +This project has benefited from funding from the United States +[National Science Foundation](https://www.nsf.gov/) (NSF) under awards DMS-1719818 and DMS-1943186. -This project has benefited from funding from the German Federal Ministry of -Education and Research through the project grant "Adaptive earth system modeling +This project has benefited from funding from the German +[Federal Ministry of Education and Research](https://www.bmbf.de) (BMBF) +through the project grant "Adaptive earth system modeling with significantly reduced computation time for exascale supercomputers (ADAPTEX)" (funding id: 16ME0668K). + +This project has benefited from funding by the +[Daimler und Benz Stiftung](https://www.daimler-benz-stiftung.de) (Daimler and Benz Foundation) +through grant no. 32-10/22. + +Trixi.jl is supported by [NumFOCUS](https://numfocus.org/) as an Affiliated Project. diff --git a/docs/src/styleguide.md b/docs/src/styleguide.md index 60e227204ca..2f28dbfcb17 100644 --- a/docs/src/styleguide.md +++ b/docs/src/styleguide.md @@ -17,11 +17,11 @@ conventions, we apply and enforce automated source code formatting * Maximum line length (strictly): **92**. * Functions that mutate their *input* are named with a trailing `!`. * Functions order their parameters [similar to Julia Base](https://docs.julialang.org/en/v1/manual/style-guide/#Write-functions-with-argument-ordering-similar-to-Julia-Base-1). - * The main modified argument comes first. For example, if the right-hand side `du` is modified, - it should come first. If only the `cache` is modified, e.g., in `prolong2interfaces!` + * The main modified argument comes first. For example, if the right-hand side `du` is modified, + it should come first. If only the `cache` is modified, e.g., in `prolong2interfaces!` and its siblings, put the `cache` first. * Otherwise, use the order `mesh, equations, solver, cache`. - * If something needs to be specified in more detail for dispatch, put the additional argument before the general one + * If something needs to be specified in more detail for dispatch, put the additional argument before the general one that is specified in more detail. For example, we use `have_nonconservative_terms(equations), equations` and `dg.mortar, dg`. * Prefer `for i in ...` to `for i = ...` for better semantic clarity and greater flexibility. @@ -55,7 +55,7 @@ julia -e 'using Pkg; Pkg.add("JuliaFormatter")' ``` You can then recursively format the core Julia files in the Trixi.jl repo by executing ```shell -julia -e 'using JuliaFormatter; format(["benchmark", "ext", "src", "utils"])' +julia -e 'using JuliaFormatter; format(["benchmark", "examples", "ext", "src", "test", "utils"])' ``` from inside the Trixi.jl repository. For convenience, there is also a script you can directly run from your terminal shell, which will automatically install JuliaFormatter in a @@ -67,12 +67,12 @@ You can get more information about using the convenience script by running it wi `--help`/`-h` flag. ### Checking formatting before committing -It can be convenient to check the formatting of source code automatically before each commit. +It can be convenient to check the formatting of source code automatically before each commit. We use git-hooks for it and provide a `pre-commit` script in the `utils` folder. The script uses -[JuliaFormatter.jl](https://github.com/domluna/JuliaFormatter.jl) just like formatting script that -runs over the whole Trixi.jl directory. -You can copy the `pre-commit`-script into `.git/hooks/pre-commit` and it will check your formatting +[JuliaFormatter.jl](https://github.com/domluna/JuliaFormatter.jl) just like formatting script that +runs over the whole Trixi.jl directory. +You can copy the `pre-commit`-script into `.git/hooks/pre-commit` and it will check your formatting before each commit. If errors are found the commit is aborted and you can add the corrections via -```shell +```shell git add -p ``` diff --git a/examples/dgmulti_1d/elixir_advection_gauss_sbp.jl b/examples/dgmulti_1d/elixir_advection_gauss_sbp.jl index d06ed05a621..09d66fe8aea 100644 --- a/examples/dgmulti_1d/elixir_advection_gauss_sbp.jl +++ b/examples/dgmulti_1d/elixir_advection_gauss_sbp.jl @@ -23,8 +23,8 @@ dg = DGMulti(polydeg = 3, cells_per_dimension = (8,) mesh = DGMultiMesh(dg, cells_per_dimension, - coordinates_min=(-1.0,), coordinates_max=(1.0,), - periodicity=true) + coordinates_min = (-1.0,), coordinates_max = (1.0,), + periodicity = true) ############################################################################### # setup the test problem (no source term needed for linear advection) @@ -49,10 +49,10 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() # analyse the solution in regular intervals and prints the results -analysis_callback = AnalysisCallback(semi, interval=100, uEltype=real(dg)) +analysis_callback = AnalysisCallback(semi, interval = 100, uEltype = real(dg)) # handles the re-calculation of the maximum Δt after each time step -stepsize_callback = StepsizeCallback(cfl=0.75) +stepsize_callback = StepsizeCallback(cfl = 0.75) # collect all callbacks such that they can be passed to the ODE solver callbacks = CallbackSet(summary_callback, analysis_callback, stepsize_callback) @@ -60,9 +60,8 @@ callbacks = CallbackSet(summary_callback, analysis_callback, stepsize_callback) ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, save_everystep = false, callback = callbacks); # Print the timer summary summary_callback() - diff --git a/examples/dgmulti_1d/elixir_euler_fdsbp_periodic.jl b/examples/dgmulti_1d/elixir_euler_fdsbp_periodic.jl index 3566185d110..6abd7118fe3 100644 --- a/examples/dgmulti_1d/elixir_euler_fdsbp_periodic.jl +++ b/examples/dgmulti_1d/elixir_euler_fdsbp_periodic.jl @@ -2,8 +2,10 @@ using Trixi, OrdinaryDiffEq dg = DGMulti(element_type = Line(), - approximation_type = periodic_derivative_operator( - derivative_order=1, accuracy_order=4, xmin=0.0, xmax=1.0, N=50), + approximation_type = periodic_derivative_operator(derivative_order = 1, + accuracy_order = 4, + xmin = 0.0, xmax = 1.0, + N = 50), surface_flux = flux_hll, volume_integral = VolumeIntegralWeakForm()) @@ -11,8 +13,8 @@ equations = CompressibleEulerEquations1D(1.4) initial_condition = initial_condition_convergence_test source_terms = source_terms_convergence_test -mesh = DGMultiMesh(dg, coordinates_min=(-1.0,), - coordinates_max=( 1.0,)) +mesh = DGMultiMesh(dg, coordinates_min = (-1.0,), + coordinates_max = (1.0,)) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, dg, source_terms = source_terms) @@ -21,15 +23,16 @@ tspan = (0.0, 0.4) ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() -alive_callback = AliveCallback(alive_interval=10) +alive_callback = AliveCallback(alive_interval = 10) analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval, uEltype=real(dg)) -stepsize_callback = StepsizeCallback(cfl=1.0) -callbacks = CallbackSet(summary_callback, alive_callback, stepsize_callback, analysis_callback) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval, uEltype = real(dg)) +stepsize_callback = StepsizeCallback(cfl = 1.0) +callbacks = CallbackSet(summary_callback, alive_callback, stepsize_callback, + analysis_callback) ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt = 0.5 * estimate_dt(mesh, dg), save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 0.5 * estimate_dt(mesh, dg), save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/dgmulti_1d/elixir_euler_flux_diff.jl b/examples/dgmulti_1d/elixir_euler_flux_diff.jl index 489b23e37b2..56a24d25d07 100644 --- a/examples/dgmulti_1d/elixir_euler_flux_diff.jl +++ b/examples/dgmulti_1d/elixir_euler_flux_diff.jl @@ -13,17 +13,17 @@ source_terms = source_terms_convergence_test cells_per_dimension = (8,) mesh = DGMultiMesh(dg, cells_per_dimension, - coordinates_min=(-1.0,), coordinates_max=(1.0,), periodicity=true) + coordinates_min = (-1.0,), coordinates_max = (1.0,), periodicity = true) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, dg; - source_terms=source_terms) + source_terms = source_terms) tspan = (0.0, 1.1) ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() -alive_callback = AliveCallback(alive_interval=10) +alive_callback = AliveCallback(alive_interval = 10) analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval, uEltype=real(dg)) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval, uEltype = real(dg)) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback) @@ -31,7 +31,7 @@ callbacks = CallbackSet(summary_callback, ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt = 0.5 * estimate_dt(mesh, dg), save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 0.5 * estimate_dt(mesh, dg), save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/dgmulti_2d/elixir_advection_diffusion.jl b/examples/dgmulti_2d/elixir_advection_diffusion.jl index 8a79e9700ac..ce7b0e745a4 100644 --- a/examples/dgmulti_2d/elixir_advection_diffusion.jl +++ b/examples/dgmulti_2d/elixir_advection_diffusion.jl @@ -11,48 +11,52 @@ initial_condition_zero(x, t, equations::LinearScalarAdvectionEquation2D) = SVect initial_condition = initial_condition_zero # tag different boundary segments -left(x, tol=50*eps()) = abs(x[1] + 1) < tol -right(x, tol=50*eps()) = abs(x[1] - 1) < tol -bottom(x, tol=50*eps()) = abs(x[2] + 1) < tol -top(x, tol=50*eps()) = abs(x[2] - 1) < tol +left(x, tol = 50 * eps()) = abs(x[1] + 1) < tol +right(x, tol = 50 * eps()) = abs(x[1] - 1) < tol +bottom(x, tol = 50 * eps()) = abs(x[2] + 1) < tol +top(x, tol = 50 * eps()) = abs(x[2] - 1) < tol is_on_boundary = Dict(:left => left, :right => right, :top => top, :bottom => bottom) cells_per_dimension = (16, 16) mesh = DGMultiMesh(dg, cells_per_dimension; is_on_boundary) # BC types -boundary_condition_left = BoundaryConditionDirichlet((x, t, equations) -> SVector(1 + 0.1 * x[2])) +boundary_condition_left = BoundaryConditionDirichlet((x, t, equations) -> SVector(1 + + 0.1 * + x[2])) boundary_condition_zero = BoundaryConditionDirichlet((x, t, equations) -> SVector(0.0)) boundary_condition_neumann_zero = BoundaryConditionNeumann((x, t, equations) -> SVector(0.0)) # define inviscid boundary conditions boundary_conditions = (; :left => boundary_condition_left, - :bottom => boundary_condition_zero, - :top => boundary_condition_do_nothing, - :right => boundary_condition_do_nothing) + :bottom => boundary_condition_zero, + :top => boundary_condition_do_nothing, + :right => boundary_condition_do_nothing) # define viscous boundary conditions boundary_conditions_parabolic = (; :left => boundary_condition_left, - :bottom => boundary_condition_zero, - :top => boundary_condition_zero, - :right => boundary_condition_neumann_zero) + :bottom => boundary_condition_zero, + :top => boundary_condition_zero, + :right => boundary_condition_neumann_zero) -semi = SemidiscretizationHyperbolicParabolic(mesh, (equations, equations_parabolic), initial_condition, dg; - boundary_conditions=(boundary_conditions, boundary_conditions_parabolic)) +semi = SemidiscretizationHyperbolicParabolic(mesh, (equations, equations_parabolic), + initial_condition, dg; + boundary_conditions = (boundary_conditions, + boundary_conditions_parabolic)) tspan = (0.0, 1.5) ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() -alive_callback = AliveCallback(alive_interval=10) +alive_callback = AliveCallback(alive_interval = 10) analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval, uEltype=real(dg)) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval, uEltype = real(dg)) callbacks = CallbackSet(summary_callback, alive_callback) ############################################################################### # run the simulation time_int_tol = 1e-6 -sol = solve(ode, RDPK3SpFSAL49(); abstol=time_int_tol, reltol=time_int_tol, - ode_default_options()..., callback=callbacks) +sol = solve(ode, RDPK3SpFSAL49(); abstol = time_int_tol, reltol = time_int_tol, + ode_default_options()..., callback = callbacks) summary_callback() # print the timer summary diff --git a/examples/dgmulti_2d/elixir_advection_diffusion_nonperiodic.jl b/examples/dgmulti_2d/elixir_advection_diffusion_nonperiodic.jl index 7e87d9f097d..d2f11f18507 100644 --- a/examples/dgmulti_2d/elixir_advection_diffusion_nonperiodic.jl +++ b/examples/dgmulti_2d/elixir_advection_diffusion_nonperiodic.jl @@ -16,61 +16,63 @@ equations_parabolic = LaplaceDiffusion2D(diffusivity(), equations) # to numerical partial differential equations. # [DOI](https://doi.org/10.1007/978-3-319-41640-3_6). function initial_condition_erikkson_johnson(x, t, equations) - l = 4 - epsilon = diffusivity() # Note: this requires epsilon < 0.6 due to the sqrt - lambda_1 = (-1 + sqrt(1 - 4 * epsilon * l)) / (-2 * epsilon) - lambda_2 = (-1 - sqrt(1 - 4 * epsilon * l)) / (-2 * epsilon) - r1 = (1 + sqrt(1 + 4 * pi^2 * epsilon^2)) / (2 * epsilon) - s1 = (1 - sqrt(1 + 4 * pi^2 * epsilon^2)) / (2 * epsilon) - u = exp(-l * t) * (exp(lambda_1 * x[1]) - exp(lambda_2 * x[1])) + - cos(pi * x[2]) * (exp(s1 * x[1]) - exp(r1 * x[1])) / (exp(-s1) - exp(-r1)) - return SVector{1}(u) + l = 4 + epsilon = diffusivity() # Note: this requires epsilon < 0.6 due to the sqrt + lambda_1 = (-1 + sqrt(1 - 4 * epsilon * l)) / (-2 * epsilon) + lambda_2 = (-1 - sqrt(1 - 4 * epsilon * l)) / (-2 * epsilon) + r1 = (1 + sqrt(1 + 4 * pi^2 * epsilon^2)) / (2 * epsilon) + s1 = (1 - sqrt(1 + 4 * pi^2 * epsilon^2)) / (2 * epsilon) + u = exp(-l * t) * (exp(lambda_1 * x[1]) - exp(lambda_2 * x[1])) + + cos(pi * x[2]) * (exp(s1 * x[1]) - exp(r1 * x[1])) / (exp(-s1) - exp(-r1)) + return SVector{1}(u) end initial_condition = initial_condition_erikkson_johnson # tag different boundary segments -left(x, tol=50*eps()) = abs(x[1] + 1) < tol -right(x, tol=50*eps()) = abs(x[1]) < tol -bottom(x, tol=50*eps()) = abs(x[2] + 0.5) < tol -top(x, tol=50*eps()) = abs(x[2] - 0.5) < tol -entire_boundary(x, tol=50*eps()) = true +left(x, tol = 50 * eps()) = abs(x[1] + 1) < tol +right(x, tol = 50 * eps()) = abs(x[1]) < tol +bottom(x, tol = 50 * eps()) = abs(x[2] + 0.5) < tol +top(x, tol = 50 * eps()) = abs(x[2] - 0.5) < tol +entire_boundary(x, tol = 50 * eps()) = true is_on_boundary = Dict(:left => left, :right => right, :top => top, :bottom => bottom, :entire_boundary => entire_boundary) cells_per_dimension = (16, 16) mesh = DGMultiMesh(dg, cells_per_dimension; - coordinates_min=(-1.0, -0.5), - coordinates_max=(0.0, 0.5), + coordinates_min = (-1.0, -0.5), + coordinates_max = (0.0, 0.5), is_on_boundary) # BC types boundary_condition = BoundaryConditionDirichlet(initial_condition) # define inviscid boundary conditions, enforce "do nothing" boundary condition at the outflow -boundary_conditions = (; :left => boundary_condition, - :top => boundary_condition, - :bottom => boundary_condition, - :right => boundary_condition_do_nothing) +boundary_conditions = (; :left => boundary_condition, + :top => boundary_condition, + :bottom => boundary_condition, + :right => boundary_condition_do_nothing) # define viscous boundary conditions boundary_conditions_parabolic = (; :entire_boundary => boundary_condition) -semi = SemidiscretizationHyperbolicParabolic(mesh, (equations, equations_parabolic), initial_condition, dg; - boundary_conditions=(boundary_conditions, boundary_conditions_parabolic)) +semi = SemidiscretizationHyperbolicParabolic(mesh, (equations, equations_parabolic), + initial_condition, dg; + boundary_conditions = (boundary_conditions, + boundary_conditions_parabolic)) tspan = (0.0, 1.5) ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() -alive_callback = AliveCallback(alive_interval=10) +alive_callback = AliveCallback(alive_interval = 10) analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval, uEltype=real(dg)) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval, uEltype = real(dg)) callbacks = CallbackSet(summary_callback, alive_callback) ############################################################################### # run the simulation time_int_tol = 1e-8 -sol = solve(ode, RDPK3SpFSAL49(); abstol=time_int_tol, reltol=time_int_tol, - ode_default_options()..., callback=callbacks) +sol = solve(ode, RDPK3SpFSAL49(); abstol = time_int_tol, reltol = time_int_tol, + ode_default_options()..., callback = callbacks) summary_callback() # print the timer summary diff --git a/examples/dgmulti_2d/elixir_advection_diffusion_periodic.jl b/examples/dgmulti_2d/elixir_advection_diffusion_periodic.jl index 76512f1e39f..c498e5468d3 100644 --- a/examples/dgmulti_2d/elixir_advection_diffusion_periodic.jl +++ b/examples/dgmulti_2d/elixir_advection_diffusion_periodic.jl @@ -8,12 +8,12 @@ equations = LinearScalarAdvectionEquation2D(0.0, 0.0) equations_parabolic = LaplaceDiffusion2D(5.0e-1, equations) function initial_condition_sharp_gaussian(x, t, equations::LinearScalarAdvectionEquation2D) - return SVector(exp(-100 * (x[1]^2 + x[2]^2))) + return SVector(exp(-100 * (x[1]^2 + x[2]^2))) end initial_condition = initial_condition_sharp_gaussian cells_per_dimension = (16, 16) -mesh = DGMultiMesh(dg, cells_per_dimension, periodicity=true) +mesh = DGMultiMesh(dg, cells_per_dimension, periodicity = true) semi = SemidiscretizationHyperbolicParabolic(mesh, (equations, equations_parabolic), initial_condition, dg) @@ -21,16 +21,16 @@ tspan = (0.0, 0.1) ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() -alive_callback = AliveCallback(alive_interval=10) +alive_callback = AliveCallback(alive_interval = 10) analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval, uEltype=real(dg)) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval, uEltype = real(dg)) callbacks = CallbackSet(summary_callback, alive_callback, analysis_callback) ############################################################################### # run the simulation time_int_tol = 1e-6 -sol = solve(ode, RDPK3SpFSAL49(); abstol=time_int_tol, reltol=time_int_tol, - dt = time_int_tol, ode_default_options()..., callback=callbacks) +sol = solve(ode, RDPK3SpFSAL49(); abstol = time_int_tol, reltol = time_int_tol, + dt = time_int_tol, ode_default_options()..., callback = callbacks) summary_callback() # print the timer summary diff --git a/examples/dgmulti_2d/elixir_euler_bilinear.jl b/examples/dgmulti_2d/elixir_euler_bilinear.jl index bdd582610ea..cd498bf39b8 100644 --- a/examples/dgmulti_2d/elixir_euler_bilinear.jl +++ b/examples/dgmulti_2d/elixir_euler_bilinear.jl @@ -10,27 +10,28 @@ initial_condition = initial_condition_convergence_test source_terms = source_terms_convergence_test # example where we tag two separate boundary segments of the mesh -top_boundary(x, tol=50*eps()) = abs(x[2]-1) top_boundary, :rest => rest_of_boundary) function mapping(xi, eta) - x = xi + 0.1 * sin(pi * xi) * sin(pi * eta) - y = eta + 0.1 * sin(pi * xi) * sin(pi * eta) - return SVector(x, y) + x = xi + 0.1 * sin(pi * xi) * sin(pi * eta) + y = eta + 0.1 * sin(pi * xi) * sin(pi * eta) + return SVector(x, y) end cells_per_dimension = (16, 16) -vertex_coordinates, EToV = StartUpDG.uniform_mesh(dg.basis.element_type, cells_per_dimension...) +vertex_coordinates, EToV = StartUpDG.uniform_mesh(dg.basis.element_type, + cells_per_dimension...) for i in eachindex(vertex_coordinates[1]) - vx, vy = getindex.(vertex_coordinates, i) - setindex!.(vertex_coordinates, mapping(vx, vy), i) + vx, vy = getindex.(vertex_coordinates, i) + setindex!.(vertex_coordinates, mapping(vx, vy), i) end -mesh = DGMultiMesh(dg, vertex_coordinates, EToV, is_on_boundary=is_on_boundary) +mesh = DGMultiMesh(dg, vertex_coordinates, EToV, is_on_boundary = is_on_boundary) boundary_condition_convergence_test = BoundaryConditionDirichlet(initial_condition) boundary_conditions = (; :top => boundary_condition_convergence_test, - :rest => boundary_condition_convergence_test) + :rest => boundary_condition_convergence_test) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, dg, source_terms = source_terms, @@ -40,15 +41,15 @@ tspan = (0.0, 0.4) ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() -alive_callback = AliveCallback(alive_interval=10) +alive_callback = AliveCallback(alive_interval = 10) analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval, uEltype=real(dg)) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval, uEltype = real(dg)) callbacks = CallbackSet(summary_callback, alive_callback, analysis_callback) ############################################################################### # run the simulation -sol = solve(ode, RDPK3SpFSAL49(); abstol=1.0e-6, reltol=1.0e-6, - ode_default_options()..., callback=callbacks); +sol = solve(ode, RDPK3SpFSAL49(); abstol = 1.0e-6, reltol = 1.0e-6, + ode_default_options()..., callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/dgmulti_2d/elixir_euler_brown_minion_vortex.jl b/examples/dgmulti_2d/elixir_euler_brown_minion_vortex.jl index 4bb05c0b062..e7830c4736b 100644 --- a/examples/dgmulti_2d/elixir_euler_brown_minion_vortex.jl +++ b/examples/dgmulti_2d/elixir_euler_brown_minion_vortex.jl @@ -1,6 +1,6 @@ using Trixi, OrdinaryDiffEq -dg = DGMulti(polydeg=4, element_type = Quad(), approximation_type = Polynomial(), +dg = DGMulti(polydeg = 4, element_type = Quad(), approximation_type = Polynomial(), surface_integral = SurfaceIntegralWeakForm(FluxLaxFriedrichs()), volume_integral = VolumeIntegralFluxDifferencing(flux_ranocha)) @@ -16,38 +16,38 @@ incompressible version. [DOI: 10.1006/jcph.1995.1205](https://doi.org/10.1006/jcph.1995.1205) """ function initial_condition_BM_vortex(x, t, equations::CompressibleEulerEquations2D) - pbar = 9.0 / equations.gamma - delta = 0.05 - epsilon = 30 - H = (x[2] < 0) ? tanh(epsilon * (x[2] + 0.25)) : tanh(epsilon * (0.25 - x[2])) - rho = 1.0 - v1 = H - v2 = delta * cos(2.0 * pi * x[1]) - p = pbar - return prim2cons(SVector(rho, v1, v2, p), equations) + pbar = 9.0 / equations.gamma + delta = 0.05 + epsilon = 30 + H = (x[2] < 0) ? tanh(epsilon * (x[2] + 0.25)) : tanh(epsilon * (0.25 - x[2])) + rho = 1.0 + v1 = H + v2 = delta * cos(2.0 * pi * x[1]) + p = pbar + return prim2cons(SVector(rho, v1, v2, p), equations) end initial_condition = initial_condition_BM_vortex cells_per_dimension = (16, 16) mesh = DGMultiMesh(dg, cells_per_dimension, - coordinates_min=(-0.5, -0.5), coordinates_max=(0.5, 0.5), - periodicity=true) + coordinates_min = (-0.5, -0.5), coordinates_max = (0.5, 0.5), + periodicity = true) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, dg) tspan = (0.0, 1.0) ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() -alive_callback = AliveCallback(alive_interval=10) +alive_callback = AliveCallback(alive_interval = 10) analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval, uEltype=real(dg)) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval, uEltype = real(dg)) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback) ############################################################################### # run the simulation tol = 1.0e-8 -sol = solve(ode, RDPK3SpFSAL49(); abstol=tol, reltol=tol, - ode_default_options()..., callback=callbacks); +sol = solve(ode, RDPK3SpFSAL49(); abstol = tol, reltol = tol, + ode_default_options()..., callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/dgmulti_2d/elixir_euler_curved.jl b/examples/dgmulti_2d/elixir_euler_curved.jl index 39e3a0a0360..48662f4b12b 100644 --- a/examples/dgmulti_2d/elixir_euler_curved.jl +++ b/examples/dgmulti_2d/elixir_euler_curved.jl @@ -10,21 +10,21 @@ initial_condition = initial_condition_convergence_test source_terms = source_terms_convergence_test # example where we tag two separate boundary segments of the mesh -top_boundary(x, tol=50*eps()) = abs(x[2]-1) top_boundary, :rest => rest_of_boundary) function mapping(xi, eta) - x = xi + 0.1 * sin(pi * xi) * sin(pi * eta) - y = eta + 0.1 * sin(pi * xi) * sin(pi * eta) - return SVector(x, y) + x = xi + 0.1 * sin(pi * xi) * sin(pi * eta) + y = eta + 0.1 * sin(pi * xi) * sin(pi * eta) + return SVector(x, y) end cells_per_dimension = (16, 16) -mesh = DGMultiMesh(dg, cells_per_dimension, mapping, is_on_boundary=is_on_boundary) +mesh = DGMultiMesh(dg, cells_per_dimension, mapping, is_on_boundary = is_on_boundary) boundary_condition_convergence_test = BoundaryConditionDirichlet(initial_condition) boundary_conditions = (; :top => boundary_condition_convergence_test, - :rest => boundary_condition_convergence_test) + :rest => boundary_condition_convergence_test) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, dg, source_terms = source_terms, @@ -34,16 +34,16 @@ tspan = (0.0, 0.4) ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() -alive_callback = AliveCallback(alive_interval=10) +alive_callback = AliveCallback(alive_interval = 10) analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval, uEltype=real(dg)) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval, uEltype = real(dg)) callbacks = CallbackSet(summary_callback, alive_callback, analysis_callback) ############################################################################### # run the simulation alg = RDPK3SpFSAL49() -sol = solve(ode, alg; abstol=1.0e-6, reltol=1.0e-6, - ode_default_options()..., callback=callbacks); +sol = solve(ode, alg; abstol = 1.0e-6, reltol = 1.0e-6, + ode_default_options()..., callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/dgmulti_2d/elixir_euler_fdsbp_periodic.jl b/examples/dgmulti_2d/elixir_euler_fdsbp_periodic.jl index d41ca2c5b34..3a73089b566 100644 --- a/examples/dgmulti_2d/elixir_euler_fdsbp_periodic.jl +++ b/examples/dgmulti_2d/elixir_euler_fdsbp_periodic.jl @@ -2,8 +2,10 @@ using Trixi, OrdinaryDiffEq dg = DGMulti(element_type = Quad(), - approximation_type = periodic_derivative_operator( - derivative_order=1, accuracy_order=4, xmin=0.0, xmax=1.0, N=50), + approximation_type = periodic_derivative_operator(derivative_order = 1, + accuracy_order = 4, + xmin = 0.0, xmax = 1.0, + N = 50), surface_flux = flux_hll, volume_integral = VolumeIntegralWeakForm()) @@ -11,8 +13,8 @@ equations = CompressibleEulerEquations2D(1.4) initial_condition = initial_condition_convergence_test source_terms = source_terms_convergence_test -mesh = DGMultiMesh(dg, coordinates_min=(-1.0, -1.0), - coordinates_max=( 1.0, 1.0)) +mesh = DGMultiMesh(dg, coordinates_min = (-1.0, -1.0), + coordinates_max = (1.0, 1.0)) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, dg, source_terms = source_terms) @@ -21,15 +23,16 @@ tspan = (0.0, 0.4) ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() -alive_callback = AliveCallback(alive_interval=10) +alive_callback = AliveCallback(alive_interval = 10) analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval, uEltype=real(dg)) -stepsize_callback = StepsizeCallback(cfl=1.0) -callbacks = CallbackSet(summary_callback, alive_callback, stepsize_callback, analysis_callback) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval, uEltype = real(dg)) +stepsize_callback = StepsizeCallback(cfl = 1.0) +callbacks = CallbackSet(summary_callback, alive_callback, stepsize_callback, + analysis_callback) ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt = 0.5 * estimate_dt(mesh, dg), save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 0.5 * estimate_dt(mesh, dg), save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/dgmulti_2d/elixir_euler_hohqmesh.jl b/examples/dgmulti_2d/elixir_euler_hohqmesh.jl index b9a24dc2450..f534b5bc8ad 100644 --- a/examples/dgmulti_2d/elixir_euler_hohqmesh.jl +++ b/examples/dgmulti_2d/elixir_euler_hohqmesh.jl @@ -15,11 +15,11 @@ initial_condition = initial_condition_convergence_test source_terms = source_terms_convergence_test boundary_condition_convergence_test = BoundaryConditionDirichlet(initial_condition) -boundary_conditions = (; :Slant => boundary_condition_convergence_test, - :Bezier => boundary_condition_convergence_test, - :Right => boundary_condition_convergence_test, - :Bottom => boundary_condition_convergence_test, - :Top => boundary_condition_convergence_test ) +boundary_conditions = (; :Slant => boundary_condition_convergence_test, + :Bezier => boundary_condition_convergence_test, + :Right => boundary_condition_convergence_test, + :Bottom => boundary_condition_convergence_test, + :Top => boundary_condition_convergence_test) ############################################################################### # Get the DG approximation space @@ -32,8 +32,9 @@ dg = DGMulti(polydeg = 8, element_type = Quad(), approximation_type = SBP(), # Get the curved quad mesh from a file (downloads the file if not available locally) default_mesh_file = joinpath(@__DIR__, "mesh_trixi_unstructured_mesh_docs.mesh") -isfile(default_mesh_file) || download("https://gist.githubusercontent.com/andrewwinters5000/52056f1487853fab63b7f4ed7f171c80/raw/9d573387dfdbb8bce2a55db7246f4207663ac07f/mesh_trixi_unstructured_mesh_docs.mesh", - default_mesh_file) +isfile(default_mesh_file) || + download("https://gist.githubusercontent.com/andrewwinters5000/52056f1487853fab63b7f4ed7f171c80/raw/9d573387dfdbb8bce2a55db7246f4207663ac07f/mesh_trixi_unstructured_mesh_docs.mesh", + default_mesh_file) mesh_file = default_mesh_file mesh = DGMultiMesh(dg, mesh_file) @@ -42,8 +43,8 @@ mesh = DGMultiMesh(dg, mesh_file) # create the semi discretization object semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, dg, - source_terms=source_terms, - boundary_conditions=boundary_conditions) + source_terms = source_terms, + boundary_conditions = boundary_conditions) ############################################################################### # ODE solvers, callbacks etc. @@ -54,9 +55,9 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval, uEltype=real(dg)) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval, uEltype = real(dg)) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) callbacks = CallbackSet(summary_callback, analysis_callback, @@ -66,7 +67,7 @@ callbacks = CallbackSet(summary_callback, # run the simulation time_int_tol = 1e-8 -sol = solve(ode, RDPK3SpFSAL49(); abstol=time_int_tol, reltol=time_int_tol, - dt = time_int_tol, ode_default_options()..., callback=callbacks) +sol = solve(ode, RDPK3SpFSAL49(); abstol = time_int_tol, reltol = time_int_tol, + dt = time_int_tol, ode_default_options()..., callback = callbacks) summary_callback() # print the timer summary diff --git a/examples/dgmulti_2d/elixir_euler_kelvin_helmholtz_instability.jl b/examples/dgmulti_2d/elixir_euler_kelvin_helmholtz_instability.jl index 39e98d1a2c5..14de0bf0e8b 100644 --- a/examples/dgmulti_2d/elixir_euler_kelvin_helmholtz_instability.jl +++ b/examples/dgmulti_2d/elixir_euler_kelvin_helmholtz_instability.jl @@ -15,23 +15,24 @@ A version of the classical Kelvin-Helmholtz instability based on of the Euler Equations [arXiv: 2102.06017](https://arxiv.org/abs/2102.06017) """ -function initial_condition_kelvin_helmholtz_instability(x, t, equations::CompressibleEulerEquations2D) - # change discontinuity to tanh - # typical resolution 128^2, 256^2 - # domain size is [-1,+1]^2 - slope = 15 - amplitude = 0.02 - B = tanh(slope * x[2] + 7.5) - tanh(slope * x[2] - 7.5) - rho = 0.5 + 0.75 * B - v1 = 0.5 * (B - 1) - v2 = 0.1 * sin(2 * pi * x[1]) - p = 1.0 - return prim2cons(SVector(rho, v1, v2, p), equations) +function initial_condition_kelvin_helmholtz_instability(x, t, + equations::CompressibleEulerEquations2D) + # change discontinuity to tanh + # typical resolution 128^2, 256^2 + # domain size is [-1,+1]^2 + slope = 15 + amplitude = 0.02 + B = tanh(slope * x[2] + 7.5) - tanh(slope * x[2] - 7.5) + rho = 0.5 + 0.75 * B + v1 = 0.5 * (B - 1) + v2 = 0.1 * sin(2 * pi * x[1]) + p = 1.0 + return prim2cons(SVector(rho, v1, v2, p), equations) end initial_condition = initial_condition_kelvin_helmholtz_instability cells_per_dimension = (32, 32) -mesh = DGMultiMesh(dg, cells_per_dimension; periodicity=true) +mesh = DGMultiMesh(dg, cells_per_dimension; periodicity = true) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, dg) @@ -39,9 +40,9 @@ tspan = (0.0, 1.0) ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() -alive_callback = AliveCallback(alive_interval=10) +alive_callback = AliveCallback(alive_interval = 10) analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval, uEltype=real(dg)) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval, uEltype = real(dg)) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback) @@ -49,7 +50,7 @@ callbacks = CallbackSet(summary_callback, ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt = estimate_dt(mesh, dg), save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = estimate_dt(mesh, dg), save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/dgmulti_2d/elixir_euler_rayleigh_taylor_instability.jl b/examples/dgmulti_2d/elixir_euler_rayleigh_taylor_instability.jl index f5adc7bf83c..49c8b28eaf8 100644 --- a/examples/dgmulti_2d/elixir_euler_rayleigh_taylor_instability.jl +++ b/examples/dgmulti_2d/elixir_euler_rayleigh_taylor_instability.jl @@ -29,34 +29,34 @@ defined below. """ @inline function initial_condition_rayleigh_taylor_instability(x, t, equations::CompressibleEulerEquations2D, - slope=1000) - tol = 1e2*eps() - - if x[2] < 0.5 - p = 2*x[2] + 1 - else - p = x[2] + 3/2 - end - - # smooth the discontinuity to avoid ambiguity at element interfaces - smoothed_heaviside(x, left, right) = left + 0.5*(1 + tanh(slope * x)) * (right-left) - rho = smoothed_heaviside(x[2] - 0.5, 2.0, 1.0) - - c = sqrt(equations.gamma * p / rho) - # the velocity is multiplied by sin(pi*y)^6 as in Remacle et al. 2003 to ensure that the - # initial condition satisfies reflective boundary conditions at the top/bottom boundaries. - v = -0.025 * c * cos(8*pi*x[1]) * sin(pi*x[2])^6 - u = 0.0 - - return prim2cons(SVector(rho, u, v, p), equations) + slope = 1000) + tol = 1e2 * eps() + + if x[2] < 0.5 + p = 2 * x[2] + 1 + else + p = x[2] + 3 / 2 + end + + # smooth the discontinuity to avoid ambiguity at element interfaces + smoothed_heaviside(x, left, right) = left + 0.5 * (1 + tanh(slope * x)) * (right - left) + rho = smoothed_heaviside(x[2] - 0.5, 2.0, 1.0) + + c = sqrt(equations.gamma * p / rho) + # the velocity is multiplied by sin(pi*y)^6 as in Remacle et al. 2003 to ensure that the + # initial condition satisfies reflective boundary conditions at the top/bottom boundaries. + v = -0.025 * c * cos(8 * pi * x[1]) * sin(pi * x[2])^6 + u = 0.0 + + return prim2cons(SVector(rho, u, v, p), equations) end @inline function source_terms_rayleigh_taylor_instability(u, x, t, equations::CompressibleEulerEquations2D) - g = 1.0 - rho, rho_v1, rho_v2, rho_e = u + g = 1.0 + rho, rho_v1, rho_v2, rho_e = u - return SVector(0.0, 0.0, g*rho, g*rho_v2) + return SVector(0.0, 0.0, g * rho, g * rho_v2) end # numerical parameters @@ -67,8 +67,8 @@ dg = DGMulti(polydeg = 3, element_type = Quad(), approximation_type = Polynomial num_elements = 16 cells_per_dimension = (num_elements, 4 * num_elements) mesh = DGMultiMesh(dg, cells_per_dimension, - coordinates_min=(0.0, 0.0), coordinates_max=(0.25, 1.0), - periodicity=(true, false)) + coordinates_min = (0.0, 0.0), coordinates_max = (0.25, 1.0), + periodicity = (true, false)) initial_condition = initial_condition_rayleigh_taylor_instability boundary_conditions = (; :entire_boundary => boundary_condition_slip_wall) @@ -86,9 +86,9 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval, uEltype=real(dg)) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval, uEltype = real(dg)) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) callbacks = CallbackSet(summary_callback, analysis_callback, @@ -97,7 +97,7 @@ callbacks = CallbackSet(summary_callback, ############################################################################### # run the simulation -sol = solve(ode, RDPK3SpFSAL49(); abstol=1.0e-6, reltol=1.0e-6, - ode_default_options()..., callback=callbacks); +sol = solve(ode, RDPK3SpFSAL49(); abstol = 1.0e-6, reltol = 1.0e-6, + ode_default_options()..., callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/dgmulti_2d/elixir_euler_shockcapturing.jl b/examples/dgmulti_2d/elixir_euler_shockcapturing.jl index 4b2a408c757..36494b268d6 100644 --- a/examples/dgmulti_2d/elixir_euler_shockcapturing.jl +++ b/examples/dgmulti_2d/elixir_euler_shockcapturing.jl @@ -10,25 +10,25 @@ equations = CompressibleEulerEquations2D(1.4) initial_condition = initial_condition_weak_blast_wave surface_flux = flux_lax_friedrichs -volume_flux = flux_ranocha +volume_flux = flux_ranocha polydeg = 3 -basis = DGMultiBasis(Quad(), polydeg, approximation_type=GaussSBP()) +basis = DGMultiBasis(Quad(), polydeg, approximation_type = GaussSBP()) indicator_sc = IndicatorHennemannGassner(equations, basis, - alpha_max=0.5, - alpha_min=0.001, - alpha_smooth=true, - variable=density_pressure) + alpha_max = 0.5, + alpha_min = 0.001, + alpha_smooth = true, + variable = density_pressure) volume_integral = VolumeIntegralShockCapturingHG(indicator_sc; - volume_flux_dg=volume_flux, - volume_flux_fv=surface_flux) + volume_flux_dg = volume_flux, + volume_flux_fv = surface_flux) dg = DGMulti(basis, surface_integral = SurfaceIntegralWeakForm(surface_flux), volume_integral = volume_integral) cells_per_dimension = (8, 8) -mesh = DGMultiMesh(dg, cells_per_dimension, periodicity=true) +mesh = DGMultiMesh(dg, cells_per_dimension, periodicity = true) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, dg) @@ -36,16 +36,15 @@ tspan = (0.0, 0.15) ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() -alive_callback = AliveCallback(alive_interval=10) +alive_callback = AliveCallback(alive_interval = 10) analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval, uEltype=real(dg)) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval, uEltype = real(dg)) callbacks = CallbackSet(summary_callback, alive_callback, analysis_callback) ############################################################################### # run the simulation -sol = solve(ode, RDPK3SpFSAL49(); abstol=1.0e-6, reltol=1.0e-6, - ode_default_options()..., callback=callbacks); +sol = solve(ode, RDPK3SpFSAL49(); abstol = 1.0e-6, reltol = 1.0e-6, + ode_default_options()..., callback = callbacks); summary_callback() # print the timer summary - diff --git a/examples/dgmulti_2d/elixir_euler_shockcapturing_curved.jl b/examples/dgmulti_2d/elixir_euler_shockcapturing_curved.jl index dad898b99b6..5e8d9e6c8e4 100644 --- a/examples/dgmulti_2d/elixir_euler_shockcapturing_curved.jl +++ b/examples/dgmulti_2d/elixir_euler_shockcapturing_curved.jl @@ -10,27 +10,27 @@ equations = CompressibleEulerEquations2D(1.4) initial_condition = initial_condition_weak_blast_wave surface_flux = flux_lax_friedrichs -volume_flux = flux_ranocha +volume_flux = flux_ranocha polydeg = 3 -basis = DGMultiBasis(Quad(), polydeg, approximation_type=GaussSBP()) +basis = DGMultiBasis(Quad(), polydeg, approximation_type = GaussSBP()) indicator_sc = IndicatorHennemannGassner(equations, basis, - alpha_max=0.5, - alpha_min=0.001, - alpha_smooth=true, - variable=density_pressure) + alpha_max = 0.5, + alpha_min = 0.001, + alpha_smooth = true, + variable = density_pressure) volume_integral = VolumeIntegralShockCapturingHG(indicator_sc; - volume_flux_dg=volume_flux, - volume_flux_fv=surface_flux) + volume_flux_dg = volume_flux, + volume_flux_fv = surface_flux) dg = DGMulti(basis, surface_integral = SurfaceIntegralWeakForm(surface_flux), volume_integral = volume_integral) function mapping(xi, eta) - x = xi + 0.1 * sin(pi * xi) * sin(pi * eta) - y = eta + 0.1 * sin(pi * xi) * sin(pi * eta) - return SVector(x, y) + x = xi + 0.1 * sin(pi * xi) * sin(pi * eta) + y = eta + 0.1 * sin(pi * xi) * sin(pi * eta) + return SVector(x, y) end cells_per_dimension = (16, 16) mesh = DGMultiMesh(dg, cells_per_dimension, mapping) @@ -41,16 +41,15 @@ tspan = (0.0, 0.15) ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() -alive_callback = AliveCallback(alive_interval=10) +alive_callback = AliveCallback(alive_interval = 10) analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval, uEltype=real(dg)) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval, uEltype = real(dg)) callbacks = CallbackSet(summary_callback, alive_callback, analysis_callback) ############################################################################### # run the simulation -sol = solve(ode, RDPK3SpFSAL49(); abstol=1.0e-6, reltol=1.0e-6, - ode_default_options()..., callback=callbacks); +sol = solve(ode, RDPK3SpFSAL49(); abstol = 1.0e-6, reltol = 1.0e-6, + ode_default_options()..., callback = callbacks); summary_callback() # print the timer summary - diff --git a/examples/dgmulti_2d/elixir_euler_triangulate_pkg_mesh.jl b/examples/dgmulti_2d/elixir_euler_triangulate_pkg_mesh.jl index c10b5e46a14..53661af259a 100644 --- a/examples/dgmulti_2d/elixir_euler_triangulate_pkg_mesh.jl +++ b/examples/dgmulti_2d/elixir_euler_triangulate_pkg_mesh.jl @@ -13,11 +13,11 @@ meshIO = StartUpDG.triangulate_domain(StartUpDG.RectangularDomainWithHole()) # the pre-defined Triangulate geometry in StartUpDG has integer boundary tags. this routine # assigns boundary faces based on these integer boundary tags. -mesh = DGMultiMesh(dg, meshIO, Dict(:outer_boundary=>1, :inner_boundary=>2)) +mesh = DGMultiMesh(dg, meshIO, Dict(:outer_boundary => 1, :inner_boundary => 2)) boundary_condition_convergence_test = BoundaryConditionDirichlet(initial_condition) boundary_conditions = (; :outer_boundary => boundary_condition_convergence_test, - :inner_boundary => boundary_condition_convergence_test) + :inner_boundary => boundary_condition_convergence_test) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, dg, source_terms = source_terms, @@ -27,14 +27,14 @@ tspan = (0.0, 0.2) ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() -alive_callback = AliveCallback(alive_interval=10) +alive_callback = AliveCallback(alive_interval = 10) analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval, uEltype=real(dg)) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval, uEltype = real(dg)) callbacks = CallbackSet(summary_callback, alive_callback, analysis_callback) ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt = 0.5 * estimate_dt(mesh, dg), save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 0.5 * estimate_dt(mesh, dg), save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/dgmulti_2d/elixir_euler_weakform.jl b/examples/dgmulti_2d/elixir_euler_weakform.jl index 486a30b37f1..ecf5e94a86b 100644 --- a/examples/dgmulti_2d/elixir_euler_weakform.jl +++ b/examples/dgmulti_2d/elixir_euler_weakform.jl @@ -10,16 +10,16 @@ initial_condition = initial_condition_convergence_test source_terms = source_terms_convergence_test # example where we tag two separate boundary segments of the mesh -top_boundary(x, tol=50*eps()) = abs(x[2]-1) top_boundary, :rest => rest_of_boundary) cells_per_dimension = (8, 8) -mesh = DGMultiMesh(dg, cells_per_dimension, is_on_boundary=is_on_boundary) +mesh = DGMultiMesh(dg, cells_per_dimension, is_on_boundary = is_on_boundary) boundary_condition_convergence_test = BoundaryConditionDirichlet(initial_condition) boundary_conditions = (; :top => boundary_condition_convergence_test, - :rest => boundary_condition_convergence_test) + :rest => boundary_condition_convergence_test) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, dg, source_terms = source_terms, @@ -29,15 +29,16 @@ tspan = (0.0, 0.4) ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() -alive_callback = AliveCallback(alive_interval=10) +alive_callback = AliveCallback(alive_interval = 10) analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval, uEltype=real(dg)) -stepsize_callback = StepsizeCallback(cfl=1.5) -callbacks = CallbackSet(summary_callback, alive_callback, stepsize_callback, analysis_callback) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval, uEltype = real(dg)) +stepsize_callback = StepsizeCallback(cfl = 1.5) +callbacks = CallbackSet(summary_callback, alive_callback, stepsize_callback, + analysis_callback) ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt = 0.5 * estimate_dt(mesh, dg), save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 0.5 * estimate_dt(mesh, dg), save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/dgmulti_2d/elixir_euler_weakform_periodic.jl b/examples/dgmulti_2d/elixir_euler_weakform_periodic.jl index c4c83fff642..307bf5cbf4a 100644 --- a/examples/dgmulti_2d/elixir_euler_weakform_periodic.jl +++ b/examples/dgmulti_2d/elixir_euler_weakform_periodic.jl @@ -10,7 +10,7 @@ initial_condition = initial_condition_convergence_test source_terms = source_terms_convergence_test cells_per_dimension = (4, 4) -mesh = DGMultiMesh(dg, cells_per_dimension, periodicity=true) +mesh = DGMultiMesh(dg, cells_per_dimension, periodicity = true) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, dg, source_terms = source_terms) @@ -18,14 +18,14 @@ tspan = (0.0, 0.4) ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() -alive_callback = AliveCallback(alive_interval=10) +alive_callback = AliveCallback(alive_interval = 10) analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval, uEltype=real(dg)) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval, uEltype = real(dg)) callbacks = CallbackSet(summary_callback, alive_callback, analysis_callback) ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt = 0.5 * estimate_dt(mesh, dg), save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 0.5 * estimate_dt(mesh, dg), save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/dgmulti_2d/elixir_mhd_reflective_wall.jl b/examples/dgmulti_2d/elixir_mhd_reflective_wall.jl index a1351cf8244..11670288526 100644 --- a/examples/dgmulti_2d/elixir_mhd_reflective_wall.jl +++ b/examples/dgmulti_2d/elixir_mhd_reflective_wall.jl @@ -8,70 +8,72 @@ using LinearAlgebra: norm, dot # for use in the MHD boundary condition equations = IdealGlmMhdEquations2D(1.4) function initial_condition_perturbation(x, t, equations::IdealGlmMhdEquations2D) - # pressure perturbation in a vertically magnetized field on the domain [-1, 1]^2 + # pressure perturbation in a vertically magnetized field on the domain [-1, 1]^2 - r2 = (x[1] + 0.25)^2 + (x[2] + 0.25)^2 + r2 = (x[1] + 0.25)^2 + (x[2] + 0.25)^2 - rho = 1.0 - v1 = 0.0 - v2 = 0.0 - v3 = 0.0 - p = 1 + 0.5 * exp(-100 * r2) + rho = 1.0 + v1 = 0.0 + v2 = 0.0 + v3 = 0.0 + p = 1 + 0.5 * exp(-100 * r2) - # the pressure and magnetic field are chosen to be strongly - # magnetized, such that p / ||B||^2 ≈ 0.01. - B1 = 0.0 - B2 = 40.0 / sqrt(4.0 * pi) - B3 = 0.0 + # the pressure and magnetic field are chosen to be strongly + # magnetized, such that p / ||B||^2 ≈ 0.01. + B1 = 0.0 + B2 = 40.0 / sqrt(4.0 * pi) + B3 = 0.0 - psi = 0.0 - return prim2cons(SVector(rho, v1, v2, v3, p, B1, B2, B3, psi), equations) + psi = 0.0 + return prim2cons(SVector(rho, v1, v2, v3, p, B1, B2, B3, psi), equations) end initial_condition = initial_condition_perturbation surface_flux = (flux_lax_friedrichs, flux_nonconservative_powell) -volume_flux = (flux_hindenlang_gassner, flux_nonconservative_powell) +volume_flux = (flux_hindenlang_gassner, flux_nonconservative_powell) -solver = DGMulti(polydeg=3, element_type = Quad(), approximation_type = GaussSBP(), +solver = DGMulti(polydeg = 3, element_type = Quad(), approximation_type = GaussSBP(), surface_integral = SurfaceIntegralWeakForm(surface_flux), volume_integral = VolumeIntegralFluxDifferencing(volume_flux)) -x_neg(x, tol=50*eps()) = abs(x[1] + 1) < tol -x_pos(x, tol=50*eps()) = abs(x[1] - 1) < tol -y_neg(x, tol=50*eps()) = abs(x[2] + 1) < tol -y_pos(x, tol=50*eps()) = abs(x[2] - 1) < tol +x_neg(x, tol = 50 * eps()) = abs(x[1] + 1) < tol +x_pos(x, tol = 50 * eps()) = abs(x[1] - 1) < tol +y_neg(x, tol = 50 * eps()) = abs(x[2] + 1) < tol +y_pos(x, tol = 50 * eps()) = abs(x[2] - 1) < tol is_on_boundary = Dict(:x_neg => x_neg, :x_pos => x_pos, :y_neg => y_neg, :y_pos => y_pos) cells_per_dimension = (16, 16) -mesh = DGMultiMesh(solver, cells_per_dimension; periodicity=(false, false), is_on_boundary) +mesh = DGMultiMesh(solver, cells_per_dimension; periodicity = (false, false), + is_on_boundary) # Create a "reflective-like" boundary condition by mirroring the velocity but leaving the magnetic field alone. # Note that this boundary condition is probably not entropy stable. -function boundary_condition_velocity_slip_wall(u_inner, normal_direction::AbstractVector, x, t, - surface_flux_function, equations::IdealGlmMhdEquations2D) +function boundary_condition_velocity_slip_wall(u_inner, normal_direction::AbstractVector, + x, t, surface_flux_function, + equations::IdealGlmMhdEquations2D) - # Normalize the vector without using `normalize` since we need to multiply by the `norm_` later - norm_ = norm(normal_direction) - normal = normal_direction / norm_ + # Normalize the vector without using `normalize` since we need to multiply by the `norm_` later + norm_ = norm(normal_direction) + normal = normal_direction / norm_ - # compute the primitive variables - rho, v1, v2, v3, p, B1, B2, B3, psi = cons2prim(u_inner, equations) + # compute the primitive variables + rho, v1, v2, v3, p, B1, B2, B3, psi = cons2prim(u_inner, equations) - v_normal = dot(normal, SVector(v1, v2)) - u_mirror = prim2cons(SVector(rho, v1 - 2 * v_normal * normal[1], - v2 - 2 * v_normal * normal[2], - v3, p, B1, B2, B3, psi), equations) + v_normal = dot(normal, SVector(v1, v2)) + u_mirror = prim2cons(SVector(rho, v1 - 2 * v_normal * normal[1], + v2 - 2 * v_normal * normal[2], + v3, p, B1, B2, B3, psi), equations) - return surface_flux_function(u_inner, u_mirror, normal, equations) * norm_ + return surface_flux_function(u_inner, u_mirror, normal, equations) * norm_ end -boundary_conditions = (; x_neg=boundary_condition_velocity_slip_wall, - x_pos=boundary_condition_velocity_slip_wall, - y_neg=boundary_condition_do_nothing, - y_pos=BoundaryConditionDirichlet(initial_condition)) +boundary_conditions = (; x_neg = boundary_condition_velocity_slip_wall, + x_pos = boundary_condition_velocity_slip_wall, + y_neg = boundary_condition_do_nothing, + y_pos = BoundaryConditionDirichlet(initial_condition)) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver; - boundary_conditions=boundary_conditions) + boundary_conditions = boundary_conditions) ############################################################################### # ODE solvers, callbacks etc. @@ -82,12 +84,13 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval, uEltype=real(solver)) -alive_callback = AliveCallback(alive_interval=10) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval, + uEltype = real(solver)) +alive_callback = AliveCallback(alive_interval = 10) cfl = 0.5 -stepsize_callback = StepsizeCallback(cfl=cfl) -glm_speed_callback = GlmSpeedCallback(glm_scale=0.5, cfl=cfl) +stepsize_callback = StepsizeCallback(cfl = cfl) +glm_speed_callback = GlmSpeedCallback(glm_scale = 0.5, cfl = cfl) callbacks = CallbackSet(summary_callback, analysis_callback, @@ -98,8 +101,8 @@ callbacks = CallbackSet(summary_callback, ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1e-5, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1e-5, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/dgmulti_2d/elixir_mhd_weak_blast_wave.jl b/examples/dgmulti_2d/elixir_mhd_weak_blast_wave.jl index bf5045ce8b0..663301e189f 100644 --- a/examples/dgmulti_2d/elixir_mhd_weak_blast_wave.jl +++ b/examples/dgmulti_2d/elixir_mhd_weak_blast_wave.jl @@ -11,14 +11,14 @@ initial_condition = initial_condition_weak_blast_wave surface_flux = (flux_lax_friedrichs, flux_nonconservative_powell) volume_flux = (flux_hindenlang_gassner, flux_nonconservative_powell) -dg = DGMulti(polydeg=3, element_type = Quad(), approximation_type = Polynomial(), +dg = DGMulti(polydeg = 3, element_type = Quad(), approximation_type = Polynomial(), surface_integral = SurfaceIntegralWeakForm(surface_flux), volume_integral = VolumeIntegralFluxDifferencing(volume_flux)) cells_per_dimension = (16, 16) mesh = DGMultiMesh(dg, cells_per_dimension, - coordinates_min=(-2.0, -2.0), coordinates_max=(2.0, 2.0), - periodicity=true) + coordinates_min = (-2.0, -2.0), coordinates_max = (2.0, 2.0), + periodicity = true) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, dg) ############################################################################### @@ -30,13 +30,13 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval, uEltype=real(dg)) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval, uEltype = real(dg)) +alive_callback = AliveCallback(analysis_interval = analysis_interval) cfl = 1.0 -stepsize_callback = StepsizeCallback(cfl=cfl) +stepsize_callback = StepsizeCallback(cfl = cfl) -glm_speed_callback = GlmSpeedCallback(glm_scale=0.5, cfl=cfl) +glm_speed_callback = GlmSpeedCallback(glm_scale = 0.5, cfl = cfl) callbacks = CallbackSet(summary_callback, analysis_callback, @@ -47,8 +47,8 @@ callbacks = CallbackSet(summary_callback, ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/dgmulti_2d/elixir_mhd_weak_blast_wave_SBP.jl b/examples/dgmulti_2d/elixir_mhd_weak_blast_wave_SBP.jl index 9c8dfcb3801..3dc070a7296 100644 --- a/examples/dgmulti_2d/elixir_mhd_weak_blast_wave_SBP.jl +++ b/examples/dgmulti_2d/elixir_mhd_weak_blast_wave_SBP.jl @@ -15,13 +15,13 @@ initial_condition = initial_condition_weak_blast_wave surface_flux = (flux_lax_friedrichs, flux_nonconservative_powell) volume_flux = (flux_hindenlang_gassner, flux_nonconservative_powell) -dg = DGMulti(polydeg=3, element_type = Quad(), approximation_type = SBP(), +dg = DGMulti(polydeg = 3, element_type = Quad(), approximation_type = SBP(), surface_integral = SurfaceIntegralWeakForm(surface_flux), volume_integral = VolumeIntegralFluxDifferencing(volume_flux)) mesh = DGMultiMesh(dg, cells_per_dimension, - coordinates_min=(-2.0, -2.0), coordinates_max=(2.0, 2.0), - periodicity=true) + coordinates_min = (-2.0, -2.0), coordinates_max = (2.0, 2.0), + periodicity = true) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, dg) ############################################################################### @@ -33,8 +33,8 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval, uEltype=real(dg)) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval, uEltype = real(dg)) +alive_callback = AliveCallback(analysis_interval = analysis_interval) # See comment above and https://github.com/trixi-framework/Trixi.jl/issues/881 # DGMulti uses a conservative timestep estimate, so we can use a large CFL here. @@ -46,8 +46,7 @@ alive_callback = AliveCallback(analysis_interval=analysis_interval) callbacks = CallbackSet(summary_callback, analysis_callback, #stepsize_callback, - alive_callback, - #=glm_speed_callback=#) + alive_callback) #=glm_speed_callback=# ############################################################################### # run the simulation @@ -56,7 +55,7 @@ callbacks = CallbackSet(summary_callback, # sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), # dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback # save_everystep=false, callback=callbacks); -sol = solve(ode, RDPK3SpFSAL49(); abstol=1.0e-8, reltol=1.0e-8, - ode_default_options()..., callback=callbacks) +sol = solve(ode, RDPK3SpFSAL49(); abstol = 1.0e-8, reltol = 1.0e-8, + ode_default_options()..., callback = callbacks) summary_callback() # print the timer summary diff --git a/examples/dgmulti_2d/elixir_navierstokes_convergence.jl b/examples/dgmulti_2d/elixir_navierstokes_convergence.jl index 23c9c2e8ed4..38cf3d7984b 100644 --- a/examples/dgmulti_2d/elixir_navierstokes_convergence.jl +++ b/examples/dgmulti_2d/elixir_navierstokes_convergence.jl @@ -10,169 +10,180 @@ mu() = 0.01 equations = CompressibleEulerEquations2D(1.4) # Note: If you change the Navier-Stokes parameters here, also change them in the initial condition # I really do not like this structure but it should work for now -equations_parabolic = CompressibleNavierStokesDiffusion2D(equations, mu=mu(), Prandtl=prandtl_number(), - gradient_variables=GradientVariablesPrimitive()) +equations_parabolic = CompressibleNavierStokesDiffusion2D(equations, mu = mu(), + Prandtl = prandtl_number(), + gradient_variables = GradientVariablesPrimitive()) # Create DG solver with polynomial degree = 3 and (local) Lax-Friedrichs/Rusanov flux as surface flux dg = DGMulti(polydeg = 3, element_type = Tri(), approximation_type = Polynomial(), surface_integral = SurfaceIntegralWeakForm(flux_lax_friedrichs), volume_integral = VolumeIntegralWeakForm()) -top_bottom(x, tol=50*eps()) = abs(abs(x[2]) - 1) < tol +top_bottom(x, tol = 50 * eps()) = abs(abs(x[2]) - 1) < tol is_on_boundary = Dict(:top_bottom => top_bottom) cells_per_dimension = (16, 16) -mesh = DGMultiMesh(dg, cells_per_dimension; periodicity=(true, false), is_on_boundary) +mesh = DGMultiMesh(dg, cells_per_dimension; periodicity = (true, false), is_on_boundary) # Note: the initial condition cannot be specialized to `CompressibleNavierStokesDiffusion2D` # since it is called by both the parabolic solver (which passes in `CompressibleNavierStokesDiffusion2D`) # and by the initial condition (which passes in `CompressibleEulerEquations2D`). # This convergence test setup was originally derived by Andrew Winters (@andrewwinters5000) function initial_condition_navier_stokes_convergence_test(x, t, equations) - # Amplitude and shift - A = 0.5 - c = 2.0 + # Amplitude and shift + A = 0.5 + c = 2.0 - # convenience values for trig. functions - pi_x = pi * x[1] - pi_y = pi * x[2] - pi_t = pi * t + # convenience values for trig. functions + pi_x = pi * x[1] + pi_y = pi * x[2] + pi_t = pi * t - rho = c + A * sin(pi_x) * cos(pi_y) * cos(pi_t) - v1 = sin(pi_x) * log(x[2] + 2.0) * (1.0 - exp(-A * (x[2] - 1.0)) ) * cos(pi_t) - v2 = v1 - p = rho^2 + rho = c + A * sin(pi_x) * cos(pi_y) * cos(pi_t) + v1 = sin(pi_x) * log(x[2] + 2.0) * (1.0 - exp(-A * (x[2] - 1.0))) * cos(pi_t) + v2 = v1 + p = rho^2 - return prim2cons(SVector(rho, v1, v2, p), equations) + return prim2cons(SVector(rho, v1, v2, p), equations) end @inline function source_terms_navier_stokes_convergence_test(u, x, t, equations) - y = x[2] - - # TODO: parabolic - # we currently need to hardcode these parameters until we fix the "combined equation" issue - # see also https://github.com/trixi-framework/Trixi.jl/pull/1160 - inv_gamma_minus_one = inv(equations.gamma - 1) - Pr = prandtl_number() - mu_ = mu() - - # Same settings as in `initial_condition` - # Amplitude and shift - A = 0.5 - c = 2.0 - - # convenience values for trig. functions - pi_x = pi * x[1] - pi_y = pi * x[2] - pi_t = pi * t - - # compute the manufactured solution and all necessary derivatives - rho = c + A * sin(pi_x) * cos(pi_y) * cos(pi_t) - rho_t = -pi * A * sin(pi_x) * cos(pi_y) * sin(pi_t) - rho_x = pi * A * cos(pi_x) * cos(pi_y) * cos(pi_t) - rho_y = -pi * A * sin(pi_x) * sin(pi_y) * cos(pi_t) - rho_xx = -pi * pi * A * sin(pi_x) * cos(pi_y) * cos(pi_t) - rho_yy = -pi * pi * A * sin(pi_x) * cos(pi_y) * cos(pi_t) - - v1 = sin(pi_x) * log(y + 2.0) * (1.0 - exp(-A * (y - 1.0))) * cos(pi_t) - v1_t = -pi * sin(pi_x) * log(y + 2.0) * (1.0 - exp(-A * (y - 1.0))) * sin(pi_t) - v1_x = pi * cos(pi_x) * log(y + 2.0) * (1.0 - exp(-A * (y - 1.0))) * cos(pi_t) - v1_y = sin(pi_x) * (A * log(y + 2.0) * exp(-A * (y - 1.0)) + (1.0 - exp(-A * (y - 1.0))) / (y + 2.0)) * cos(pi_t) - v1_xx = -pi * pi * sin(pi_x) * log(y + 2.0) * (1.0 - exp(-A * (y - 1.0))) * cos(pi_t) - v1_xy = pi * cos(pi_x) * (A * log(y + 2.0) * exp(-A * (y - 1.0)) + (1.0 - exp(-A * (y - 1.0))) / (y + 2.0)) * cos(pi_t) - v1_yy = (sin(pi_x) * ( 2.0 * A * exp(-A * (y - 1.0)) / (y + 2.0) - - A * A * log(y + 2.0) * exp(-A * (y - 1.0)) - - (1.0 - exp(-A * (y - 1.0))) / ((y + 2.0) * (y + 2.0))) * cos(pi_t)) - v2 = v1 - v2_t = v1_t - v2_x = v1_x - v2_y = v1_y - v2_xx = v1_xx - v2_xy = v1_xy - v2_yy = v1_yy - - p = rho * rho - p_t = 2.0 * rho * rho_t - p_x = 2.0 * rho * rho_x - p_y = 2.0 * rho * rho_y - p_xx = 2.0 * rho * rho_xx + 2.0 * rho_x * rho_x - p_yy = 2.0 * rho * rho_yy + 2.0 * rho_y * rho_y - - # Note this simplifies slightly because the ansatz assumes that v1 = v2 - E = p * inv_gamma_minus_one + 0.5 * rho * (v1^2 + v2^2) - E_t = p_t * inv_gamma_minus_one + rho_t * v1^2 + 2.0 * rho * v1 * v1_t - E_x = p_x * inv_gamma_minus_one + rho_x * v1^2 + 2.0 * rho * v1 * v1_x - E_y = p_y * inv_gamma_minus_one + rho_y * v1^2 + 2.0 * rho * v1 * v1_y - - # Some convenience constants - T_const = equations.gamma * inv_gamma_minus_one / Pr - inv_rho_cubed = 1.0 / (rho^3) - - # compute the source terms - # density equation - du1 = rho_t + rho_x * v1 + rho * v1_x + rho_y * v2 + rho * v2_y - - # x-momentum equation - du2 = ( rho_t * v1 + rho * v1_t + p_x + rho_x * v1^2 - + 2.0 * rho * v1 * v1_x - + rho_y * v1 * v2 - + rho * v1_y * v2 - + rho * v1 * v2_y - # stress tensor from x-direction - - 4.0 / 3.0 * v1_xx * mu_ - + 2.0 / 3.0 * v2_xy * mu_ - - v1_yy * mu_ - - v2_xy * mu_ ) - # y-momentum equation - du3 = ( rho_t * v2 + rho * v2_t + p_y + rho_x * v1 * v2 - + rho * v1_x * v2 - + rho * v1 * v2_x - + rho_y * v2^2 - + 2.0 * rho * v2 * v2_y - # stress tensor from y-direction - - v1_xy * mu_ - - v2_xx * mu_ - - 4.0 / 3.0 * v2_yy * mu_ - + 2.0 / 3.0 * v1_xy * mu_ ) - # total energy equation - du4 = ( E_t + v1_x * (E + p) + v1 * (E_x + p_x) - + v2_y * (E + p) + v2 * (E_y + p_y) - # stress tensor and temperature gradient terms from x-direction - - 4.0 / 3.0 * v1_xx * v1 * mu_ - + 2.0 / 3.0 * v2_xy * v1 * mu_ - - 4.0 / 3.0 * v1_x * v1_x * mu_ - + 2.0 / 3.0 * v2_y * v1_x * mu_ - - v1_xy * v2 * mu_ - - v2_xx * v2 * mu_ - - v1_y * v2_x * mu_ - - v2_x * v2_x * mu_ - - T_const * inv_rho_cubed * ( p_xx * rho * rho - - 2.0 * p_x * rho * rho_x - + 2.0 * p * rho_x * rho_x - - p * rho * rho_xx ) * mu_ - # stress tensor and temperature gradient terms from y-direction - - v1_yy * v1 * mu_ - - v2_xy * v1 * mu_ - - v1_y * v1_y * mu_ - - v2_x * v1_y * mu_ - - 4.0 / 3.0 * v2_yy * v2 * mu_ - + 2.0 / 3.0 * v1_xy * v2 * mu_ - - 4.0 / 3.0 * v2_y * v2_y * mu_ - + 2.0 / 3.0 * v1_x * v2_y * mu_ - - T_const * inv_rho_cubed * ( p_yy * rho * rho - - 2.0 * p_y * rho * rho_y - + 2.0 * p * rho_y * rho_y - - p * rho * rho_yy ) * mu_ ) - - return SVector(du1, du2, du3, du4) + y = x[2] + + # TODO: parabolic + # we currently need to hardcode these parameters until we fix the "combined equation" issue + # see also https://github.com/trixi-framework/Trixi.jl/pull/1160 + inv_gamma_minus_one = inv(equations.gamma - 1) + Pr = prandtl_number() + mu_ = mu() + + # Same settings as in `initial_condition` + # Amplitude and shift + A = 0.5 + c = 2.0 + + # convenience values for trig. functions + pi_x = pi * x[1] + pi_y = pi * x[2] + pi_t = pi * t + + # compute the manufactured solution and all necessary derivatives + rho = c + A * sin(pi_x) * cos(pi_y) * cos(pi_t) + rho_t = -pi * A * sin(pi_x) * cos(pi_y) * sin(pi_t) + rho_x = pi * A * cos(pi_x) * cos(pi_y) * cos(pi_t) + rho_y = -pi * A * sin(pi_x) * sin(pi_y) * cos(pi_t) + rho_xx = -pi * pi * A * sin(pi_x) * cos(pi_y) * cos(pi_t) + rho_yy = -pi * pi * A * sin(pi_x) * cos(pi_y) * cos(pi_t) + + v1 = sin(pi_x) * log(y + 2.0) * (1.0 - exp(-A * (y - 1.0))) * cos(pi_t) + v1_t = -pi * sin(pi_x) * log(y + 2.0) * (1.0 - exp(-A * (y - 1.0))) * sin(pi_t) + v1_x = pi * cos(pi_x) * log(y + 2.0) * (1.0 - exp(-A * (y - 1.0))) * cos(pi_t) + v1_y = sin(pi_x) * + (A * log(y + 2.0) * exp(-A * (y - 1.0)) + + (1.0 - exp(-A * (y - 1.0))) / (y + 2.0)) * cos(pi_t) + v1_xx = -pi * pi * sin(pi_x) * log(y + 2.0) * (1.0 - exp(-A * (y - 1.0))) * cos(pi_t) + v1_xy = pi * cos(pi_x) * + (A * log(y + 2.0) * exp(-A * (y - 1.0)) + + (1.0 - exp(-A * (y - 1.0))) / (y + 2.0)) * cos(pi_t) + v1_yy = (sin(pi_x) * + (2.0 * A * exp(-A * (y - 1.0)) / (y + 2.0) - + A * A * log(y + 2.0) * exp(-A * (y - 1.0)) - + (1.0 - exp(-A * (y - 1.0))) / ((y + 2.0) * (y + 2.0))) * cos(pi_t)) + v2 = v1 + v2_t = v1_t + v2_x = v1_x + v2_y = v1_y + v2_xx = v1_xx + v2_xy = v1_xy + v2_yy = v1_yy + + p = rho * rho + p_t = 2.0 * rho * rho_t + p_x = 2.0 * rho * rho_x + p_y = 2.0 * rho * rho_y + p_xx = 2.0 * rho * rho_xx + 2.0 * rho_x * rho_x + p_yy = 2.0 * rho * rho_yy + 2.0 * rho_y * rho_y + + # Note this simplifies slightly because the ansatz assumes that v1 = v2 + E = p * inv_gamma_minus_one + 0.5 * rho * (v1^2 + v2^2) + E_t = p_t * inv_gamma_minus_one + rho_t * v1^2 + 2.0 * rho * v1 * v1_t + E_x = p_x * inv_gamma_minus_one + rho_x * v1^2 + 2.0 * rho * v1 * v1_x + E_y = p_y * inv_gamma_minus_one + rho_y * v1^2 + 2.0 * rho * v1 * v1_y + + # Some convenience constants + T_const = equations.gamma * inv_gamma_minus_one / Pr + inv_rho_cubed = 1.0 / (rho^3) + + # compute the source terms + # density equation + du1 = rho_t + rho_x * v1 + rho * v1_x + rho_y * v2 + rho * v2_y + + # x-momentum equation + du2 = (rho_t * v1 + rho * v1_t + p_x + rho_x * v1^2 + + 2.0 * rho * v1 * v1_x + + rho_y * v1 * v2 + + rho * v1_y * v2 + + rho * v1 * v2_y - + # stress tensor from x-direction + 4.0 / 3.0 * v1_xx * mu_ + + 2.0 / 3.0 * v2_xy * mu_ - + v1_yy * mu_ - + v2_xy * mu_) + # y-momentum equation + du3 = (rho_t * v2 + rho * v2_t + p_y + rho_x * v1 * v2 + + rho * v1_x * v2 + + rho * v1 * v2_x + + rho_y * v2^2 + + 2.0 * rho * v2 * v2_y - + # stress tensor from y-direction + v1_xy * mu_ - + v2_xx * mu_ - + 4.0 / 3.0 * v2_yy * mu_ + + 2.0 / 3.0 * v1_xy * mu_) + # total energy equation + du4 = (E_t + v1_x * (E + p) + v1 * (E_x + p_x) + + v2_y * (E + p) + v2 * (E_y + p_y) - + # stress tensor and temperature gradient terms from x-direction + 4.0 / 3.0 * v1_xx * v1 * mu_ + + 2.0 / 3.0 * v2_xy * v1 * mu_ - + 4.0 / 3.0 * v1_x * v1_x * mu_ + + 2.0 / 3.0 * v2_y * v1_x * mu_ - + v1_xy * v2 * mu_ - + v2_xx * v2 * mu_ - + v1_y * v2_x * mu_ - + v2_x * v2_x * mu_ - + T_const * inv_rho_cubed * + (p_xx * rho * rho - + 2.0 * p_x * rho * rho_x + + 2.0 * p * rho_x * rho_x - + p * rho * rho_xx) * mu_ - + # stress tensor and temperature gradient terms from y-direction + v1_yy * v1 * mu_ - + v2_xy * v1 * mu_ - + v1_y * v1_y * mu_ - + v2_x * v1_y * mu_ - + 4.0 / 3.0 * v2_yy * v2 * mu_ + + 2.0 / 3.0 * v1_xy * v2 * mu_ - + 4.0 / 3.0 * v2_y * v2_y * mu_ + + 2.0 / 3.0 * v1_x * v2_y * mu_ - + T_const * inv_rho_cubed * + (p_yy * rho * rho - + 2.0 * p_y * rho * rho_y + + 2.0 * p * rho_y * rho_y - + p * rho * rho_yy) * mu_) + + return SVector(du1, du2, du3, du4) end initial_condition = initial_condition_navier_stokes_convergence_test # BC types -velocity_bc_top_bottom = NoSlip((x, t, equations) -> initial_condition_navier_stokes_convergence_test(x, t, equations)[2:3]) +velocity_bc_top_bottom = NoSlip((x, t, equations) -> initial_condition_navier_stokes_convergence_test(x, + t, + equations)[2:3]) heat_bc_top_bottom = Adiabatic((x, t, equations) -> 0.0) -boundary_condition_top_bottom = BoundaryConditionNavierStokesWall(velocity_bc_top_bottom, heat_bc_top_bottom) +boundary_condition_top_bottom = BoundaryConditionNavierStokesWall(velocity_bc_top_bottom, + heat_bc_top_bottom) # define inviscid boundary conditions boundary_conditions = (; :top_bottom => boundary_condition_slip_wall) @@ -180,10 +191,11 @@ boundary_conditions = (; :top_bottom => boundary_condition_slip_wall) # define viscous boundary conditions boundary_conditions_parabolic = (; :top_bottom => boundary_condition_top_bottom) -semi = SemidiscretizationHyperbolicParabolic(mesh, (equations, equations_parabolic), initial_condition, dg; - boundary_conditions=(boundary_conditions, boundary_conditions_parabolic), - source_terms=source_terms_navier_stokes_convergence_test) - +semi = SemidiscretizationHyperbolicParabolic(mesh, (equations, equations_parabolic), + initial_condition, dg; + boundary_conditions = (boundary_conditions, + boundary_conditions_parabolic), + source_terms = source_terms_navier_stokes_convergence_test) ############################################################################### # ODE solvers, callbacks etc. @@ -193,15 +205,15 @@ tspan = (0.0, 0.5) ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() -alive_callback = AliveCallback(alive_interval=10) +alive_callback = AliveCallback(alive_interval = 10) analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval, uEltype=real(dg)) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval, uEltype = real(dg)) callbacks = CallbackSet(summary_callback, alive_callback) ############################################################################### # run the simulation time_int_tol = 1e-8 -sol = solve(ode, RDPK3SpFSAL49(); abstol=time_int_tol, reltol=time_int_tol, - ode_default_options()..., callback=callbacks) +sol = solve(ode, RDPK3SpFSAL49(); abstol = time_int_tol, reltol = time_int_tol, + ode_default_options()..., callback = callbacks) summary_callback() # print the timer summary diff --git a/examples/dgmulti_2d/elixir_navierstokes_convergence_curved.jl b/examples/dgmulti_2d/elixir_navierstokes_convergence_curved.jl index 86b5ae64348..87ffd0e0995 100644 --- a/examples/dgmulti_2d/elixir_navierstokes_convergence_curved.jl +++ b/examples/dgmulti_2d/elixir_navierstokes_convergence_curved.jl @@ -10,24 +10,26 @@ mu() = 0.01 equations = CompressibleEulerEquations2D(1.4) # Note: If you change the Navier-Stokes parameters here, also change them in the initial condition # I really do not like this structure but it should work for now -equations_parabolic = CompressibleNavierStokesDiffusion2D(equations, mu=mu(), Prandtl=prandtl_number(), - gradient_variables=GradientVariablesPrimitive()) +equations_parabolic = CompressibleNavierStokesDiffusion2D(equations, mu = mu(), + Prandtl = prandtl_number(), + gradient_variables = GradientVariablesPrimitive()) # Create DG solver with polynomial degree = 3 and (local) Lax-Friedrichs/Rusanov flux as surface flux dg = DGMulti(polydeg = 3, element_type = Tri(), approximation_type = Polynomial(), surface_integral = SurfaceIntegralWeakForm(flux_lax_friedrichs), volume_integral = VolumeIntegralWeakForm()) -top_bottom(x, tol=50*eps()) = abs(abs(x[2]) - 1) < tol +top_bottom(x, tol = 50 * eps()) = abs(abs(x[2]) - 1) < tol is_on_boundary = Dict(:top_bottom => top_bottom) function mapping(xi, eta) - x = xi + 0.1 * sin(pi * xi) * sin(pi * eta) - y = eta + 0.1 * sin(pi * xi) * sin(pi * eta) - return SVector(x, y) + x = xi + 0.1 * sin(pi * xi) * sin(pi * eta) + y = eta + 0.1 * sin(pi * xi) * sin(pi * eta) + return SVector(x, y) end cells_per_dimension = (16, 16) -mesh = DGMultiMesh(dg, cells_per_dimension, mapping; periodicity=(true, false), is_on_boundary) +mesh = DGMultiMesh(dg, cells_per_dimension, mapping; periodicity = (true, false), + is_on_boundary) # This initial condition is taken from `examples/dgmulti_2d/elixir_navierstokes_convergence.jl` @@ -36,150 +38,160 @@ mesh = DGMultiMesh(dg, cells_per_dimension, mapping; periodicity=(true, false), # and by the initial condition (which passes in `CompressibleEulerEquations2D`). # This convergence test setup was originally derived by Andrew Winters (@andrewwinters5000) function initial_condition_navier_stokes_convergence_test(x, t, equations) - # Amplitude and shift - A = 0.5 - c = 2.0 + # Amplitude and shift + A = 0.5 + c = 2.0 - # convenience values for trig. functions - pi_x = pi * x[1] - pi_y = pi * x[2] - pi_t = pi * t + # convenience values for trig. functions + pi_x = pi * x[1] + pi_y = pi * x[2] + pi_t = pi * t - rho = c + A * sin(pi_x) * cos(pi_y) * cos(pi_t) - v1 = sin(pi_x) * log(x[2] + 2.0) * (1.0 - exp(-A * (x[2] - 1.0)) ) * cos(pi_t) - v2 = v1 - p = rho^2 + rho = c + A * sin(pi_x) * cos(pi_y) * cos(pi_t) + v1 = sin(pi_x) * log(x[2] + 2.0) * (1.0 - exp(-A * (x[2] - 1.0))) * cos(pi_t) + v2 = v1 + p = rho^2 - return prim2cons(SVector(rho, v1, v2, p), equations) + return prim2cons(SVector(rho, v1, v2, p), equations) end @inline function source_terms_navier_stokes_convergence_test(u, x, t, equations) - y = x[2] - - # TODO: parabolic - # we currently need to hardcode these parameters until we fix the "combined equation" issue - # see also https://github.com/trixi-framework/Trixi.jl/pull/1160 - inv_gamma_minus_one = inv(equations.gamma - 1) - Pr = prandtl_number() - mu_ = mu() - - # Same settings as in `initial_condition` - # Amplitude and shift - A = 0.5 - c = 2.0 - - # convenience values for trig. functions - pi_x = pi * x[1] - pi_y = pi * x[2] - pi_t = pi * t - - # compute the manufactured solution and all necessary derivatives - rho = c + A * sin(pi_x) * cos(pi_y) * cos(pi_t) - rho_t = -pi * A * sin(pi_x) * cos(pi_y) * sin(pi_t) - rho_x = pi * A * cos(pi_x) * cos(pi_y) * cos(pi_t) - rho_y = -pi * A * sin(pi_x) * sin(pi_y) * cos(pi_t) - rho_xx = -pi * pi * A * sin(pi_x) * cos(pi_y) * cos(pi_t) - rho_yy = -pi * pi * A * sin(pi_x) * cos(pi_y) * cos(pi_t) - - v1 = sin(pi_x) * log(y + 2.0) * (1.0 - exp(-A * (y - 1.0))) * cos(pi_t) - v1_t = -pi * sin(pi_x) * log(y + 2.0) * (1.0 - exp(-A * (y - 1.0))) * sin(pi_t) - v1_x = pi * cos(pi_x) * log(y + 2.0) * (1.0 - exp(-A * (y - 1.0))) * cos(pi_t) - v1_y = sin(pi_x) * (A * log(y + 2.0) * exp(-A * (y - 1.0)) + (1.0 - exp(-A * (y - 1.0))) / (y + 2.0)) * cos(pi_t) - v1_xx = -pi * pi * sin(pi_x) * log(y + 2.0) * (1.0 - exp(-A * (y - 1.0))) * cos(pi_t) - v1_xy = pi * cos(pi_x) * (A * log(y + 2.0) * exp(-A * (y - 1.0)) + (1.0 - exp(-A * (y - 1.0))) / (y + 2.0)) * cos(pi_t) - v1_yy = (sin(pi_x) * ( 2.0 * A * exp(-A * (y - 1.0)) / (y + 2.0) - - A * A * log(y + 2.0) * exp(-A * (y - 1.0)) - - (1.0 - exp(-A * (y - 1.0))) / ((y + 2.0) * (y + 2.0))) * cos(pi_t)) - v2 = v1 - v2_t = v1_t - v2_x = v1_x - v2_y = v1_y - v2_xx = v1_xx - v2_xy = v1_xy - v2_yy = v1_yy - - p = rho * rho - p_t = 2.0 * rho * rho_t - p_x = 2.0 * rho * rho_x - p_y = 2.0 * rho * rho_y - p_xx = 2.0 * rho * rho_xx + 2.0 * rho_x * rho_x - p_yy = 2.0 * rho * rho_yy + 2.0 * rho_y * rho_y - - # Note this simplifies slightly because the ansatz assumes that v1 = v2 - E = p * inv_gamma_minus_one + 0.5 * rho * (v1^2 + v2^2) - E_t = p_t * inv_gamma_minus_one + rho_t * v1^2 + 2.0 * rho * v1 * v1_t - E_x = p_x * inv_gamma_minus_one + rho_x * v1^2 + 2.0 * rho * v1 * v1_x - E_y = p_y * inv_gamma_minus_one + rho_y * v1^2 + 2.0 * rho * v1 * v1_y - - # Some convenience constants - T_const = equations.gamma * inv_gamma_minus_one / Pr - inv_rho_cubed = 1.0 / (rho^3) - - # compute the source terms - # density equation - du1 = rho_t + rho_x * v1 + rho * v1_x + rho_y * v2 + rho * v2_y - - # x-momentum equation - du2 = ( rho_t * v1 + rho * v1_t + p_x + rho_x * v1^2 - + 2.0 * rho * v1 * v1_x - + rho_y * v1 * v2 - + rho * v1_y * v2 - + rho * v1 * v2_y - # stress tensor from x-direction - - 4.0 / 3.0 * v1_xx * mu_ - + 2.0 / 3.0 * v2_xy * mu_ - - v1_yy * mu_ - - v2_xy * mu_ ) - # y-momentum equation - du3 = ( rho_t * v2 + rho * v2_t + p_y + rho_x * v1 * v2 - + rho * v1_x * v2 - + rho * v1 * v2_x - + rho_y * v2^2 - + 2.0 * rho * v2 * v2_y - # stress tensor from y-direction - - v1_xy * mu_ - - v2_xx * mu_ - - 4.0 / 3.0 * v2_yy * mu_ - + 2.0 / 3.0 * v1_xy * mu_ ) - # total energy equation - du4 = ( E_t + v1_x * (E + p) + v1 * (E_x + p_x) - + v2_y * (E + p) + v2 * (E_y + p_y) - # stress tensor and temperature gradient terms from x-direction - - 4.0 / 3.0 * v1_xx * v1 * mu_ - + 2.0 / 3.0 * v2_xy * v1 * mu_ - - 4.0 / 3.0 * v1_x * v1_x * mu_ - + 2.0 / 3.0 * v2_y * v1_x * mu_ - - v1_xy * v2 * mu_ - - v2_xx * v2 * mu_ - - v1_y * v2_x * mu_ - - v2_x * v2_x * mu_ - - T_const * inv_rho_cubed * ( p_xx * rho * rho - - 2.0 * p_x * rho * rho_x - + 2.0 * p * rho_x * rho_x - - p * rho * rho_xx ) * mu_ - # stress tensor and temperature gradient terms from y-direction - - v1_yy * v1 * mu_ - - v2_xy * v1 * mu_ - - v1_y * v1_y * mu_ - - v2_x * v1_y * mu_ - - 4.0 / 3.0 * v2_yy * v2 * mu_ - + 2.0 / 3.0 * v1_xy * v2 * mu_ - - 4.0 / 3.0 * v2_y * v2_y * mu_ - + 2.0 / 3.0 * v1_x * v2_y * mu_ - - T_const * inv_rho_cubed * ( p_yy * rho * rho - - 2.0 * p_y * rho * rho_y - + 2.0 * p * rho_y * rho_y - - p * rho * rho_yy ) * mu_ ) - - return SVector(du1, du2, du3, du4) + y = x[2] + + # TODO: parabolic + # we currently need to hardcode these parameters until we fix the "combined equation" issue + # see also https://github.com/trixi-framework/Trixi.jl/pull/1160 + inv_gamma_minus_one = inv(equations.gamma - 1) + Pr = prandtl_number() + mu_ = mu() + + # Same settings as in `initial_condition` + # Amplitude and shift + A = 0.5 + c = 2.0 + + # convenience values for trig. functions + pi_x = pi * x[1] + pi_y = pi * x[2] + pi_t = pi * t + + # compute the manufactured solution and all necessary derivatives + rho = c + A * sin(pi_x) * cos(pi_y) * cos(pi_t) + rho_t = -pi * A * sin(pi_x) * cos(pi_y) * sin(pi_t) + rho_x = pi * A * cos(pi_x) * cos(pi_y) * cos(pi_t) + rho_y = -pi * A * sin(pi_x) * sin(pi_y) * cos(pi_t) + rho_xx = -pi * pi * A * sin(pi_x) * cos(pi_y) * cos(pi_t) + rho_yy = -pi * pi * A * sin(pi_x) * cos(pi_y) * cos(pi_t) + + v1 = sin(pi_x) * log(y + 2.0) * (1.0 - exp(-A * (y - 1.0))) * cos(pi_t) + v1_t = -pi * sin(pi_x) * log(y + 2.0) * (1.0 - exp(-A * (y - 1.0))) * sin(pi_t) + v1_x = pi * cos(pi_x) * log(y + 2.0) * (1.0 - exp(-A * (y - 1.0))) * cos(pi_t) + v1_y = sin(pi_x) * + (A * log(y + 2.0) * exp(-A * (y - 1.0)) + + (1.0 - exp(-A * (y - 1.0))) / (y + 2.0)) * cos(pi_t) + v1_xx = -pi * pi * sin(pi_x) * log(y + 2.0) * (1.0 - exp(-A * (y - 1.0))) * cos(pi_t) + v1_xy = pi * cos(pi_x) * + (A * log(y + 2.0) * exp(-A * (y - 1.0)) + + (1.0 - exp(-A * (y - 1.0))) / (y + 2.0)) * cos(pi_t) + v1_yy = (sin(pi_x) * + (2.0 * A * exp(-A * (y - 1.0)) / (y + 2.0) - + A * A * log(y + 2.0) * exp(-A * (y - 1.0)) - + (1.0 - exp(-A * (y - 1.0))) / ((y + 2.0) * (y + 2.0))) * cos(pi_t)) + v2 = v1 + v2_t = v1_t + v2_x = v1_x + v2_y = v1_y + v2_xx = v1_xx + v2_xy = v1_xy + v2_yy = v1_yy + + p = rho * rho + p_t = 2.0 * rho * rho_t + p_x = 2.0 * rho * rho_x + p_y = 2.0 * rho * rho_y + p_xx = 2.0 * rho * rho_xx + 2.0 * rho_x * rho_x + p_yy = 2.0 * rho * rho_yy + 2.0 * rho_y * rho_y + + # Note this simplifies slightly because the ansatz assumes that v1 = v2 + E = p * inv_gamma_minus_one + 0.5 * rho * (v1^2 + v2^2) + E_t = p_t * inv_gamma_minus_one + rho_t * v1^2 + 2.0 * rho * v1 * v1_t + E_x = p_x * inv_gamma_minus_one + rho_x * v1^2 + 2.0 * rho * v1 * v1_x + E_y = p_y * inv_gamma_minus_one + rho_y * v1^2 + 2.0 * rho * v1 * v1_y + + # Some convenience constants + T_const = equations.gamma * inv_gamma_minus_one / Pr + inv_rho_cubed = 1.0 / (rho^3) + + # compute the source terms + # density equation + du1 = rho_t + rho_x * v1 + rho * v1_x + rho_y * v2 + rho * v2_y + + # x-momentum equation + du2 = (rho_t * v1 + rho * v1_t + p_x + rho_x * v1^2 + + 2.0 * rho * v1 * v1_x + + rho_y * v1 * v2 + + rho * v1_y * v2 + + rho * v1 * v2_y - + # stress tensor from x-direction + 4.0 / 3.0 * v1_xx * mu_ + + 2.0 / 3.0 * v2_xy * mu_ - + v1_yy * mu_ - + v2_xy * mu_) + # y-momentum equation + du3 = (rho_t * v2 + rho * v2_t + p_y + rho_x * v1 * v2 + + rho * v1_x * v2 + + rho * v1 * v2_x + + rho_y * v2^2 + + 2.0 * rho * v2 * v2_y - + # stress tensor from y-direction + v1_xy * mu_ - + v2_xx * mu_ - + 4.0 / 3.0 * v2_yy * mu_ + + 2.0 / 3.0 * v1_xy * mu_) + # total energy equation + du4 = (E_t + v1_x * (E + p) + v1 * (E_x + p_x) + + v2_y * (E + p) + v2 * (E_y + p_y) - + # stress tensor and temperature gradient terms from x-direction + 4.0 / 3.0 * v1_xx * v1 * mu_ + + 2.0 / 3.0 * v2_xy * v1 * mu_ - + 4.0 / 3.0 * v1_x * v1_x * mu_ + + 2.0 / 3.0 * v2_y * v1_x * mu_ - + v1_xy * v2 * mu_ - + v2_xx * v2 * mu_ - + v1_y * v2_x * mu_ - + v2_x * v2_x * mu_ - + T_const * inv_rho_cubed * + (p_xx * rho * rho - + 2.0 * p_x * rho * rho_x + + 2.0 * p * rho_x * rho_x - + p * rho * rho_xx) * mu_ - + # stress tensor and temperature gradient terms from y-direction + v1_yy * v1 * mu_ - + v2_xy * v1 * mu_ - + v1_y * v1_y * mu_ - + v2_x * v1_y * mu_ - + 4.0 / 3.0 * v2_yy * v2 * mu_ + + 2.0 / 3.0 * v1_xy * v2 * mu_ - + 4.0 / 3.0 * v2_y * v2_y * mu_ + + 2.0 / 3.0 * v1_x * v2_y * mu_ - + T_const * inv_rho_cubed * + (p_yy * rho * rho - + 2.0 * p_y * rho * rho_y + + 2.0 * p * rho_y * rho_y - + p * rho * rho_yy) * mu_) + + return SVector(du1, du2, du3, du4) end initial_condition = initial_condition_navier_stokes_convergence_test # BC types -velocity_bc_top_bottom = NoSlip((x, t, equations) -> initial_condition_navier_stokes_convergence_test(x, t, equations)[2:3]) +velocity_bc_top_bottom = NoSlip((x, t, equations) -> initial_condition_navier_stokes_convergence_test(x, + t, + equations)[2:3]) heat_bc_top_bottom = Adiabatic((x, t, equations) -> 0.0) -boundary_condition_top_bottom = BoundaryConditionNavierStokesWall(velocity_bc_top_bottom, heat_bc_top_bottom) +boundary_condition_top_bottom = BoundaryConditionNavierStokesWall(velocity_bc_top_bottom, + heat_bc_top_bottom) # define inviscid boundary conditions boundary_conditions = (; :top_bottom => boundary_condition_slip_wall) @@ -187,10 +199,11 @@ boundary_conditions = (; :top_bottom => boundary_condition_slip_wall) # define viscous boundary conditions boundary_conditions_parabolic = (; :top_bottom => boundary_condition_top_bottom) -semi = SemidiscretizationHyperbolicParabolic(mesh, (equations, equations_parabolic), initial_condition, dg; - boundary_conditions=(boundary_conditions, boundary_conditions_parabolic), - source_terms=source_terms_navier_stokes_convergence_test) - +semi = SemidiscretizationHyperbolicParabolic(mesh, (equations, equations_parabolic), + initial_condition, dg; + boundary_conditions = (boundary_conditions, + boundary_conditions_parabolic), + source_terms = source_terms_navier_stokes_convergence_test) ############################################################################### # ODE solvers, callbacks etc. @@ -200,15 +213,15 @@ tspan = (0.0, 0.5) ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() -alive_callback = AliveCallback(alive_interval=10) +alive_callback = AliveCallback(alive_interval = 10) analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval, uEltype=real(dg)) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval, uEltype = real(dg)) callbacks = CallbackSet(summary_callback, alive_callback) ############################################################################### # run the simulation time_int_tol = 1e-8 -sol = solve(ode, RDPK3SpFSAL49(); abstol=time_int_tol, reltol=time_int_tol, - ode_default_options()..., callback=callbacks) +sol = solve(ode, RDPK3SpFSAL49(); abstol = time_int_tol, reltol = time_int_tol, + ode_default_options()..., callback = callbacks) summary_callback() # print the timer summary diff --git a/examples/dgmulti_2d/elixir_navierstokes_lid_driven_cavity.jl b/examples/dgmulti_2d/elixir_navierstokes_lid_driven_cavity.jl index 97b779ebaf9..7c55cbf0ccf 100644 --- a/examples/dgmulti_2d/elixir_navierstokes_lid_driven_cavity.jl +++ b/examples/dgmulti_2d/elixir_navierstokes_lid_driven_cavity.jl @@ -9,28 +9,27 @@ prandtl_number() = 0.72 mu() = 0.001 equations = CompressibleEulerEquations2D(1.4) -equations_parabolic = CompressibleNavierStokesDiffusion2D(equations, mu=mu(), - Prandtl=prandtl_number()) - +equations_parabolic = CompressibleNavierStokesDiffusion2D(equations, mu = mu(), + Prandtl = prandtl_number()) # Create DG solver with polynomial degree = 3 and (local) Lax-Friedrichs/Rusanov flux as surface flux dg = DGMulti(polydeg = 3, element_type = Quad(), approximation_type = GaussSBP(), surface_integral = SurfaceIntegralWeakForm(flux_lax_friedrichs), volume_integral = VolumeIntegralFluxDifferencing(flux_ranocha)) -top(x, tol=50*eps()) = abs(x[2] - 1) < tol -rest_of_boundary(x, tol=50*eps()) = !top(x, tol) +top(x, tol = 50 * eps()) = abs(x[2] - 1) < tol +rest_of_boundary(x, tol = 50 * eps()) = !top(x, tol) is_on_boundary = Dict(:top => top, :rest_of_boundary => rest_of_boundary) cells_per_dimension = (16, 16) mesh = DGMultiMesh(dg, cells_per_dimension; is_on_boundary) function initial_condition_cavity(x, t, equations::CompressibleEulerEquations2D) - Ma = 0.1 - rho = 1.0 - u, v = 0.0, 0.0 - p = 1.0 / (Ma^2 * equations.gamma) - return prim2cons(SVector(rho, u, v, p), equations) + Ma = 0.1 + rho = 1.0 + u, v = 0.0, 0.0 + p = 1.0 / (Ma^2 * equations.gamma) + return prim2cons(SVector(rho, u, v, p), equations) end initial_condition = initial_condition_cavity @@ -43,15 +42,16 @@ boundary_condition_cavity = BoundaryConditionNavierStokesWall(velocity_bc_cavity # define inviscid boundary conditions boundary_conditions = (; :top => boundary_condition_slip_wall, - :rest_of_boundary => boundary_condition_slip_wall) + :rest_of_boundary => boundary_condition_slip_wall) # define viscous boundary conditions boundary_conditions_parabolic = (; :top => boundary_condition_lid, - :rest_of_boundary => boundary_condition_cavity) - -semi = SemidiscretizationHyperbolicParabolic(mesh, (equations, equations_parabolic), initial_condition, dg; - boundary_conditions=(boundary_conditions, boundary_conditions_parabolic)) + :rest_of_boundary => boundary_condition_cavity) +semi = SemidiscretizationHyperbolicParabolic(mesh, (equations, equations_parabolic), + initial_condition, dg; + boundary_conditions = (boundary_conditions, + boundary_conditions_parabolic)) ############################################################################### # ODE solvers, callbacks etc. @@ -61,15 +61,15 @@ tspan = (0.0, 10.0) ode = semidiscretize(semi, tspan); summary_callback = SummaryCallback() -alive_callback = AliveCallback(alive_interval=10) +alive_callback = AliveCallback(alive_interval = 10) analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval, uEltype=real(dg)) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval, uEltype = real(dg)) callbacks = CallbackSet(summary_callback, alive_callback) ############################################################################### # run the simulation time_int_tol = 1e-8 -sol = solve(ode, RDPK3SpFSAL49(); abstol=time_int_tol, reltol=time_int_tol, - ode_default_options()..., callback=callbacks) +sol = solve(ode, RDPK3SpFSAL49(); abstol = time_int_tol, reltol = time_int_tol, + ode_default_options()..., callback = callbacks) summary_callback() # print the timer summary diff --git a/examples/dgmulti_2d/elixir_shallowwater_source_terms.jl b/examples/dgmulti_2d/elixir_shallowwater_source_terms.jl index 3551c863ff2..f7120d8091b 100644 --- a/examples/dgmulti_2d/elixir_shallowwater_source_terms.jl +++ b/examples/dgmulti_2d/elixir_shallowwater_source_terms.jl @@ -4,24 +4,23 @@ using Trixi ############################################################################### # semidiscretization of the shallow water equations -equations = ShallowWaterEquations2D(gravity_constant=9.81) +equations = ShallowWaterEquations2D(gravity_constant = 9.81) initial_condition = initial_condition_convergence_test volume_flux = (flux_wintermeyer_etal, flux_nonconservative_wintermeyer_etal) surface_flux = (flux_lax_friedrichs, flux_nonconservative_fjordholm_etal) -dg = DGMulti(polydeg=3, element_type = Quad(), approximation_type = SBP(), +dg = DGMulti(polydeg = 3, element_type = Quad(), approximation_type = SBP(), surface_integral = SurfaceIntegralWeakForm(surface_flux), volume_integral = VolumeIntegralFluxDifferencing(volume_flux)) cells_per_dimension = (8, 8) mesh = DGMultiMesh(dg, cells_per_dimension, - coordinates_min=(0.0, 0.0), coordinates_max=(sqrt(2), sqrt(2)), - periodicity=true) - + coordinates_min = (0.0, 0.0), coordinates_max = (sqrt(2), sqrt(2)), + periodicity = true) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, dg; - source_terms=source_terms_convergence_test) + source_terms = source_terms_convergence_test) ############################################################################### # ODE solvers, callbacks etc. @@ -32,8 +31,8 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval, uEltype=real(dg)) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval, uEltype = real(dg)) +alive_callback = AliveCallback(analysis_interval = analysis_interval) callbacks = CallbackSet(summary_callback, analysis_callback, @@ -42,7 +41,7 @@ callbacks = CallbackSet(summary_callback, ############################################################################### # run the simulation -sol = solve(ode, RDPK3SpFSAL49(); abstol=1.0e-7, reltol=1.0e-7, - ode_default_options()..., callback=callbacks); +sol = solve(ode, RDPK3SpFSAL49(); abstol = 1.0e-7, reltol = 1.0e-7, + ode_default_options()..., callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/dgmulti_3d/elixir_advection_tensor_wedge.jl b/examples/dgmulti_3d/elixir_advection_tensor_wedge.jl index 4f43f2571a3..e877e602547 100644 --- a/examples/dgmulti_3d/elixir_advection_tensor_wedge.jl +++ b/examples/dgmulti_3d/elixir_advection_tensor_wedge.jl @@ -16,17 +16,15 @@ dg = DGMulti(element_type = Wedge(), surface_flux = flux_lax_friedrichs, polydeg = tensor_polydeg) - cells_per_dimension = (8, 8, 8) -mesh = DGMultiMesh(dg, +mesh = DGMultiMesh(dg, cells_per_dimension, - coordinates_min = (-1.0, -1.0, -1.0), + coordinates_min = (-1.0, -1.0, -1.0), coordinates_max = (1.0, 1.0, 1.0), periodicity = true) - semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, dg, - boundary_conditions=boundary_condition_periodic) + boundary_conditions = boundary_condition_periodic) ############################################################################### # ODE solvers, callbacks etc. @@ -37,20 +35,20 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval, uEltype=real(dg)) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval, uEltype = real(dg)) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) # The StepsizeCallback handles the re-calculation of the maximum Δt after each time step -stepsize_callback = StepsizeCallback(cfl=1.0) - -callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, stepsize_callback) +stepsize_callback = StepsizeCallback(cfl = 1.0) +callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, + stepsize_callback) ############################################################################### # run the simulation sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), dt = 1.0, - save_everystep=false, callback=callbacks); + save_everystep = false, callback = callbacks); -summary_callback() # print the timer summary \ No newline at end of file +summary_callback() # print the timer summary diff --git a/examples/dgmulti_3d/elixir_euler_curved.jl b/examples/dgmulti_3d/elixir_euler_curved.jl index d8c4df5dd64..67c84b50974 100644 --- a/examples/dgmulti_3d/elixir_euler_curved.jl +++ b/examples/dgmulti_3d/elixir_euler_curved.jl @@ -1,7 +1,7 @@ using Trixi, OrdinaryDiffEq -dg = DGMulti(polydeg = 3, element_type = Hex(), approximation_type=SBP(), +dg = DGMulti(polydeg = 3, element_type = Hex(), approximation_type = SBP(), surface_integral = SurfaceIntegralWeakForm(flux_hll), volume_integral = VolumeIntegralFluxDifferencing(flux_ranocha)) @@ -10,22 +10,22 @@ initial_condition = initial_condition_convergence_test source_terms = source_terms_convergence_test # example where we tag two separate boundary segments of the mesh -top_boundary(x, tol=50*eps()) = abs(x[2] - 1) < tol -rest_of_boundary(x, tol=50*eps()) = !top_boundary(x, tol) +top_boundary(x, tol = 50 * eps()) = abs(x[2] - 1) < tol +rest_of_boundary(x, tol = 50 * eps()) = !top_boundary(x, tol) is_on_boundary = Dict(:top => top_boundary, :rest => rest_of_boundary) function mapping(xi, eta, zeta) - x = xi + 0.1 * sin(pi * xi) * sin(pi * eta) - y = eta + 0.1 * sin(pi * xi) * sin(pi * eta) - z = zeta + 0.1 * sin(pi * xi) * sin(pi * eta) - return SVector(x, y, z) + x = xi + 0.1 * sin(pi * xi) * sin(pi * eta) + y = eta + 0.1 * sin(pi * xi) * sin(pi * eta) + z = zeta + 0.1 * sin(pi * xi) * sin(pi * eta) + return SVector(x, y, z) end cells_per_dimension = (4, 4, 4) -mesh = DGMultiMesh(dg, cells_per_dimension, mapping, is_on_boundary=is_on_boundary) +mesh = DGMultiMesh(dg, cells_per_dimension, mapping, is_on_boundary = is_on_boundary) boundary_condition_convergence_test = BoundaryConditionDirichlet(initial_condition) boundary_conditions = (; :top => boundary_condition_convergence_test, - :rest => boundary_condition_convergence_test) + :rest => boundary_condition_convergence_test) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, dg, source_terms = source_terms, @@ -35,14 +35,14 @@ tspan = (0.0, 0.1) ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() -alive_callback = AliveCallback(alive_interval=10) +alive_callback = AliveCallback(alive_interval = 10) analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval, uEltype=real(dg)) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval, uEltype = real(dg)) callbacks = CallbackSet(summary_callback, alive_callback, analysis_callback) ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt = 0.5 * estimate_dt(mesh, dg), save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 0.5 * estimate_dt(mesh, dg), save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/dgmulti_3d/elixir_euler_fdsbp_periodic.jl b/examples/dgmulti_3d/elixir_euler_fdsbp_periodic.jl index 35f7aee8795..0eb38674689 100644 --- a/examples/dgmulti_3d/elixir_euler_fdsbp_periodic.jl +++ b/examples/dgmulti_3d/elixir_euler_fdsbp_periodic.jl @@ -10,19 +10,20 @@ equations = CompressibleEulerEquations3D(1.4) initial_condition = initial_condition_convergence_test source_terms = source_terms_convergence_test -volume_flux = flux_ranocha +volume_flux = flux_ranocha solver = DGMulti(element_type = Hex(), - approximation_type = periodic_derivative_operator( - derivative_order=1, accuracy_order=4, xmin=0.0, xmax=1.0, N=20), + approximation_type = periodic_derivative_operator(derivative_order = 1, + accuracy_order = 4, + xmin = 0.0, xmax = 1.0, + N = 20), surface_flux = flux_lax_friedrichs, volume_integral = VolumeIntegralFluxDifferencing(volume_flux)) -mesh = DGMultiMesh(solver, coordinates_min=(-1.0, -1.0, -1.0), - coordinates_max=( 1.0, 1.0, 1.0)) +mesh = DGMultiMesh(solver, coordinates_min = (-1.0, -1.0, -1.0), + coordinates_max = (1.0, 1.0, 1.0)) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver; - source_terms=source_terms) - + source_terms = source_terms) ############################################################################### # ODE solvers, callbacks etc. @@ -33,14 +34,14 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval, uEltype=real(solver)) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval, + uEltype = real(solver)) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback) - ############################################################################### # run the simulation diff --git a/examples/dgmulti_3d/elixir_euler_taylor_green_vortex.jl b/examples/dgmulti_3d/elixir_euler_taylor_green_vortex.jl index 253d2486468..fea43ad4d26 100644 --- a/examples/dgmulti_3d/elixir_euler_taylor_green_vortex.jl +++ b/examples/dgmulti_3d/elixir_euler_taylor_green_vortex.jl @@ -12,35 +12,38 @@ equations = CompressibleEulerEquations3D(1.4) The classical inviscid Taylor-Green vortex. """ -function initial_condition_taylor_green_vortex(x, t, equations::CompressibleEulerEquations3D) - A = 1.0 # magnitude of speed - Ms = 0.1 # maximum Mach number - - rho = 1.0 - v1 = A * sin(x[1]) * cos(x[2]) * cos(x[3]) - v2 = -A * cos(x[1]) * sin(x[2]) * cos(x[3]) - v3 = 0.0 - p = (A / Ms)^2 * rho / equations.gamma # scaling to get Ms - p = p + 1.0/16.0 * A^2 * rho * (cos(2*x[1])*cos(2*x[3]) + 2*cos(2*x[2]) + 2*cos(2*x[1]) + cos(2*x[2])*cos(2*x[3])) - - return prim2cons(SVector(rho, v1, v2, v3, p), equations) +function initial_condition_taylor_green_vortex(x, t, + equations::CompressibleEulerEquations3D) + A = 1.0 # magnitude of speed + Ms = 0.1 # maximum Mach number + + rho = 1.0 + v1 = A * sin(x[1]) * cos(x[2]) * cos(x[3]) + v2 = -A * cos(x[1]) * sin(x[2]) * cos(x[3]) + v3 = 0.0 + p = (A / Ms)^2 * rho / equations.gamma # scaling to get Ms + p = p + + 1.0 / 16.0 * A^2 * rho * + (cos(2 * x[1]) * cos(2 * x[3]) + 2 * cos(2 * x[2]) + 2 * cos(2 * x[1]) + + cos(2 * x[2]) * cos(2 * x[3])) + + return prim2cons(SVector(rho, v1, v2, v3, p), equations) end initial_condition = initial_condition_taylor_green_vortex -volume_flux = flux_ranocha +volume_flux = flux_ranocha surface_flux = flux_lax_friedrichs solver = DGMulti(polydeg = 3, element_type = Hex(), approximation_type = Polynomial(), - surface_integral= SurfaceIntegralWeakForm(surface_flux), - volume_integral = VolumeIntegralFluxDifferencing(volume_flux)) + surface_integral = SurfaceIntegralWeakForm(surface_flux), + volume_integral = VolumeIntegralFluxDifferencing(volume_flux)) cells_per_dimension = (8, 8, 8) mesh = DGMultiMesh(solver, cells_per_dimension, - coordinates_min=(-pi, -pi, -pi), coordinates_max=(pi, pi, pi), - periodicity=true) + coordinates_min = (-pi, -pi, -pi), coordinates_max = (pi, pi, pi), + periodicity = true) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver) - ############################################################################### # ODE solvers, callbacks etc. @@ -50,14 +53,14 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval, uEltype=real(solver)) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval, + uEltype = real(solver)) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback) - ############################################################################### # run the simulation diff --git a/examples/dgmulti_3d/elixir_euler_weakform.jl b/examples/dgmulti_3d/elixir_euler_weakform.jl index b167377af51..6e06b35c4f6 100644 --- a/examples/dgmulti_3d/elixir_euler_weakform.jl +++ b/examples/dgmulti_3d/elixir_euler_weakform.jl @@ -10,16 +10,16 @@ initial_condition = initial_condition_convergence_test source_terms = source_terms_convergence_test # example where we tag two separate boundary segments of the mesh -top_boundary(x, tol=50*eps()) = abs(x[2] - 1) < tol -rest_of_boundary(x, tol=50*eps()) = !top_boundary(x, tol) +top_boundary(x, tol = 50 * eps()) = abs(x[2] - 1) < tol +rest_of_boundary(x, tol = 50 * eps()) = !top_boundary(x, tol) is_on_boundary = Dict(:top => top_boundary, :rest => rest_of_boundary) cells_per_dimension = (4, 4, 4) -mesh = DGMultiMesh(dg, cells_per_dimension, is_on_boundary=is_on_boundary) +mesh = DGMultiMesh(dg, cells_per_dimension, is_on_boundary = is_on_boundary) boundary_condition_convergence_test = BoundaryConditionDirichlet(initial_condition) boundary_conditions = (; :top => boundary_condition_convergence_test, - :rest => boundary_condition_convergence_test) + :rest => boundary_condition_convergence_test) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, dg, source_terms = source_terms, @@ -29,14 +29,14 @@ tspan = (0.0, 0.1) ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() -alive_callback = AliveCallback(alive_interval=10) +alive_callback = AliveCallback(alive_interval = 10) analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval, uEltype=real(dg)) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval, uEltype = real(dg)) callbacks = CallbackSet(summary_callback, alive_callback, analysis_callback) ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt = 0.5 * estimate_dt(mesh, dg), save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 0.5 * estimate_dt(mesh, dg), save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/dgmulti_3d/elixir_euler_weakform_periodic.jl b/examples/dgmulti_3d/elixir_euler_weakform_periodic.jl index 6b17d4bba65..bc963a3a2fd 100644 --- a/examples/dgmulti_3d/elixir_euler_weakform_periodic.jl +++ b/examples/dgmulti_3d/elixir_euler_weakform_periodic.jl @@ -10,7 +10,7 @@ initial_condition = initial_condition_convergence_test source_terms = source_terms_convergence_test cells_per_dimension = (4, 4, 4) -mesh = DGMultiMesh(dg, cells_per_dimension, periodicity=true) +mesh = DGMultiMesh(dg, cells_per_dimension, periodicity = true) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, dg, source_terms = source_terms) @@ -19,14 +19,14 @@ tspan = (0.0, 0.1) ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() -alive_callback = AliveCallback(alive_interval=10) +alive_callback = AliveCallback(alive_interval = 10) analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval, uEltype=real(dg)) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval, uEltype = real(dg)) callbacks = CallbackSet(summary_callback, alive_callback, analysis_callback) ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt = 0.5 * estimate_dt(mesh, dg), save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 0.5 * estimate_dt(mesh, dg), save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/dgmulti_3d/elixir_navierstokes_convergence.jl b/examples/dgmulti_3d/elixir_navierstokes_convergence.jl index 9a237b2d2fc..5fa0ad7ce60 100644 --- a/examples/dgmulti_3d/elixir_navierstokes_convergence.jl +++ b/examples/dgmulti_3d/elixir_navierstokes_convergence.jl @@ -8,219 +8,225 @@ prandtl_number() = 0.72 mu() = 0.01 equations = CompressibleEulerEquations3D(1.4) -equations_parabolic = CompressibleNavierStokesDiffusion3D(equations, mu=mu(), Prandtl=prandtl_number(), - gradient_variables=GradientVariablesPrimitive()) +equations_parabolic = CompressibleNavierStokesDiffusion3D(equations, mu = mu(), + Prandtl = prandtl_number(), + gradient_variables = GradientVariablesPrimitive()) # Create DG solver with polynomial degree = 3 and (local) Lax-Friedrichs/Rusanov flux as surface flux dg = DGMulti(polydeg = 3, element_type = Hex(), approximation_type = Polynomial(), surface_integral = SurfaceIntegralWeakForm(flux_lax_friedrichs), volume_integral = VolumeIntegralWeakForm()) -top_bottom(x, tol=50*eps()) = abs(abs(x[2]) - 1) < tol +top_bottom(x, tol = 50 * eps()) = abs(abs(x[2]) - 1) < tol is_on_boundary = Dict(:top_bottom => top_bottom) cells_per_dimension = (8, 8, 8) -mesh = DGMultiMesh(dg, cells_per_dimension; periodicity=(true, false, true), is_on_boundary) +mesh = DGMultiMesh(dg, cells_per_dimension; periodicity = (true, false, true), + is_on_boundary) # Note: the initial condition cannot be specialized to `CompressibleNavierStokesDiffusion3D` # since it is called by both the parabolic solver (which passes in `CompressibleNavierStokesDiffusion3D`) # and by the initial condition (which passes in `CompressibleEulerEquations3D`). # This convergence test setup was originally derived by Andrew Winters (@andrewwinters5000) function initial_condition_navier_stokes_convergence_test(x, t, equations) - # Constants. OBS! Must match those in `source_terms_navier_stokes_convergence_test` - c = 2.0 - A1 = 0.5 - A2 = 1.0 - A3 = 0.5 - - # Convenience values for trig. functions - pi_x = pi * x[1] - pi_y = pi * x[2] - pi_z = pi * x[3] - pi_t = pi * t - - rho = c + A1 * sin(pi_x) * cos(pi_y) * sin(pi_z) * cos(pi_t) - v1 = A2 * sin(pi_x) * log(x[2] + 2.0) * (1.0 - exp(-A3 * (x[2] - 1.0))) * sin(pi_z) * cos(pi_t) - v2 = v1 - v3 = v1 - p = rho^2 - - return prim2cons(SVector(rho, v1, v2, v3, p), equations) + # Constants. OBS! Must match those in `source_terms_navier_stokes_convergence_test` + c = 2.0 + A1 = 0.5 + A2 = 1.0 + A3 = 0.5 + + # Convenience values for trig. functions + pi_x = pi * x[1] + pi_y = pi * x[2] + pi_z = pi * x[3] + pi_t = pi * t + + rho = c + A1 * sin(pi_x) * cos(pi_y) * sin(pi_z) * cos(pi_t) + v1 = A2 * sin(pi_x) * log(x[2] + 2.0) * (1.0 - exp(-A3 * (x[2] - 1.0))) * sin(pi_z) * + cos(pi_t) + v2 = v1 + v3 = v1 + p = rho^2 + + return prim2cons(SVector(rho, v1, v2, v3, p), equations) end @inline function source_terms_navier_stokes_convergence_test(u, x, t, equations) - # TODO: parabolic - # we currently need to hardcode these parameters until we fix the "combined equation" issue - # see also https://github.com/trixi-framework/Trixi.jl/pull/1160 - inv_gamma_minus_one = inv(equations.gamma - 1) - Pr = prandtl_number() - mu_ = mu() - - # Constants. OBS! Must match those in `initial_condition_navier_stokes_convergence_test` - c = 2.0 - A1 = 0.5 - A2 = 1.0 - A3 = 0.5 - - # Convenience values for trig. functions - pi_x = pi * x[1] - pi_y = pi * x[2] - pi_z = pi * x[3] - pi_t = pi * t - - # Define auxiliary functions for the strange function of the y variable - # to make expressions easier to read - g = log(x[2] + 2.0) * (1.0 - exp(-A3 * (x[2] - 1.0))) - g_y = ( A3 * log(x[2] + 2.0) * exp(-A3 * (x[2] - 1.0)) - + (1.0 - exp(-A3 * (x[2] - 1.0))) / (x[2] + 2.0) ) - g_yy = ( 2.0 * A3 * exp(-A3 * (x[2] - 1.0)) / (x[2] + 2.0) - - (1.0 - exp(-A3 * (x[2] - 1.0))) / ((x[2] + 2.0)^2) - - A3^2 * log(x[2] + 2.0) * exp(-A3 * (x[2] - 1.0)) ) - - # Density and its derivatives - rho = c + A1 * sin(pi_x) * cos(pi_y) * sin(pi_z) * cos(pi_t) - rho_t = -pi * A1 * sin(pi_x) * cos(pi_y) * sin(pi_z) * sin(pi_t) - rho_x = pi * A1 * cos(pi_x) * cos(pi_y) * sin(pi_z) * cos(pi_t) - rho_y = -pi * A1 * sin(pi_x) * sin(pi_y) * sin(pi_z) * cos(pi_t) - rho_z = pi * A1 * sin(pi_x) * cos(pi_y) * cos(pi_z) * cos(pi_t) - rho_xx = -pi^2 * (rho - c) - rho_yy = -pi^2 * (rho - c) - rho_zz = -pi^2 * (rho - c) - - # Velocities and their derivatives - # v1 terms - v1 = A2 * sin(pi_x) * g * sin(pi_z) * cos(pi_t) - v1_t = -pi * A2 * sin(pi_x) * g * sin(pi_z) * sin(pi_t) - v1_x = pi * A2 * cos(pi_x) * g * sin(pi_z) * cos(pi_t) - v1_y = A2 * sin(pi_x) * g_y * sin(pi_z) * cos(pi_t) - v1_z = pi * A2 * sin(pi_x) * g * cos(pi_z) * cos(pi_t) - v1_xx = -pi^2 * v1 - v1_yy = A2 * sin(pi_x) * g_yy * sin(pi_z) * cos(pi_t) - v1_zz = -pi^2 * v1 - v1_xy = pi * A2 * cos(pi_x) * g_y * sin(pi_z) * cos(pi_t) - v1_xz = pi^2 * A2 * cos(pi_x) * g * cos(pi_z) * cos(pi_t) - v1_yz = pi * A2 * sin(pi_x) * g_y * cos(pi_z) * cos(pi_t) - # v2 terms (simplifies from ansatz) - v2 = v1 - v2_t = v1_t - v2_x = v1_x - v2_y = v1_y - v2_z = v1_z - v2_xx = v1_xx - v2_yy = v1_yy - v2_zz = v1_zz - v2_xy = v1_xy - v2_yz = v1_yz - # v3 terms (simplifies from ansatz) - v3 = v1 - v3_t = v1_t - v3_x = v1_x - v3_y = v1_y - v3_z = v1_z - v3_xx = v1_xx - v3_yy = v1_yy - v3_zz = v1_zz - v3_xz = v1_xz - v3_yz = v1_yz - - # Pressure and its derivatives - p = rho^2 - p_t = 2.0 * rho * rho_t - p_x = 2.0 * rho * rho_x - p_y = 2.0 * rho * rho_y - p_z = 2.0 * rho * rho_z - - # Total energy and its derivatives; simiplifies from ansatz that v2 = v1 and v3 = v1 - E = p * inv_gamma_minus_one + 1.5 * rho * v1^2 - E_t = p_t * inv_gamma_minus_one + 1.5 * rho_t * v1^2 + 3.0 * rho * v1 * v1_t - E_x = p_x * inv_gamma_minus_one + 1.5 * rho_x * v1^2 + 3.0 * rho * v1 * v1_x - E_y = p_y * inv_gamma_minus_one + 1.5 * rho_y * v1^2 + 3.0 * rho * v1 * v1_y - E_z = p_z * inv_gamma_minus_one + 1.5 * rho_z * v1^2 + 3.0 * rho * v1 * v1_z - - # Divergence of Fick's law ∇⋅∇q = kappa ∇⋅∇T; simplifies because p = rho², so T = p/rho = rho - kappa = equations.gamma * inv_gamma_minus_one / Pr - q_xx = kappa * rho_xx # kappa T_xx - q_yy = kappa * rho_yy # kappa T_yy - q_zz = kappa * rho_zz # kappa T_zz - - # Stress tensor and its derivatives (exploit symmetry) - tau11 = 4.0 / 3.0 * v1_x - 2.0 / 3.0 * (v2_y + v3_z) - tau12 = v1_y + v2_x - tau13 = v1_z + v3_x - tau22 = 4.0 / 3.0 * v2_y - 2.0 / 3.0 * (v1_x + v3_z) - tau23 = v2_z + v3_y - tau33 = 4.0 / 3.0 * v3_z - 2.0 / 3.0 * (v1_x + v2_y) - - tau11_x = 4.0 / 3.0 * v1_xx - 2.0 / 3.0 * (v2_xy + v3_xz) - tau12_x = v1_xy + v2_xx - tau13_x = v1_xz + v3_xx - - tau12_y = v1_yy + v2_xy - tau22_y = 4.0 / 3.0 * v2_yy - 2.0 / 3.0 * (v1_xy + v3_yz) - tau23_y = v2_yz + v3_yy - - tau13_z = v1_zz + v3_xz - tau23_z = v2_zz + v3_yz - tau33_z = 4.0 / 3.0 * v3_zz - 2.0 / 3.0 * (v1_xz + v2_yz) - - # Compute the source terms - # Density equation - du1 = ( rho_t + rho_x * v1 + rho * v1_x - + rho_y * v2 + rho * v2_y - + rho_z * v3 + rho * v3_z ) - # x-momentum equation - du2 = ( rho_t * v1 + rho * v1_t + p_x + rho_x * v1^2 - + 2.0 * rho * v1 * v1_x - + rho_y * v1 * v2 - + rho * v1_y * v2 - + rho * v1 * v2_y - + rho_z * v1 * v3 - + rho * v1_z * v3 - + rho * v1 * v3_z - - mu_ * (tau11_x + tau12_y + tau13_z) ) - # y-momentum equation - du3 = ( rho_t * v2 + rho * v2_t + p_y + rho_x * v1 * v2 - + rho * v1_x * v2 - + rho * v1 * v2_x - + rho_y * v2^2 - + 2.0 * rho * v2 * v2_y - + rho_z * v2 * v3 - + rho * v2_z * v3 - + rho * v2 * v3_z - - mu_ * (tau12_x + tau22_y + tau23_z) ) - # z-momentum equation - du4 = ( rho_t * v3 + rho * v3_t + p_z + rho_x * v1 * v3 - + rho * v1_x * v3 - + rho * v1 * v3_x - + rho_y * v2 * v3 - + rho * v2_y * v3 - + rho * v2 * v3_y - + rho_z * v3^2 - + 2.0 * rho * v3 * v3_z - - mu_ * (tau13_x + tau23_y + tau33_z) ) - # Total energy equation - du5 = ( E_t + v1_x * (E + p) + v1 * (E_x + p_x) - + v2_y * (E + p) + v2 * (E_y + p_y) - + v3_z * (E + p) + v3 * (E_z + p_z) - # stress tensor and temperature gradient from x-direction - - mu_ * ( q_xx + v1_x * tau11 + v2_x * tau12 + v3_x * tau13 - + v1 * tau11_x + v2 * tau12_x + v3 * tau13_x) - # stress tensor and temperature gradient terms from y-direction - - mu_ * ( q_yy + v1_y * tau12 + v2_y * tau22 + v3_y * tau23 - + v1 * tau12_y + v2 * tau22_y + v3 * tau23_y) - # stress tensor and temperature gradient terms from z-direction - - mu_ * ( q_zz + v1_z * tau13 + v2_z * tau23 + v3_z * tau33 - + v1 * tau13_z + v2 * tau23_z + v3 * tau33_z) ) - - return SVector(du1, du2, du3, du4, du5) + # TODO: parabolic + # we currently need to hardcode these parameters until we fix the "combined equation" issue + # see also https://github.com/trixi-framework/Trixi.jl/pull/1160 + inv_gamma_minus_one = inv(equations.gamma - 1) + Pr = prandtl_number() + mu_ = mu() + + # Constants. OBS! Must match those in `initial_condition_navier_stokes_convergence_test` + c = 2.0 + A1 = 0.5 + A2 = 1.0 + A3 = 0.5 + + # Convenience values for trig. functions + pi_x = pi * x[1] + pi_y = pi * x[2] + pi_z = pi * x[3] + pi_t = pi * t + + # Define auxiliary functions for the strange function of the y variable + # to make expressions easier to read + g = log(x[2] + 2.0) * (1.0 - exp(-A3 * (x[2] - 1.0))) + g_y = (A3 * log(x[2] + 2.0) * exp(-A3 * (x[2] - 1.0)) + + (1.0 - exp(-A3 * (x[2] - 1.0))) / (x[2] + 2.0)) + g_yy = (2.0 * A3 * exp(-A3 * (x[2] - 1.0)) / (x[2] + 2.0) - + (1.0 - exp(-A3 * (x[2] - 1.0))) / ((x[2] + 2.0)^2) - + A3^2 * log(x[2] + 2.0) * exp(-A3 * (x[2] - 1.0))) + + # Density and its derivatives + rho = c + A1 * sin(pi_x) * cos(pi_y) * sin(pi_z) * cos(pi_t) + rho_t = -pi * A1 * sin(pi_x) * cos(pi_y) * sin(pi_z) * sin(pi_t) + rho_x = pi * A1 * cos(pi_x) * cos(pi_y) * sin(pi_z) * cos(pi_t) + rho_y = -pi * A1 * sin(pi_x) * sin(pi_y) * sin(pi_z) * cos(pi_t) + rho_z = pi * A1 * sin(pi_x) * cos(pi_y) * cos(pi_z) * cos(pi_t) + rho_xx = -pi^2 * (rho - c) + rho_yy = -pi^2 * (rho - c) + rho_zz = -pi^2 * (rho - c) + + # Velocities and their derivatives + # v1 terms + v1 = A2 * sin(pi_x) * g * sin(pi_z) * cos(pi_t) + v1_t = -pi * A2 * sin(pi_x) * g * sin(pi_z) * sin(pi_t) + v1_x = pi * A2 * cos(pi_x) * g * sin(pi_z) * cos(pi_t) + v1_y = A2 * sin(pi_x) * g_y * sin(pi_z) * cos(pi_t) + v1_z = pi * A2 * sin(pi_x) * g * cos(pi_z) * cos(pi_t) + v1_xx = -pi^2 * v1 + v1_yy = A2 * sin(pi_x) * g_yy * sin(pi_z) * cos(pi_t) + v1_zz = -pi^2 * v1 + v1_xy = pi * A2 * cos(pi_x) * g_y * sin(pi_z) * cos(pi_t) + v1_xz = pi^2 * A2 * cos(pi_x) * g * cos(pi_z) * cos(pi_t) + v1_yz = pi * A2 * sin(pi_x) * g_y * cos(pi_z) * cos(pi_t) + # v2 terms (simplifies from ansatz) + v2 = v1 + v2_t = v1_t + v2_x = v1_x + v2_y = v1_y + v2_z = v1_z + v2_xx = v1_xx + v2_yy = v1_yy + v2_zz = v1_zz + v2_xy = v1_xy + v2_yz = v1_yz + # v3 terms (simplifies from ansatz) + v3 = v1 + v3_t = v1_t + v3_x = v1_x + v3_y = v1_y + v3_z = v1_z + v3_xx = v1_xx + v3_yy = v1_yy + v3_zz = v1_zz + v3_xz = v1_xz + v3_yz = v1_yz + + # Pressure and its derivatives + p = rho^2 + p_t = 2.0 * rho * rho_t + p_x = 2.0 * rho * rho_x + p_y = 2.0 * rho * rho_y + p_z = 2.0 * rho * rho_z + + # Total energy and its derivatives; simiplifies from ansatz that v2 = v1 and v3 = v1 + E = p * inv_gamma_minus_one + 1.5 * rho * v1^2 + E_t = p_t * inv_gamma_minus_one + 1.5 * rho_t * v1^2 + 3.0 * rho * v1 * v1_t + E_x = p_x * inv_gamma_minus_one + 1.5 * rho_x * v1^2 + 3.0 * rho * v1 * v1_x + E_y = p_y * inv_gamma_minus_one + 1.5 * rho_y * v1^2 + 3.0 * rho * v1 * v1_y + E_z = p_z * inv_gamma_minus_one + 1.5 * rho_z * v1^2 + 3.0 * rho * v1 * v1_z + + # Divergence of Fick's law ∇⋅∇q = kappa ∇⋅∇T; simplifies because p = rho², so T = p/rho = rho + kappa = equations.gamma * inv_gamma_minus_one / Pr + q_xx = kappa * rho_xx # kappa T_xx + q_yy = kappa * rho_yy # kappa T_yy + q_zz = kappa * rho_zz # kappa T_zz + + # Stress tensor and its derivatives (exploit symmetry) + tau11 = 4.0 / 3.0 * v1_x - 2.0 / 3.0 * (v2_y + v3_z) + tau12 = v1_y + v2_x + tau13 = v1_z + v3_x + tau22 = 4.0 / 3.0 * v2_y - 2.0 / 3.0 * (v1_x + v3_z) + tau23 = v2_z + v3_y + tau33 = 4.0 / 3.0 * v3_z - 2.0 / 3.0 * (v1_x + v2_y) + + tau11_x = 4.0 / 3.0 * v1_xx - 2.0 / 3.0 * (v2_xy + v3_xz) + tau12_x = v1_xy + v2_xx + tau13_x = v1_xz + v3_xx + + tau12_y = v1_yy + v2_xy + tau22_y = 4.0 / 3.0 * v2_yy - 2.0 / 3.0 * (v1_xy + v3_yz) + tau23_y = v2_yz + v3_yy + + tau13_z = v1_zz + v3_xz + tau23_z = v2_zz + v3_yz + tau33_z = 4.0 / 3.0 * v3_zz - 2.0 / 3.0 * (v1_xz + v2_yz) + + # Compute the source terms + # Density equation + du1 = (rho_t + rho_x * v1 + rho * v1_x + + rho_y * v2 + rho * v2_y + + rho_z * v3 + rho * v3_z) + # x-momentum equation + du2 = (rho_t * v1 + rho * v1_t + p_x + rho_x * v1^2 + + 2.0 * rho * v1 * v1_x + + rho_y * v1 * v2 + + rho * v1_y * v2 + + rho * v1 * v2_y + + rho_z * v1 * v3 + + rho * v1_z * v3 + + rho * v1 * v3_z - + mu_ * (tau11_x + tau12_y + tau13_z)) + # y-momentum equation + du3 = (rho_t * v2 + rho * v2_t + p_y + rho_x * v1 * v2 + + rho * v1_x * v2 + + rho * v1 * v2_x + + rho_y * v2^2 + + 2.0 * rho * v2 * v2_y + + rho_z * v2 * v3 + + rho * v2_z * v3 + + rho * v2 * v3_z - + mu_ * (tau12_x + tau22_y + tau23_z)) + # z-momentum equation + du4 = (rho_t * v3 + rho * v3_t + p_z + rho_x * v1 * v3 + + rho * v1_x * v3 + + rho * v1 * v3_x + + rho_y * v2 * v3 + + rho * v2_y * v3 + + rho * v2 * v3_y + + rho_z * v3^2 + + 2.0 * rho * v3 * v3_z - + mu_ * (tau13_x + tau23_y + tau33_z)) + # Total energy equation + du5 = (E_t + v1_x * (E + p) + v1 * (E_x + p_x) + + v2_y * (E + p) + v2 * (E_y + p_y) + + v3_z * (E + p) + v3 * (E_z + p_z) - + # stress tensor and temperature gradient from x-direction + mu_ * (q_xx + v1_x * tau11 + v2_x * tau12 + v3_x * tau13 + + v1 * tau11_x + v2 * tau12_x + v3 * tau13_x) - + # stress tensor and temperature gradient terms from y-direction + mu_ * (q_yy + v1_y * tau12 + v2_y * tau22 + v3_y * tau23 + + v1 * tau12_y + v2 * tau22_y + v3 * tau23_y) - + # stress tensor and temperature gradient terms from z-direction + mu_ * (q_zz + v1_z * tau13 + v2_z * tau23 + v3_z * tau33 + + v1 * tau13_z + v2 * tau23_z + v3 * tau33_z)) + + return SVector(du1, du2, du3, du4, du5) end initial_condition = initial_condition_navier_stokes_convergence_test # BC types -velocity_bc_top_bottom = NoSlip((x, t, equations) -> initial_condition_navier_stokes_convergence_test(x, t, equations)[2:4]) +velocity_bc_top_bottom = NoSlip((x, t, equations) -> initial_condition_navier_stokes_convergence_test(x, + t, + equations)[2:4]) heat_bc_top_bottom = Adiabatic((x, t, equations) -> 0.0) -boundary_condition_top_bottom = BoundaryConditionNavierStokesWall(velocity_bc_top_bottom, heat_bc_top_bottom) +boundary_condition_top_bottom = BoundaryConditionNavierStokesWall(velocity_bc_top_bottom, + heat_bc_top_bottom) # define inviscid boundary conditions boundary_conditions = (; :top_bottom => boundary_condition_slip_wall) @@ -228,10 +234,11 @@ boundary_conditions = (; :top_bottom => boundary_condition_slip_wall) # define viscous boundary conditions boundary_conditions_parabolic = (; :top_bottom => boundary_condition_top_bottom) -semi = SemidiscretizationHyperbolicParabolic(mesh, (equations, equations_parabolic), initial_condition, dg; - boundary_conditions=(boundary_conditions, boundary_conditions_parabolic), - source_terms=source_terms_navier_stokes_convergence_test) - +semi = SemidiscretizationHyperbolicParabolic(mesh, (equations, equations_parabolic), + initial_condition, dg; + boundary_conditions = (boundary_conditions, + boundary_conditions_parabolic), + source_terms = source_terms_navier_stokes_convergence_test) ############################################################################### # ODE solvers, callbacks etc. @@ -241,15 +248,15 @@ tspan = (0.0, 1.0) ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() -alive_callback = AliveCallback(alive_interval=10) +alive_callback = AliveCallback(alive_interval = 10) analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval, uEltype=real(dg)) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval, uEltype = real(dg)) callbacks = CallbackSet(summary_callback, alive_callback, analysis_callback) ############################################################################### # run the simulation time_int_tol = 1e-8 -sol = solve(ode, RDPK3SpFSAL49(); abstol=time_int_tol, reltol=time_int_tol, - ode_default_options()..., callback=callbacks) +sol = solve(ode, RDPK3SpFSAL49(); abstol = time_int_tol, reltol = time_int_tol, + ode_default_options()..., callback = callbacks) summary_callback() # print the timer summary diff --git a/examples/dgmulti_3d/elixir_navierstokes_convergence_curved.jl b/examples/dgmulti_3d/elixir_navierstokes_convergence_curved.jl index c14d6620803..c58d78d2581 100644 --- a/examples/dgmulti_3d/elixir_navierstokes_convergence_curved.jl +++ b/examples/dgmulti_3d/elixir_navierstokes_convergence_curved.jl @@ -8,25 +8,27 @@ prandtl_number() = 0.72 mu() = 0.01 equations = CompressibleEulerEquations3D(1.4) -equations_parabolic = CompressibleNavierStokesDiffusion3D(equations, mu=mu(), Prandtl=prandtl_number(), - gradient_variables=GradientVariablesPrimitive()) +equations_parabolic = CompressibleNavierStokesDiffusion3D(equations, mu = mu(), + Prandtl = prandtl_number(), + gradient_variables = GradientVariablesPrimitive()) # Create DG solver with polynomial degree = 3 and (local) Lax-Friedrichs/Rusanov flux as surface flux dg = DGMulti(polydeg = 3, element_type = Hex(), approximation_type = Polynomial(), surface_integral = SurfaceIntegralWeakForm(flux_lax_friedrichs), volume_integral = VolumeIntegralWeakForm()) -top_bottom(x, tol=50*eps()) = abs(abs(x[2]) - 1) < tol +top_bottom(x, tol = 50 * eps()) = abs(abs(x[2]) - 1) < tol is_on_boundary = Dict(:top_bottom => top_bottom) function mapping(xi, eta, zeta) - x = xi + 0.1 * sin(pi * xi) * sin(pi * eta) - y = eta + 0.1 * sin(pi * xi) * sin(pi * eta) - z = zeta + 0.1 * sin(pi * xi) * sin(pi * eta) - return SVector(x, y, z) + x = xi + 0.1 * sin(pi * xi) * sin(pi * eta) + y = eta + 0.1 * sin(pi * xi) * sin(pi * eta) + z = zeta + 0.1 * sin(pi * xi) * sin(pi * eta) + return SVector(x, y, z) end cells_per_dimension = (8, 8, 8) -mesh = DGMultiMesh(dg, cells_per_dimension, mapping; periodicity=(true, false, true), is_on_boundary) +mesh = DGMultiMesh(dg, cells_per_dimension, mapping; periodicity = (true, false, true), + is_on_boundary) # This initial condition is taken from `examples/dgmulti_3d/elixir_navierstokes_convergence.jl` @@ -35,200 +37,204 @@ mesh = DGMultiMesh(dg, cells_per_dimension, mapping; periodicity=(true, false, t # and by the initial condition (which passes in `CompressibleEulerEquations3D`). # This convergence test setup was originally derived by Andrew Winters (@andrewwinters5000) function initial_condition_navier_stokes_convergence_test(x, t, equations) - # Constants. OBS! Must match those in `source_terms_navier_stokes_convergence_test` - c = 2.0 - A1 = 0.5 - A2 = 1.0 - A3 = 0.5 - - # Convenience values for trig. functions - pi_x = pi * x[1] - pi_y = pi * x[2] - pi_z = pi * x[3] - pi_t = pi * t - - rho = c + A1 * sin(pi_x) * cos(pi_y) * sin(pi_z) * cos(pi_t) - v1 = A2 * sin(pi_x) * log(x[2] + 2.0) * (1.0 - exp(-A3 * (x[2] - 1.0))) * sin(pi_z) * cos(pi_t) - v2 = v1 - v3 = v1 - p = rho^2 - - return prim2cons(SVector(rho, v1, v2, v3, p), equations) + # Constants. OBS! Must match those in `source_terms_navier_stokes_convergence_test` + c = 2.0 + A1 = 0.5 + A2 = 1.0 + A3 = 0.5 + + # Convenience values for trig. functions + pi_x = pi * x[1] + pi_y = pi * x[2] + pi_z = pi * x[3] + pi_t = pi * t + + rho = c + A1 * sin(pi_x) * cos(pi_y) * sin(pi_z) * cos(pi_t) + v1 = A2 * sin(pi_x) * log(x[2] + 2.0) * (1.0 - exp(-A3 * (x[2] - 1.0))) * sin(pi_z) * + cos(pi_t) + v2 = v1 + v3 = v1 + p = rho^2 + + return prim2cons(SVector(rho, v1, v2, v3, p), equations) end @inline function source_terms_navier_stokes_convergence_test(u, x, t, equations) - # TODO: parabolic - # we currently need to hardcode these parameters until we fix the "combined equation" issue - # see also https://github.com/trixi-framework/Trixi.jl/pull/1160 - inv_gamma_minus_one = inv(equations.gamma - 1) - Pr = prandtl_number() - mu_ = mu() - - # Constants. OBS! Must match those in `initial_condition_navier_stokes_convergence_test` - c = 2.0 - A1 = 0.5 - A2 = 1.0 - A3 = 0.5 - - # Convenience values for trig. functions - pi_x = pi * x[1] - pi_y = pi * x[2] - pi_z = pi * x[3] - pi_t = pi * t - - # Define auxiliary functions for the strange function of the y variable - # to make expressions easier to read - g = log(x[2] + 2.0) * (1.0 - exp(-A3 * (x[2] - 1.0))) - g_y = ( A3 * log(x[2] + 2.0) * exp(-A3 * (x[2] - 1.0)) - + (1.0 - exp(-A3 * (x[2] - 1.0))) / (x[2] + 2.0) ) - g_yy = ( 2.0 * A3 * exp(-A3 * (x[2] - 1.0)) / (x[2] + 2.0) - - (1.0 - exp(-A3 * (x[2] - 1.0))) / ((x[2] + 2.0)^2) - - A3^2 * log(x[2] + 2.0) * exp(-A3 * (x[2] - 1.0)) ) - - # Density and its derivatives - rho = c + A1 * sin(pi_x) * cos(pi_y) * sin(pi_z) * cos(pi_t) - rho_t = -pi * A1 * sin(pi_x) * cos(pi_y) * sin(pi_z) * sin(pi_t) - rho_x = pi * A1 * cos(pi_x) * cos(pi_y) * sin(pi_z) * cos(pi_t) - rho_y = -pi * A1 * sin(pi_x) * sin(pi_y) * sin(pi_z) * cos(pi_t) - rho_z = pi * A1 * sin(pi_x) * cos(pi_y) * cos(pi_z) * cos(pi_t) - rho_xx = -pi^2 * (rho - c) - rho_yy = -pi^2 * (rho - c) - rho_zz = -pi^2 * (rho - c) - - # Velocities and their derivatives - # v1 terms - v1 = A2 * sin(pi_x) * g * sin(pi_z) * cos(pi_t) - v1_t = -pi * A2 * sin(pi_x) * g * sin(pi_z) * sin(pi_t) - v1_x = pi * A2 * cos(pi_x) * g * sin(pi_z) * cos(pi_t) - v1_y = A2 * sin(pi_x) * g_y * sin(pi_z) * cos(pi_t) - v1_z = pi * A2 * sin(pi_x) * g * cos(pi_z) * cos(pi_t) - v1_xx = -pi^2 * v1 - v1_yy = A2 * sin(pi_x) * g_yy * sin(pi_z) * cos(pi_t) - v1_zz = -pi^2 * v1 - v1_xy = pi * A2 * cos(pi_x) * g_y * sin(pi_z) * cos(pi_t) - v1_xz = pi^2 * A2 * cos(pi_x) * g * cos(pi_z) * cos(pi_t) - v1_yz = pi * A2 * sin(pi_x) * g_y * cos(pi_z) * cos(pi_t) - # v2 terms (simplifies from ansatz) - v2 = v1 - v2_t = v1_t - v2_x = v1_x - v2_y = v1_y - v2_z = v1_z - v2_xx = v1_xx - v2_yy = v1_yy - v2_zz = v1_zz - v2_xy = v1_xy - v2_yz = v1_yz - # v3 terms (simplifies from ansatz) - v3 = v1 - v3_t = v1_t - v3_x = v1_x - v3_y = v1_y - v3_z = v1_z - v3_xx = v1_xx - v3_yy = v1_yy - v3_zz = v1_zz - v3_xz = v1_xz - v3_yz = v1_yz - - # Pressure and its derivatives - p = rho^2 - p_t = 2.0 * rho * rho_t - p_x = 2.0 * rho * rho_x - p_y = 2.0 * rho * rho_y - p_z = 2.0 * rho * rho_z - - # Total energy and its derivatives; simiplifies from ansatz that v2 = v1 and v3 = v1 - E = p * inv_gamma_minus_one + 1.5 * rho * v1^2 - E_t = p_t * inv_gamma_minus_one + 1.5 * rho_t * v1^2 + 3.0 * rho * v1 * v1_t - E_x = p_x * inv_gamma_minus_one + 1.5 * rho_x * v1^2 + 3.0 * rho * v1 * v1_x - E_y = p_y * inv_gamma_minus_one + 1.5 * rho_y * v1^2 + 3.0 * rho * v1 * v1_y - E_z = p_z * inv_gamma_minus_one + 1.5 * rho_z * v1^2 + 3.0 * rho * v1 * v1_z - - # Divergence of Fick's law ∇⋅∇q = kappa ∇⋅∇T; simplifies because p = rho², so T = p/rho = rho - kappa = equations.gamma * inv_gamma_minus_one / Pr - q_xx = kappa * rho_xx # kappa T_xx - q_yy = kappa * rho_yy # kappa T_yy - q_zz = kappa * rho_zz # kappa T_zz - - # Stress tensor and its derivatives (exploit symmetry) - tau11 = 4.0 / 3.0 * v1_x - 2.0 / 3.0 * (v2_y + v3_z) - tau12 = v1_y + v2_x - tau13 = v1_z + v3_x - tau22 = 4.0 / 3.0 * v2_y - 2.0 / 3.0 * (v1_x + v3_z) - tau23 = v2_z + v3_y - tau33 = 4.0 / 3.0 * v3_z - 2.0 / 3.0 * (v1_x + v2_y) - - tau11_x = 4.0 / 3.0 * v1_xx - 2.0 / 3.0 * (v2_xy + v3_xz) - tau12_x = v1_xy + v2_xx - tau13_x = v1_xz + v3_xx - - tau12_y = v1_yy + v2_xy - tau22_y = 4.0 / 3.0 * v2_yy - 2.0 / 3.0 * (v1_xy + v3_yz) - tau23_y = v2_yz + v3_yy - - tau13_z = v1_zz + v3_xz - tau23_z = v2_zz + v3_yz - tau33_z = 4.0 / 3.0 * v3_zz - 2.0 / 3.0 * (v1_xz + v2_yz) - - # Compute the source terms - # Density equation - du1 = ( rho_t + rho_x * v1 + rho * v1_x - + rho_y * v2 + rho * v2_y - + rho_z * v3 + rho * v3_z ) - # x-momentum equation - du2 = ( rho_t * v1 + rho * v1_t + p_x + rho_x * v1^2 - + 2.0 * rho * v1 * v1_x - + rho_y * v1 * v2 - + rho * v1_y * v2 - + rho * v1 * v2_y - + rho_z * v1 * v3 - + rho * v1_z * v3 - + rho * v1 * v3_z - - mu_ * (tau11_x + tau12_y + tau13_z) ) - # y-momentum equation - du3 = ( rho_t * v2 + rho * v2_t + p_y + rho_x * v1 * v2 - + rho * v1_x * v2 - + rho * v1 * v2_x - + rho_y * v2^2 - + 2.0 * rho * v2 * v2_y - + rho_z * v2 * v3 - + rho * v2_z * v3 - + rho * v2 * v3_z - - mu_ * (tau12_x + tau22_y + tau23_z) ) - # z-momentum equation - du4 = ( rho_t * v3 + rho * v3_t + p_z + rho_x * v1 * v3 - + rho * v1_x * v3 - + rho * v1 * v3_x - + rho_y * v2 * v3 - + rho * v2_y * v3 - + rho * v2 * v3_y - + rho_z * v3^2 - + 2.0 * rho * v3 * v3_z - - mu_ * (tau13_x + tau23_y + tau33_z) ) - # Total energy equation - du5 = ( E_t + v1_x * (E + p) + v1 * (E_x + p_x) - + v2_y * (E + p) + v2 * (E_y + p_y) - + v3_z * (E + p) + v3 * (E_z + p_z) - # stress tensor and temperature gradient from x-direction - - mu_ * ( q_xx + v1_x * tau11 + v2_x * tau12 + v3_x * tau13 - + v1 * tau11_x + v2 * tau12_x + v3 * tau13_x) - # stress tensor and temperature gradient terms from y-direction - - mu_ * ( q_yy + v1_y * tau12 + v2_y * tau22 + v3_y * tau23 - + v1 * tau12_y + v2 * tau22_y + v3 * tau23_y) - # stress tensor and temperature gradient terms from z-direction - - mu_ * ( q_zz + v1_z * tau13 + v2_z * tau23 + v3_z * tau33 - + v1 * tau13_z + v2 * tau23_z + v3 * tau33_z) ) - - return SVector(du1, du2, du3, du4, du5) + # TODO: parabolic + # we currently need to hardcode these parameters until we fix the "combined equation" issue + # see also https://github.com/trixi-framework/Trixi.jl/pull/1160 + inv_gamma_minus_one = inv(equations.gamma - 1) + Pr = prandtl_number() + mu_ = mu() + + # Constants. OBS! Must match those in `initial_condition_navier_stokes_convergence_test` + c = 2.0 + A1 = 0.5 + A2 = 1.0 + A3 = 0.5 + + # Convenience values for trig. functions + pi_x = pi * x[1] + pi_y = pi * x[2] + pi_z = pi * x[3] + pi_t = pi * t + + # Define auxiliary functions for the strange function of the y variable + # to make expressions easier to read + g = log(x[2] + 2.0) * (1.0 - exp(-A3 * (x[2] - 1.0))) + g_y = (A3 * log(x[2] + 2.0) * exp(-A3 * (x[2] - 1.0)) + + (1.0 - exp(-A3 * (x[2] - 1.0))) / (x[2] + 2.0)) + g_yy = (2.0 * A3 * exp(-A3 * (x[2] - 1.0)) / (x[2] + 2.0) - + (1.0 - exp(-A3 * (x[2] - 1.0))) / ((x[2] + 2.0)^2) - + A3^2 * log(x[2] + 2.0) * exp(-A3 * (x[2] - 1.0))) + + # Density and its derivatives + rho = c + A1 * sin(pi_x) * cos(pi_y) * sin(pi_z) * cos(pi_t) + rho_t = -pi * A1 * sin(pi_x) * cos(pi_y) * sin(pi_z) * sin(pi_t) + rho_x = pi * A1 * cos(pi_x) * cos(pi_y) * sin(pi_z) * cos(pi_t) + rho_y = -pi * A1 * sin(pi_x) * sin(pi_y) * sin(pi_z) * cos(pi_t) + rho_z = pi * A1 * sin(pi_x) * cos(pi_y) * cos(pi_z) * cos(pi_t) + rho_xx = -pi^2 * (rho - c) + rho_yy = -pi^2 * (rho - c) + rho_zz = -pi^2 * (rho - c) + + # Velocities and their derivatives + # v1 terms + v1 = A2 * sin(pi_x) * g * sin(pi_z) * cos(pi_t) + v1_t = -pi * A2 * sin(pi_x) * g * sin(pi_z) * sin(pi_t) + v1_x = pi * A2 * cos(pi_x) * g * sin(pi_z) * cos(pi_t) + v1_y = A2 * sin(pi_x) * g_y * sin(pi_z) * cos(pi_t) + v1_z = pi * A2 * sin(pi_x) * g * cos(pi_z) * cos(pi_t) + v1_xx = -pi^2 * v1 + v1_yy = A2 * sin(pi_x) * g_yy * sin(pi_z) * cos(pi_t) + v1_zz = -pi^2 * v1 + v1_xy = pi * A2 * cos(pi_x) * g_y * sin(pi_z) * cos(pi_t) + v1_xz = pi^2 * A2 * cos(pi_x) * g * cos(pi_z) * cos(pi_t) + v1_yz = pi * A2 * sin(pi_x) * g_y * cos(pi_z) * cos(pi_t) + # v2 terms (simplifies from ansatz) + v2 = v1 + v2_t = v1_t + v2_x = v1_x + v2_y = v1_y + v2_z = v1_z + v2_xx = v1_xx + v2_yy = v1_yy + v2_zz = v1_zz + v2_xy = v1_xy + v2_yz = v1_yz + # v3 terms (simplifies from ansatz) + v3 = v1 + v3_t = v1_t + v3_x = v1_x + v3_y = v1_y + v3_z = v1_z + v3_xx = v1_xx + v3_yy = v1_yy + v3_zz = v1_zz + v3_xz = v1_xz + v3_yz = v1_yz + + # Pressure and its derivatives + p = rho^2 + p_t = 2.0 * rho * rho_t + p_x = 2.0 * rho * rho_x + p_y = 2.0 * rho * rho_y + p_z = 2.0 * rho * rho_z + + # Total energy and its derivatives; simiplifies from ansatz that v2 = v1 and v3 = v1 + E = p * inv_gamma_minus_one + 1.5 * rho * v1^2 + E_t = p_t * inv_gamma_minus_one + 1.5 * rho_t * v1^2 + 3.0 * rho * v1 * v1_t + E_x = p_x * inv_gamma_minus_one + 1.5 * rho_x * v1^2 + 3.0 * rho * v1 * v1_x + E_y = p_y * inv_gamma_minus_one + 1.5 * rho_y * v1^2 + 3.0 * rho * v1 * v1_y + E_z = p_z * inv_gamma_minus_one + 1.5 * rho_z * v1^2 + 3.0 * rho * v1 * v1_z + + # Divergence of Fick's law ∇⋅∇q = kappa ∇⋅∇T; simplifies because p = rho², so T = p/rho = rho + kappa = equations.gamma * inv_gamma_minus_one / Pr + q_xx = kappa * rho_xx # kappa T_xx + q_yy = kappa * rho_yy # kappa T_yy + q_zz = kappa * rho_zz # kappa T_zz + + # Stress tensor and its derivatives (exploit symmetry) + tau11 = 4.0 / 3.0 * v1_x - 2.0 / 3.0 * (v2_y + v3_z) + tau12 = v1_y + v2_x + tau13 = v1_z + v3_x + tau22 = 4.0 / 3.0 * v2_y - 2.0 / 3.0 * (v1_x + v3_z) + tau23 = v2_z + v3_y + tau33 = 4.0 / 3.0 * v3_z - 2.0 / 3.0 * (v1_x + v2_y) + + tau11_x = 4.0 / 3.0 * v1_xx - 2.0 / 3.0 * (v2_xy + v3_xz) + tau12_x = v1_xy + v2_xx + tau13_x = v1_xz + v3_xx + + tau12_y = v1_yy + v2_xy + tau22_y = 4.0 / 3.0 * v2_yy - 2.0 / 3.0 * (v1_xy + v3_yz) + tau23_y = v2_yz + v3_yy + + tau13_z = v1_zz + v3_xz + tau23_z = v2_zz + v3_yz + tau33_z = 4.0 / 3.0 * v3_zz - 2.0 / 3.0 * (v1_xz + v2_yz) + + # Compute the source terms + # Density equation + du1 = (rho_t + rho_x * v1 + rho * v1_x + + rho_y * v2 + rho * v2_y + + rho_z * v3 + rho * v3_z) + # x-momentum equation + du2 = (rho_t * v1 + rho * v1_t + p_x + rho_x * v1^2 + + 2.0 * rho * v1 * v1_x + + rho_y * v1 * v2 + + rho * v1_y * v2 + + rho * v1 * v2_y + + rho_z * v1 * v3 + + rho * v1_z * v3 + + rho * v1 * v3_z - + mu_ * (tau11_x + tau12_y + tau13_z)) + # y-momentum equation + du3 = (rho_t * v2 + rho * v2_t + p_y + rho_x * v1 * v2 + + rho * v1_x * v2 + + rho * v1 * v2_x + + rho_y * v2^2 + + 2.0 * rho * v2 * v2_y + + rho_z * v2 * v3 + + rho * v2_z * v3 + + rho * v2 * v3_z - + mu_ * (tau12_x + tau22_y + tau23_z)) + # z-momentum equation + du4 = (rho_t * v3 + rho * v3_t + p_z + rho_x * v1 * v3 + + rho * v1_x * v3 + + rho * v1 * v3_x + + rho_y * v2 * v3 + + rho * v2_y * v3 + + rho * v2 * v3_y + + rho_z * v3^2 + + 2.0 * rho * v3 * v3_z - + mu_ * (tau13_x + tau23_y + tau33_z)) + # Total energy equation + du5 = (E_t + v1_x * (E + p) + v1 * (E_x + p_x) + + v2_y * (E + p) + v2 * (E_y + p_y) + + v3_z * (E + p) + v3 * (E_z + p_z) - + # stress tensor and temperature gradient from x-direction + mu_ * (q_xx + v1_x * tau11 + v2_x * tau12 + v3_x * tau13 + + v1 * tau11_x + v2 * tau12_x + v3 * tau13_x) - + # stress tensor and temperature gradient terms from y-direction + mu_ * (q_yy + v1_y * tau12 + v2_y * tau22 + v3_y * tau23 + + v1 * tau12_y + v2 * tau22_y + v3 * tau23_y) - + # stress tensor and temperature gradient terms from z-direction + mu_ * (q_zz + v1_z * tau13 + v2_z * tau23 + v3_z * tau33 + + v1 * tau13_z + v2 * tau23_z + v3 * tau33_z)) + + return SVector(du1, du2, du3, du4, du5) end initial_condition = initial_condition_navier_stokes_convergence_test # BC types -velocity_bc_top_bottom = NoSlip((x, t, equations) -> initial_condition_navier_stokes_convergence_test(x, t, equations)[2:4]) +velocity_bc_top_bottom = NoSlip((x, t, equations) -> initial_condition_navier_stokes_convergence_test(x, + t, + equations)[2:4]) heat_bc_top_bottom = Adiabatic((x, t, equations) -> 0.0) -boundary_condition_top_bottom = BoundaryConditionNavierStokesWall(velocity_bc_top_bottom, heat_bc_top_bottom) +boundary_condition_top_bottom = BoundaryConditionNavierStokesWall(velocity_bc_top_bottom, + heat_bc_top_bottom) # define inviscid boundary conditions boundary_conditions = (; :top_bottom => boundary_condition_slip_wall) @@ -236,10 +242,11 @@ boundary_conditions = (; :top_bottom => boundary_condition_slip_wall) # define viscous boundary conditions boundary_conditions_parabolic = (; :top_bottom => boundary_condition_top_bottom) -semi = SemidiscretizationHyperbolicParabolic(mesh, (equations, equations_parabolic), initial_condition, dg; - boundary_conditions=(boundary_conditions, boundary_conditions_parabolic), - source_terms=source_terms_navier_stokes_convergence_test) - +semi = SemidiscretizationHyperbolicParabolic(mesh, (equations, equations_parabolic), + initial_condition, dg; + boundary_conditions = (boundary_conditions, + boundary_conditions_parabolic), + source_terms = source_terms_navier_stokes_convergence_test) ############################################################################### # ODE solvers, callbacks etc. @@ -249,15 +256,15 @@ tspan = (0.0, 1.0) ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() -alive_callback = AliveCallback(alive_interval=10) +alive_callback = AliveCallback(alive_interval = 10) analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval, uEltype=real(dg)) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval, uEltype = real(dg)) callbacks = CallbackSet(summary_callback, alive_callback, analysis_callback) ############################################################################### # run the simulation time_int_tol = 1e-8 -sol = solve(ode, RDPK3SpFSAL49(); abstol=time_int_tol, reltol=time_int_tol, - ode_default_options()..., callback=callbacks) +sol = solve(ode, RDPK3SpFSAL49(); abstol = time_int_tol, reltol = time_int_tol, + ode_default_options()..., callback = callbacks) summary_callback() # print the timer summary diff --git a/examples/dgmulti_3d/elixir_navierstokes_taylor_green_vortex.jl b/examples/dgmulti_3d/elixir_navierstokes_taylor_green_vortex.jl index 7953838afeb..dedd8267a3b 100644 --- a/examples/dgmulti_3d/elixir_navierstokes_taylor_green_vortex.jl +++ b/examples/dgmulti_3d/elixir_navierstokes_taylor_green_vortex.jl @@ -10,26 +10,30 @@ prandtl_number() = 0.72 mu() = 6.25e-4 # equivalent to Re = 1600 equations = CompressibleEulerEquations3D(1.4) -equations_parabolic = CompressibleNavierStokesDiffusion3D(equations, mu=mu(), - Prandtl=prandtl_number()) +equations_parabolic = CompressibleNavierStokesDiffusion3D(equations, mu = mu(), + Prandtl = prandtl_number()) """ initial_condition_taylor_green_vortex(x, t, equations::CompressibleEulerEquations3D) The classical inviscid Taylor-Green vortex. """ -function initial_condition_taylor_green_vortex(x, t, equations::CompressibleEulerEquations3D) - A = 1.0 # magnitude of speed - Ms = 0.1 # maximum Mach number - - rho = 1.0 - v1 = A * sin(x[1]) * cos(x[2]) * cos(x[3]) - v2 = -A * cos(x[1]) * sin(x[2]) * cos(x[3]) - v3 = 0.0 - p = (A / Ms)^2 * rho / equations.gamma # scaling to get Ms - p = p + 1.0/16.0 * A^2 * rho * (cos(2*x[1])*cos(2*x[3]) + 2*cos(2*x[2]) + 2*cos(2*x[1]) + cos(2*x[2])*cos(2*x[3])) - - return prim2cons(SVector(rho, v1, v2, v3, p), equations) +function initial_condition_taylor_green_vortex(x, t, + equations::CompressibleEulerEquations3D) + A = 1.0 # magnitude of speed + Ms = 0.1 # maximum Mach number + + rho = 1.0 + v1 = A * sin(x[1]) * cos(x[2]) * cos(x[3]) + v2 = -A * cos(x[1]) * sin(x[2]) * cos(x[3]) + v3 = 0.0 + p = (A / Ms)^2 * rho / equations.gamma # scaling to get Ms + p = p + + 1.0 / 16.0 * A^2 * rho * + (cos(2 * x[1]) * cos(2 * x[3]) + 2 * cos(2 * x[2]) + 2 * cos(2 * x[1]) + + cos(2 * x[2]) * cos(2 * x[3])) + + return prim2cons(SVector(rho, v1, v2, v3, p), equations) end initial_condition = initial_condition_taylor_green_vortex @@ -39,11 +43,11 @@ dg = DGMulti(polydeg = 3, element_type = Hex(), approximation_type = GaussSBP(), volume_integral = VolumeIntegralFluxDifferencing(flux_ranocha)) coordinates_min = (-1.0, -1.0, -1.0) .* pi -coordinates_max = ( 1.0, 1.0, 1.0) .* pi +coordinates_max = (1.0, 1.0, 1.0) .* pi cells_per_dimension = (8, 8, 8) mesh = DGMultiMesh(dg, cells_per_dimension; coordinates_min, coordinates_max, - periodicity=(true, true, true)) + periodicity = (true, true, true)) semi = SemidiscretizationHyperbolicParabolic(mesh, (equations, equations_parabolic), initial_condition, dg) @@ -55,18 +59,18 @@ tspan = (0.0, 10.0) ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() -alive_callback = AliveCallback(alive_interval=10) +alive_callback = AliveCallback(alive_interval = 10) analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval, uEltype=real(dg), - extra_analysis_integrals=(energy_kinetic, - energy_internal, - enstrophy)) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval, uEltype = real(dg), + extra_analysis_integrals = (energy_kinetic, + energy_internal, + enstrophy)) callbacks = CallbackSet(summary_callback, alive_callback) ############################################################################### # run the simulation time_int_tol = 1e-8 -sol = solve(ode, RDPK3SpFSAL49(); abstol=time_int_tol, reltol=time_int_tol, - ode_default_options()..., callback=callbacks) +sol = solve(ode, RDPK3SpFSAL49(); abstol = time_int_tol, reltol = time_int_tol, + ode_default_options()..., callback = callbacks) summary_callback() # print the timer summary diff --git a/examples/p4est_2d_dgsem/elixir_advection_amr_solution_independent.jl b/examples/p4est_2d_dgsem/elixir_advection_amr_solution_independent.jl index 841a080947e..5a2537be4e6 100644 --- a/examples/p4est_2d_dgsem/elixir_advection_amr_solution_independent.jl +++ b/examples/p4est_2d_dgsem/elixir_advection_amr_solution_independent.jl @@ -7,74 +7,73 @@ module TrixiExtension using Trixi -struct IndicatorSolutionIndependent{Cache<:NamedTuple} <: Trixi.AbstractIndicator - cache::Cache +struct IndicatorSolutionIndependent{Cache <: NamedTuple} <: Trixi.AbstractIndicator + cache::Cache end function IndicatorSolutionIndependent(semi) - basis = semi.solver.basis - alpha = Vector{real(basis)}() - cache = (; semi.mesh, alpha) - return IndicatorSolutionIndependent{typeof(cache)}(cache) + basis = semi.solver.basis + alpha = Vector{real(basis)}() + cache = (; semi.mesh, alpha) + return IndicatorSolutionIndependent{typeof(cache)}(cache) end -function (indicator::IndicatorSolutionIndependent)(u::AbstractArray{<:Any,4}, +function (indicator::IndicatorSolutionIndependent)(u::AbstractArray{<:Any, 4}, mesh, equations, dg, cache; t, kwargs...) - - mesh = indicator.cache.mesh - alpha = indicator.cache.alpha - resize!(alpha, nelements(dg, cache)) - - #Predict the theoretical center. - advection_velocity = (0.2, -0.7) - center = t.*advection_velocity - - inner_distance = 1 - outer_distance = 1.85 - - #Iterate over all elements - for element in 1:length(alpha) - # Calculate periodic distance between cell and center. - # This requires an uncurved mesh! - coordinates = SVector(0.5 * (cache.elements.node_coordinates[1, 1, 1, element] + - cache.elements.node_coordinates[1, end, 1, element]), - 0.5 * (cache.elements.node_coordinates[2, 1, 1, element] + - cache.elements.node_coordinates[2, 1, end, element])) - - #The geometric shape of the amr should be preserved when the base_level is increased. - #This is done by looking at the original coordinates of each cell. - cell_coordinates = original_coordinates(coordinates, 5/8) - cell_distance = periodic_distance_2d(cell_coordinates, center, 10) - if cell_distance < (inner_distance+outer_distance)/2 - cell_coordinates = original_coordinates(coordinates, 5/16) - cell_distance = periodic_distance_2d(cell_coordinates, center, 10) + mesh = indicator.cache.mesh + alpha = indicator.cache.alpha + resize!(alpha, nelements(dg, cache)) + + #Predict the theoretical center. + advection_velocity = (0.2, -0.7) + center = t .* advection_velocity + + inner_distance = 1 + outer_distance = 1.85 + + #Iterate over all elements + for element in 1:length(alpha) + # Calculate periodic distance between cell and center. + # This requires an uncurved mesh! + coordinates = SVector(0.5 * (cache.elements.node_coordinates[1, 1, 1, element] + + cache.elements.node_coordinates[1, end, 1, element]), + 0.5 * (cache.elements.node_coordinates[2, 1, 1, element] + + cache.elements.node_coordinates[2, 1, end, element])) + + #The geometric shape of the amr should be preserved when the base_level is increased. + #This is done by looking at the original coordinates of each cell. + cell_coordinates = original_coordinates(coordinates, 5 / 8) + cell_distance = periodic_distance_2d(cell_coordinates, center, 10) + if cell_distance < (inner_distance + outer_distance) / 2 + cell_coordinates = original_coordinates(coordinates, 5 / 16) + cell_distance = periodic_distance_2d(cell_coordinates, center, 10) + end + + #Set alpha according to cells position inside the circles. + target_level = (cell_distance < inner_distance) + (cell_distance < outer_distance) + alpha[element] = target_level / 2 end - - #Set alpha according to cells position inside the circles. - target_level = (cell_distance < inner_distance) + (cell_distance < outer_distance) - alpha[element] = target_level/2 - end - return alpha + return alpha end # For periodic domains, distance between two points must take into account # periodic extensions of the domain function periodic_distance_2d(coordinates, center, domain_length) - dx = coordinates .- center - dx_shifted = abs.(dx .% domain_length) - dx_periodic = min.(dx_shifted, domain_length .- dx_shifted) - return sqrt(sum(dx_periodic.^2)) + dx = coordinates .- center + dx_shifted = abs.(dx .% domain_length) + dx_periodic = min.(dx_shifted, domain_length .- dx_shifted) + return sqrt(sum(dx_periodic .^ 2)) end #This takes a cells coordinates and transforms them into the coordinates of a parent-cell it originally refined from. #It does it so that the parent-cell has given cell_length. function original_coordinates(coordinates, cell_length) - offset = coordinates .% cell_length - offset_sign = sign.(offset) - border = coordinates - offset - center = border + (offset_sign .* cell_length/2) - return center + offset = coordinates .% cell_length + offset_sign = sign.(offset) + border = coordinates - offset + center = border + (offset_sign .* cell_length / 2) + return center end end # module TrixiExtension @@ -88,21 +87,19 @@ equations = LinearScalarAdvectionEquation2D(advection_velocity) initial_condition = initial_condition_gauss -solver = DGSEM(polydeg=3, surface_flux=flux_lax_friedrichs) +solver = DGSEM(polydeg = 3, surface_flux = flux_lax_friedrichs) coordinates_min = (-5.0, -5.0) -coordinates_max = ( 5.0, 5.0) +coordinates_max = (5.0, 5.0) trees_per_dimension = (1, 1) -mesh = P4estMesh(trees_per_dimension, polydeg=3, - coordinates_min=coordinates_min, coordinates_max=coordinates_max, - initial_refinement_level=4) - +mesh = P4estMesh(trees_per_dimension, polydeg = 3, + coordinates_min = coordinates_min, coordinates_max = coordinates_max, + initial_refinement_level = 4) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver) - ############################################################################### # ODE solvers, callbacks etc. @@ -112,38 +109,38 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval, - extra_analysis_integrals=(entropy,)) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval, + extra_analysis_integrals = (entropy,)) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=100, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 100, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) -amr_controller = ControllerThreeLevel(semi, TrixiExtension.IndicatorSolutionIndependent(semi), - base_level=4, - med_level=5, med_threshold=0.1, - max_level=6, max_threshold=0.6) +amr_controller = ControllerThreeLevel(semi, + TrixiExtension.IndicatorSolutionIndependent(semi), + base_level = 4, + med_level = 5, med_threshold = 0.1, + max_level = 6, max_threshold = 0.6) amr_callback = AMRCallback(semi, amr_controller, - interval=5, - adapt_initial_condition=true, - adapt_initial_condition_only_refine=true) + interval = 5, + adapt_initial_condition = true, + adapt_initial_condition_only_refine = true) -stepsize_callback = StepsizeCallback(cfl=1.6) +stepsize_callback = StepsizeCallback(cfl = 1.6) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, save_solution, amr_callback, stepsize_callback); - ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/p4est_2d_dgsem/elixir_advection_amr_unstructured_flag.jl b/examples/p4est_2d_dgsem/elixir_advection_amr_unstructured_flag.jl index 7e6d99c83b1..0a50b3644f0 100644 --- a/examples/p4est_2d_dgsem/elixir_advection_amr_unstructured_flag.jl +++ b/examples/p4est_2d_dgsem/elixir_advection_amr_unstructured_flag.jl @@ -12,18 +12,16 @@ equations = LinearScalarAdvectionEquation2D(advection_velocity) initial_condition = initial_condition_gauss boundary_condition = BoundaryConditionDirichlet(initial_condition) -boundary_conditions = Dict( - :all => boundary_condition -) +boundary_conditions = Dict(:all => boundary_condition) -solver = DGSEM(polydeg=3, surface_flux=flux_lax_friedrichs) +solver = DGSEM(polydeg = 3, surface_flux = flux_lax_friedrichs) # Deformed rectangle that looks like a waving flag, # lower and upper faces are sinus curves, left and right are vertical lines. f1(s) = SVector(-5.0, 5 * s - 5.0) -f2(s) = SVector( 5.0, 5 * s + 5.0) +f2(s) = SVector(5.0, 5 * s + 5.0) f3(s) = SVector(5 * s, -5.0 + 5 * sin(0.5 * pi * s)) -f4(s) = SVector(5 * s, 5.0 + 5 * sin(0.5 * pi * s)) +f4(s) = SVector(5 * s, 5.0 + 5 * sin(0.5 * pi * s)) faces = (f1, f2, f3, f4) # This creates a mapping that transforms [-1, 1]^2 to the domain with the faces defined above. @@ -34,17 +32,16 @@ mapping_flag = Trixi.transfinite_mapping(faces) # Unstructured mesh with 24 cells of the square domain [-1, 1]^n mesh_file = joinpath(@__DIR__, "square_unstructured_2.inp") -isfile(mesh_file) || download("https://gist.githubusercontent.com/efaulhaber/63ff2ea224409e55ee8423b3a33e316a/raw/7db58af7446d1479753ae718930741c47a3b79b7/square_unstructured_2.inp", - mesh_file) - -mesh = P4estMesh{2}(mesh_file, polydeg=3, - mapping=mapping_flag, - initial_refinement_level=1) +isfile(mesh_file) || + download("https://gist.githubusercontent.com/efaulhaber/63ff2ea224409e55ee8423b3a33e316a/raw/7db58af7446d1479753ae718930741c47a3b79b7/square_unstructured_2.inp", + mesh_file) +mesh = P4estMesh{2}(mesh_file, polydeg = 3, + mapping = mapping_flag, + initial_refinement_level = 1) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver, - boundary_conditions=boundary_conditions) - + boundary_conditions = boundary_conditions) ############################################################################### # ODE solvers, callbacks etc. @@ -55,41 +52,40 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval, - extra_analysis_integrals=(entropy,)) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval, + extra_analysis_integrals = (entropy,)) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_restart = SaveRestartCallback(interval=100, - save_final_restart=true) +save_restart = SaveRestartCallback(interval = 100, + save_final_restart = true) -save_solution = SaveSolutionCallback(interval=100, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 100, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) -amr_controller = ControllerThreeLevel(semi, IndicatorMax(semi, variable=first), - base_level=1, - med_level=2, med_threshold=0.1, - max_level=3, max_threshold=0.6) +amr_controller = ControllerThreeLevel(semi, IndicatorMax(semi, variable = first), + base_level = 1, + med_level = 2, med_threshold = 0.1, + max_level = 3, max_threshold = 0.6) amr_callback = AMRCallback(semi, amr_controller, - interval=5, - adapt_initial_condition=true, - adapt_initial_condition_only_refine=true) + interval = 5, + adapt_initial_condition = true, + adapt_initial_condition_only_refine = true) -stepsize_callback = StepsizeCallback(cfl=0.7) +stepsize_callback = StepsizeCallback(cfl = 0.7) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, save_restart, save_solution, amr_callback, stepsize_callback); - ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/p4est_2d_dgsem/elixir_advection_basic.jl b/examples/p4est_2d_dgsem/elixir_advection_basic.jl index 0b2de85da48..ed235bf839c 100644 --- a/examples/p4est_2d_dgsem/elixir_advection_basic.jl +++ b/examples/p4est_2d_dgsem/elixir_advection_basic.jl @@ -11,21 +11,21 @@ advection_velocity = (0.2, -0.7) equations = LinearScalarAdvectionEquation2D(advection_velocity) # Create DG solver with polynomial degree = 3 and (local) Lax-Friedrichs/Rusanov flux as surface flux -solver = DGSEM(polydeg=3, surface_flux=flux_lax_friedrichs) +solver = DGSEM(polydeg = 3, surface_flux = flux_lax_friedrichs) coordinates_min = (-1.0, -1.0) # minimum coordinates (min(x), min(y)) -coordinates_max = ( 1.0, 1.0) # maximum coordinates (max(x), max(y)) +coordinates_max = (1.0, 1.0) # maximum coordinates (max(x), max(y)) trees_per_dimension = (8, 8) # Create P4estMesh with 8 x 8 trees and 16 x 16 elements -mesh = P4estMesh(trees_per_dimension, polydeg=3, - coordinates_min=coordinates_min, coordinates_max=coordinates_max, - initial_refinement_level=1) +mesh = P4estMesh(trees_per_dimension, polydeg = 3, + coordinates_min = coordinates_min, coordinates_max = coordinates_max, + initial_refinement_level = 1) # A semidiscretization collects data structures and functions for the spatial discretization -semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition_convergence_test, solver) - +semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition_convergence_test, + solver) ############################################################################### # ODE solvers, callbacks etc. @@ -38,26 +38,26 @@ ode = semidiscretize(semi, (0.0, 1.0)); summary_callback = SummaryCallback() # The AnalysisCallback allows to analyse the solution in regular intervals and prints the results -analysis_callback = AnalysisCallback(semi, interval=100) +analysis_callback = AnalysisCallback(semi, interval = 100) # The SaveSolutionCallback allows to save the solution to a file in regular intervals -save_solution = SaveSolutionCallback(interval=100, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 100, + solution_variables = cons2prim) # The StepsizeCallback handles the re-calculation of the maximum Δt after each time step -stepsize_callback = StepsizeCallback(cfl=1.6) +stepsize_callback = StepsizeCallback(cfl = 1.6) # Create a CallbackSet to collect all callbacks such that they can be passed to the ODE solver -callbacks = CallbackSet(summary_callback, analysis_callback, save_solution, stepsize_callback) - +callbacks = CallbackSet(summary_callback, analysis_callback, save_solution, + stepsize_callback) ############################################################################### # run the simulation # OrdinaryDiffEq's `solve` method evolves the solution in time and executes the passed callbacks -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); # Print the timer summary summary_callback() diff --git a/examples/p4est_2d_dgsem/elixir_advection_diffusion_nonperiodic_curved.jl b/examples/p4est_2d_dgsem/elixir_advection_diffusion_nonperiodic_curved.jl index 55682f73fce..5497f13aa65 100644 --- a/examples/p4est_2d_dgsem/elixir_advection_diffusion_nonperiodic_curved.jl +++ b/examples/p4est_2d_dgsem/elixir_advection_diffusion_nonperiodic_curved.jl @@ -16,15 +16,15 @@ equations_parabolic = LaplaceDiffusion2D(diffusivity(), equations) # to numerical partial differential equations. # [DOI](https://doi.org/10.1007/978-3-319-41640-3_6). function initial_condition_eriksson_johnson(x, t, equations) - l = 4 - epsilon = diffusivity() # TODO: this requires epsilon < .6 due to sqrt - lambda_1 = (-1 + sqrt(1 - 4 * epsilon * l)) / (-2 * epsilon) - lambda_2 = (-1 - sqrt(1 - 4 * epsilon * l)) / (-2 * epsilon) - r1 = (1 + sqrt(1 + 4 * pi^2 * epsilon^2)) / (2 * epsilon) - s1 = (1 - sqrt(1 + 4 * pi^2 * epsilon^2)) / (2 * epsilon) - u = exp(-l * t) * (exp(lambda_1 * x[1]) - exp(lambda_2 * x[1])) + - cos(pi * x[2]) * (exp(s1 * x[1]) - exp(r1 * x[1])) / (exp(-s1) - exp(-r1)) - return SVector{1}(u) + l = 4 + epsilon = diffusivity() # TODO: this requires epsilon < .6 due to sqrt + lambda_1 = (-1 + sqrt(1 - 4 * epsilon * l)) / (-2 * epsilon) + lambda_2 = (-1 - sqrt(1 - 4 * epsilon * l)) / (-2 * epsilon) + r1 = (1 + sqrt(1 + 4 * pi^2 * epsilon^2)) / (2 * epsilon) + s1 = (1 - sqrt(1 + 4 * pi^2 * epsilon^2)) / (2 * epsilon) + u = exp(-l * t) * (exp(lambda_1 * x[1]) - exp(lambda_2 * x[1])) + + cos(pi * x[2]) * (exp(s1 * x[1]) - exp(r1 * x[1])) / (exp(-s1) - exp(-r1)) + return SVector{1}(u) end initial_condition = initial_condition_eriksson_johnson @@ -33,34 +33,35 @@ boundary_conditions = Dict(:x_neg => BoundaryConditionDirichlet(initial_conditio :y_pos => BoundaryConditionDirichlet(initial_condition), :x_pos => boundary_condition_do_nothing) -boundary_conditions_parabolic = Dict(:x_neg => BoundaryConditionDirichlet(initial_condition), - :x_pos => BoundaryConditionDirichlet(initial_condition), - :y_neg => BoundaryConditionDirichlet(initial_condition), +boundary_conditions_parabolic = Dict(:x_neg => BoundaryConditionDirichlet(initial_condition), + :x_pos => BoundaryConditionDirichlet(initial_condition), + :y_neg => BoundaryConditionDirichlet(initial_condition), :y_pos => BoundaryConditionDirichlet(initial_condition)) # Create DG solver with polynomial degree = 3 and (local) Lax-Friedrichs/Rusanov flux as surface flux -solver = DGSEM(polydeg=3, surface_flux=flux_lax_friedrichs) +solver = DGSEM(polydeg = 3, surface_flux = flux_lax_friedrichs) -coordinates_min = (-1.0, -0.5) -coordinates_max = ( 0.0, 0.5) +coordinates_min = (-1.0, -0.5) +coordinates_max = (0.0, 0.5) # This maps the domain [-1, 1]^2 to [-1, 0] x [-0.5, 0.5] while also # introducing a curved warping to interior nodes. function mapping(xi, eta) - x = xi + 0.1 * sin(pi * xi) * sin(pi * eta) + x = xi + 0.1 * sin(pi * xi) * sin(pi * eta) y = eta + 0.1 * sin(pi * xi) * sin(pi * eta) return SVector(0.5 * (1 + x) - 1, 0.5 * y) -end +end trees_per_dimension = (4, 4) mesh = P4estMesh(trees_per_dimension, - polydeg=3, initial_refinement_level=2, - mapping=mapping, periodicity=(false, false)) + polydeg = 3, initial_refinement_level = 2, + mapping = mapping, periodicity = (false, false)) # A semidiscretization collects data structures and functions for the spatial discretization -semi = SemidiscretizationHyperbolicParabolic(mesh, (equations, equations_parabolic), initial_condition, solver, - boundary_conditions = (boundary_conditions, boundary_conditions_parabolic)) - +semi = SemidiscretizationHyperbolicParabolic(mesh, (equations, equations_parabolic), + initial_condition, solver, + boundary_conditions = (boundary_conditions, + boundary_conditions_parabolic)) ############################################################################### # ODE solvers, callbacks etc. @@ -75,22 +76,21 @@ summary_callback = SummaryCallback() # The AnalysisCallback allows to analyse the solution in regular intervals and prints the results analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) # The AliveCallback prints short status information in regular intervals -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) # Create a CallbackSet to collect all callbacks such that they can be passed to the ODE solver callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback) - ############################################################################### # run the simulation # OrdinaryDiffEq's `solve` method evolves the solution in time and executes the passed callbacks time_int_tol = 1.0e-11 -sol = solve(ode, RDPK3SpFSAL49(); abstol=time_int_tol, reltol=time_int_tol, - ode_default_options()..., callback=callbacks) +sol = solve(ode, RDPK3SpFSAL49(); abstol = time_int_tol, reltol = time_int_tol, + ode_default_options()..., callback = callbacks) # Print the timer summary summary_callback() diff --git a/examples/p4est_2d_dgsem/elixir_advection_diffusion_periodic.jl b/examples/p4est_2d_dgsem/elixir_advection_diffusion_periodic.jl index 1cd075e84ea..0b5129e3c0f 100644 --- a/examples/p4est_2d_dgsem/elixir_advection_diffusion_periodic.jl +++ b/examples/p4est_2d_dgsem/elixir_advection_diffusion_periodic.jl @@ -9,19 +9,21 @@ advection_velocity = (1.0, 0.0) equations = LinearScalarAdvectionEquation2D(advection_velocity) equations_parabolic = LaplaceDiffusion2D(diffusivity(), equations) -function x_trans_periodic(x, domain_length=SVector(2 * pi), center=SVector(0.0)) +function x_trans_periodic(x, domain_length = SVector(2 * pi), center = SVector(0.0)) x_normalized = x .- center x_shifted = x_normalized .% domain_length - x_offset = ((x_shifted .< -0.5 * domain_length) - (x_shifted .> 0.5 * domain_length)) .* domain_length + x_offset = ((x_shifted .< -0.5 * domain_length) - (x_shifted .> 0.5 * domain_length)) .* + domain_length return center + x_shifted + x_offset end # Define initial condition (copied from "examples/tree_1d_dgsem/elixir_advection_diffusion.jl") -function initial_condition_diffusive_convergence_test(x, t, equation::LinearScalarAdvectionEquation2D) +function initial_condition_diffusive_convergence_test(x, t, + equation::LinearScalarAdvectionEquation2D) # Store translated coordinate for easy use of exact solution # Assumes that advection_velocity[2] = 0 (effectively that we are solving a 1D equation) x_trans = x_trans_periodic(x[1] - equation.advection_velocity[1] * t) - + nu = diffusivity() c = 0.0 A = 1.0 @@ -32,23 +34,22 @@ end initial_condition = initial_condition_diffusive_convergence_test # Create DG solver with polynomial degree = 3 and (local) Lax-Friedrichs/Rusanov flux as surface flux -solver = DGSEM(polydeg=3, surface_flux=flux_lax_friedrichs) +solver = DGSEM(polydeg = 3, surface_flux = flux_lax_friedrichs) coordinates_min = (-pi, -pi) # minimum coordinates (min(x), min(y)) -coordinates_max = ( pi, pi) # maximum coordinates (max(x), max(y)) +coordinates_max = (pi, pi) # maximum coordinates (max(x), max(y)) trees_per_dimension = (4, 4) mesh = P4estMesh(trees_per_dimension, - polydeg=3, initial_refinement_level=2, - coordinates_min=coordinates_min, coordinates_max=coordinates_max, - periodicity=true) + polydeg = 3, initial_refinement_level = 2, + coordinates_min = coordinates_min, coordinates_max = coordinates_max, + periodicity = true) # A semidiscretization collects data structures and functions for the spatial discretization semi = SemidiscretizationHyperbolicParabolic(mesh, (equations, equations_parabolic), initial_condition, solver) - ############################################################################### # ODE solvers, callbacks etc. @@ -62,22 +63,21 @@ summary_callback = SummaryCallback() # The AnalysisCallback allows to analyse the solution in regular intervals and prints the results analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) # The AliveCallback prints short status information in regular intervals -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) # Create a CallbackSet to collect all callbacks such that they can be passed to the ODE solver callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback) - ############################################################################### # run the simulation # OrdinaryDiffEq's `solve` method evolves the solution in time and executes the passed callbacks time_int_tol = 1.0e-11 -sol = solve(ode, RDPK3SpFSAL49(); abstol=time_int_tol, reltol=time_int_tol, - ode_default_options()..., callback=callbacks) +sol = solve(ode, RDPK3SpFSAL49(); abstol = time_int_tol, reltol = time_int_tol, + ode_default_options()..., callback = callbacks) # Print the timer summary summary_callback() diff --git a/examples/p4est_2d_dgsem/elixir_advection_diffusion_periodic_curved.jl b/examples/p4est_2d_dgsem/elixir_advection_diffusion_periodic_curved.jl index b438fb8a29c..130def37997 100644 --- a/examples/p4est_2d_dgsem/elixir_advection_diffusion_periodic_curved.jl +++ b/examples/p4est_2d_dgsem/elixir_advection_diffusion_periodic_curved.jl @@ -9,19 +9,21 @@ advection_velocity = (1.0, 0.0) equations = LinearScalarAdvectionEquation2D(advection_velocity) equations_parabolic = LaplaceDiffusion2D(diffusivity(), equations) -function x_trans_periodic(x, domain_length=SVector(2 * pi), center=SVector(0.0)) +function x_trans_periodic(x, domain_length = SVector(2 * pi), center = SVector(0.0)) x_normalized = x .- center x_shifted = x_normalized .% domain_length - x_offset = ((x_shifted .< -0.5 * domain_length) - (x_shifted .> 0.5 * domain_length)) .* domain_length + x_offset = ((x_shifted .< -0.5 * domain_length) - (x_shifted .> 0.5 * domain_length)) .* + domain_length return center + x_shifted + x_offset end # Define initial condition (copied from "examples/tree_1d_dgsem/elixir_advection_diffusion.jl") -function initial_condition_diffusive_convergence_test(x, t, equation::LinearScalarAdvectionEquation2D) +function initial_condition_diffusive_convergence_test(x, t, + equation::LinearScalarAdvectionEquation2D) # Store translated coordinate for easy use of exact solution # Assumes that advection_velocity[2] = 0 (effectively that we are solving a 1D equation) x_trans = x_trans_periodic(x[1] - equation.advection_velocity[1] * t) - + nu = diffusivity() c = 0.0 A = 1.0 @@ -32,28 +34,27 @@ end initial_condition = initial_condition_diffusive_convergence_test # Create DG solver with polynomial degree = 3 and (local) Lax-Friedrichs/Rusanov flux as surface flux -solver = DGSEM(polydeg=3, surface_flux=flux_lax_friedrichs) +solver = DGSEM(polydeg = 3, surface_flux = flux_lax_friedrichs) # This maps the domain [-1, 1]^2 to [-pi, pi]^2 while also # introducing a curved warping to interior nodes. function mapping(xi, eta) - x = xi + 0.1 * sin(pi * xi) * sin(pi * eta) - y = eta + 0.1 * sin(pi * xi) * sin(pi * eta) - return pi * SVector(x, y) + x = xi + 0.1 * sin(pi * xi) * sin(pi * eta) + y = eta + 0.1 * sin(pi * xi) * sin(pi * eta) + return pi * SVector(x, y) end trees_per_dimension = (4, 4) mesh = P4estMesh(trees_per_dimension, - polydeg=3, initial_refinement_level=2, - mapping=mapping, - periodicity=true) + polydeg = 3, initial_refinement_level = 2, + mapping = mapping, + periodicity = true) # A semidiscretization collects data structures and functions for the spatial discretization semi = SemidiscretizationHyperbolicParabolic(mesh, (equations, equations_parabolic), initial_condition, solver) - ############################################################################### # ODE solvers, callbacks etc. @@ -67,22 +68,21 @@ summary_callback = SummaryCallback() # The AnalysisCallback allows to analyse the solution in regular intervals and prints the results analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) # The AliveCallback prints short status information in regular intervals -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) # Create a CallbackSet to collect all callbacks such that they can be passed to the ODE solver callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback) - ############################################################################### # run the simulation # OrdinaryDiffEq's `solve` method evolves the solution in time and executes the passed callbacks time_int_tol = 1.0e-11 -sol = solve(ode, RDPK3SpFSAL49(); abstol=time_int_tol, reltol=time_int_tol, - ode_default_options()..., callback=callbacks) +sol = solve(ode, RDPK3SpFSAL49(); abstol = time_int_tol, reltol = time_int_tol, + ode_default_options()..., callback = callbacks) # Print the timer summary summary_callback() diff --git a/examples/p4est_2d_dgsem/elixir_advection_extended.jl b/examples/p4est_2d_dgsem/elixir_advection_extended.jl index 6d8e7030ac0..66a5b7e0f5b 100644 --- a/examples/p4est_2d_dgsem/elixir_advection_extended.jl +++ b/examples/p4est_2d_dgsem/elixir_advection_extended.jl @@ -12,31 +12,28 @@ initial_condition = initial_condition_convergence_test # BCs must be passed as Dict boundary_condition = BoundaryConditionDirichlet(initial_condition) -boundary_conditions = Dict( - :x_neg => boundary_condition, - :x_pos => boundary_condition, - :y_neg => boundary_condition, - :y_pos => boundary_condition -) +boundary_conditions = Dict(:x_neg => boundary_condition, + :x_pos => boundary_condition, + :y_neg => boundary_condition, + :y_pos => boundary_condition) # Create DG solver with polynomial degree = 3 and (local) Lax-Friedrichs/Rusanov flux as surface flux -solver = DGSEM(polydeg=3, surface_flux=flux_lax_friedrichs) +solver = DGSEM(polydeg = 3, surface_flux = flux_lax_friedrichs) # The initial condition is 2-periodic coordinates_min = (-1.5, 1.3) # minimum coordinates (min(x), min(y)) -coordinates_max = ( 0.5, 5.3) # maximum coordinates (max(x), max(y)) +coordinates_max = (0.5, 5.3) # maximum coordinates (max(x), max(y)) trees_per_dimension = (19, 37) # Create curved mesh with 19 x 37 elements -mesh = P4estMesh(trees_per_dimension, polydeg=3, - coordinates_min=coordinates_min, coordinates_max=coordinates_max, - periodicity=false) +mesh = P4estMesh(trees_per_dimension, polydeg = 3, + coordinates_min = coordinates_min, coordinates_max = coordinates_max, + periodicity = false) # A semidiscretization collects data structures and functions for the spatial discretization semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver, - boundary_conditions=boundary_conditions) - + boundary_conditions = boundary_conditions) ############################################################################### # ODE solvers, callbacks etc. @@ -51,24 +48,24 @@ summary_callback = SummaryCallback() # The AnalysisCallback allows to analyse the solution in regular intervals and prints the results analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval, - extra_analysis_integrals=(entropy, energy_total)) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval, + extra_analysis_integrals = (entropy, energy_total)) # The AliveCallback prints short status information in regular intervals -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) # The SaveRestartCallback allows to save a file from which a Trixi.jl simulation can be restarted -save_restart = SaveRestartCallback(interval=100, - save_final_restart=true) +save_restart = SaveRestartCallback(interval = 100, + save_final_restart = true) # The SaveSolutionCallback allows to save the solution to a file in regular intervals -save_solution = SaveSolutionCallback(interval=100, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 100, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) # The StepsizeCallback handles the re-calculation of the maximum Δt after each time step -stepsize_callback = StepsizeCallback(cfl=1.6) +stepsize_callback = StepsizeCallback(cfl = 1.6) # Create a CallbackSet to collect all callbacks such that they can be passed to the ODE solver callbacks = CallbackSet(summary_callback, @@ -76,14 +73,13 @@ callbacks = CallbackSet(summary_callback, save_restart, save_solution, stepsize_callback) - ############################################################################### # run the simulation # OrdinaryDiffEq's `solve` method evolves the solution in time and executes the passed callbacks -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); # Print the timer summary summary_callback() diff --git a/examples/p4est_2d_dgsem/elixir_advection_nonconforming_flag.jl b/examples/p4est_2d_dgsem/elixir_advection_nonconforming_flag.jl index 0e6e314ebd7..b47b0d61192 100644 --- a/examples/p4est_2d_dgsem/elixir_advection_nonconforming_flag.jl +++ b/examples/p4est_2d_dgsem/elixir_advection_nonconforming_flag.jl @@ -2,7 +2,6 @@ using OrdinaryDiffEq using Trixi - ############################################################################### # semidiscretization of the linear advection equation @@ -10,42 +9,44 @@ advection_velocity = (0.2, -0.7) equations = LinearScalarAdvectionEquation2D(advection_velocity) # Create DG solver with polynomial degree = 4 and (local) Lax-Friedrichs/Rusanov flux as surface flux -solver = DGSEM(polydeg=4, surface_flux=flux_lax_friedrichs) +solver = DGSEM(polydeg = 4, surface_flux = flux_lax_friedrichs) # Deformed rectangle that looks like a waving flag, # lower and upper faces are sinus curves, left and right are vertical lines. f1(s) = SVector(-1.0, s - 1.0) -f2(s) = SVector( 1.0, s + 1.0) +f2(s) = SVector(1.0, s + 1.0) f3(s) = SVector(s, -1.0 + sin(0.5 * pi * s)) -f4(s) = SVector(s, 1.0 + sin(0.5 * pi * s)) +f4(s) = SVector(s, 1.0 + sin(0.5 * pi * s)) # Create P4estMesh with 3 x 2 trees and 6 x 4 elements, # approximate the geometry with a smaller polydeg for testing. trees_per_dimension = (3, 2) -mesh = P4estMesh(trees_per_dimension, polydeg=3, - faces=(f1, f2, f3, f4), - initial_refinement_level=1) +mesh = P4estMesh(trees_per_dimension, polydeg = 3, + faces = (f1, f2, f3, f4), + initial_refinement_level = 1) # Refine bottom left quadrant of each tree to level 4 function refine_fn(p4est, which_tree, quadrant) - quadrant_obj = unsafe_load(quadrant) - if quadrant_obj.x == 0 && quadrant_obj.y == 0 && quadrant_obj.level < 4 - # return true (refine) - return Cint(1) - else - # return false (don't refine) - return Cint(0) - end + quadrant_obj = unsafe_load(quadrant) + if quadrant_obj.x == 0 && quadrant_obj.y == 0 && quadrant_obj.level < 4 + # return true (refine) + return Cint(1) + else + # return false (don't refine) + return Cint(0) + end end # Refine recursively until each bottom left quadrant of a tree has level 4 # The mesh will be rebalanced before the simulation starts -refine_fn_c = @cfunction(refine_fn, Cint, (Ptr{Trixi.p4est_t}, Ptr{Trixi.p4est_topidx_t}, Ptr{Trixi.p4est_quadrant_t})) +refine_fn_c = @cfunction(refine_fn, Cint, + (Ptr{Trixi.p4est_t}, Ptr{Trixi.p4est_topidx_t}, + Ptr{Trixi.p4est_quadrant_t})) Trixi.refine_p4est!(mesh.p4est, true, refine_fn_c, C_NULL) # A semidiscretization collects data structures and functions for the spatial discretization -semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition_convergence_test, solver) - +semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition_convergence_test, + solver) ############################################################################### # ODE solvers, callbacks etc. @@ -58,26 +59,26 @@ ode = semidiscretize(semi, (0.0, 0.2)); summary_callback = SummaryCallback() # The AnalysisCallback allows to analyse the solution in regular intervals and prints the results -analysis_callback = AnalysisCallback(semi, interval=100) +analysis_callback = AnalysisCallback(semi, interval = 100) # The SaveSolutionCallback allows to save the solution to a file in regular intervals -save_solution = SaveSolutionCallback(interval=100, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 100, + solution_variables = cons2prim) # The StepsizeCallback handles the re-calculation of the maximum Δt after each time step -stepsize_callback = StepsizeCallback(cfl=1.6) +stepsize_callback = StepsizeCallback(cfl = 1.6) # Create a CallbackSet to collect all callbacks such that they can be passed to the ODE solver -callbacks = CallbackSet(summary_callback, analysis_callback, save_solution, stepsize_callback) - +callbacks = CallbackSet(summary_callback, analysis_callback, save_solution, + stepsize_callback) ############################################################################### # run the simulation # OrdinaryDiffEq's `solve` method evolves the solution in time and executes the passed callbacks -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); # Print the timer summary summary_callback() diff --git a/examples/p4est_2d_dgsem/elixir_advection_restart.jl b/examples/p4est_2d_dgsem/elixir_advection_restart.jl index 52917616a6a..4f43e122ab3 100644 --- a/examples/p4est_2d_dgsem/elixir_advection_restart.jl +++ b/examples/p4est_2d_dgsem/elixir_advection_restart.jl @@ -10,7 +10,6 @@ restart_file = "restart_000021.h5" trixi_include(@__MODULE__, joinpath(@__DIR__, elixir_file)) - ############################################################################### # adapt the parameters that have changed compared to "elixir_advection_extended.jl" @@ -21,7 +20,7 @@ restart_filename = joinpath("out", restart_file) mesh = load_mesh(restart_filename) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver, - boundary_conditions=boundary_conditions) + boundary_conditions = boundary_conditions) tspan = (load_time(restart_filename), 2.0) dt = load_dt(restart_filename) @@ -30,14 +29,13 @@ ode = semidiscretize(semi, tspan, restart_filename); # Do not overwrite the initial snapshot written by elixir_advection_extended.jl. save_solution.condition.save_initial_solution = false -integrator = init(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=dt, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +integrator = init(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = dt, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); # Get the last time index and work with that. load_timestep!(integrator, restart_filename) - ############################################################################### # run the simulation diff --git a/examples/p4est_2d_dgsem/elixir_advection_unstructured_flag.jl b/examples/p4est_2d_dgsem/elixir_advection_unstructured_flag.jl index 9f5b813639f..37fcc547f60 100644 --- a/examples/p4est_2d_dgsem/elixir_advection_unstructured_flag.jl +++ b/examples/p4est_2d_dgsem/elixir_advection_unstructured_flag.jl @@ -3,7 +3,6 @@ using Downloads: download using OrdinaryDiffEq using Trixi - ############################################################################### # semidiscretization of the linear advection equation @@ -13,19 +12,17 @@ equations = LinearScalarAdvectionEquation2D(advection_velocity) initial_condition = initial_condition_convergence_test boundary_condition = BoundaryConditionDirichlet(initial_condition) -boundary_conditions = Dict( - :all => boundary_condition -) +boundary_conditions = Dict(:all => boundary_condition) # Create DG solver with polynomial degree = 3 and (local) Lax-Friedrichs/Rusanov flux as surface flux -solver = DGSEM(polydeg=3, surface_flux=flux_lax_friedrichs) +solver = DGSEM(polydeg = 3, surface_flux = flux_lax_friedrichs) # Deformed rectangle that looks like a waving flag, # lower and upper faces are sinus curves, left and right are vertical lines. f1(s) = SVector(-1.0, s - 1.0) -f2(s) = SVector( 1.0, s + 1.0) +f2(s) = SVector(1.0, s + 1.0) f3(s) = SVector(s, -1.0 + sin(0.5 * pi * s)) -f4(s) = SVector(s, 1.0 + sin(0.5 * pi * s)) +f4(s) = SVector(s, 1.0 + sin(0.5 * pi * s)) faces = (f1, f2, f3, f4) Trixi.validate_faces(faces) @@ -33,16 +30,17 @@ mapping_flag = Trixi.transfinite_mapping(faces) # Unstructured mesh with 24 cells of the square domain [-1, 1]^n mesh_file = joinpath(@__DIR__, "square_unstructured_2.inp") -isfile(mesh_file) || download("https://gist.githubusercontent.com/efaulhaber/63ff2ea224409e55ee8423b3a33e316a/raw/7db58af7446d1479753ae718930741c47a3b79b7/square_unstructured_2.inp", - mesh_file) +isfile(mesh_file) || + download("https://gist.githubusercontent.com/efaulhaber/63ff2ea224409e55ee8423b3a33e316a/raw/7db58af7446d1479753ae718930741c47a3b79b7/square_unstructured_2.inp", + mesh_file) -mesh = P4estMesh{2}(mesh_file, polydeg=3, - mapping=mapping_flag, - initial_refinement_level=2) +mesh = P4estMesh{2}(mesh_file, polydeg = 3, + mapping = mapping_flag, + initial_refinement_level = 2) # A semidiscretization collects data structures and functions for the spatial discretization -semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver, boundary_conditions=boundary_conditions) - +semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver, + boundary_conditions = boundary_conditions) ############################################################################### # ODE solvers, callbacks etc. @@ -56,26 +54,26 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() # The AnalysisCallback allows to analyse the solution in regular intervals and prints the results -analysis_callback = AnalysisCallback(semi, interval=100) +analysis_callback = AnalysisCallback(semi, interval = 100) # The SaveSolutionCallback allows to save the solution to a file in regular intervals -save_solution = SaveSolutionCallback(interval=100, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 100, + solution_variables = cons2prim) # The StepsizeCallback handles the re-calculation of the maximum Δt after each time step -stepsize_callback = StepsizeCallback(cfl=1.4) +stepsize_callback = StepsizeCallback(cfl = 1.4) # Create a CallbackSet to collect all callbacks such that they can be passed to the ODE solver -callbacks = CallbackSet(summary_callback, analysis_callback, save_solution, stepsize_callback) - +callbacks = CallbackSet(summary_callback, analysis_callback, save_solution, + stepsize_callback) ############################################################################### # run the simulation # OrdinaryDiffEq's `solve` method evolves the solution in time and executes the passed callbacks -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); # Print the timer summary summary_callback() diff --git a/examples/p4est_2d_dgsem/elixir_euler_blast_wave_amr.jl b/examples/p4est_2d_dgsem/elixir_euler_blast_wave_amr.jl index e3f33fb0d28..0ca4fdc2eb7 100644 --- a/examples/p4est_2d_dgsem/elixir_euler_blast_wave_amr.jl +++ b/examples/p4est_2d_dgsem/elixir_euler_blast_wave_amr.jl @@ -17,49 +17,48 @@ A medium blast wave taken from [arXiv: 2008.12044](https://arxiv.org/abs/2008.12044) """ function initial_condition_blast_wave(x, t, equations::CompressibleEulerEquations2D) - # Modified From Hennemann & Gassner JCP paper 2020 (Sec. 6.3) -> "medium blast wave" - # Set up polar coordinates - inicenter = SVector(0.0, 0.0) - x_norm = x[1] - inicenter[1] - y_norm = x[2] - inicenter[2] - r = sqrt(x_norm^2 + y_norm^2) - phi = atan(y_norm, x_norm) - sin_phi, cos_phi = sincos(phi) - - # Calculate primitive variables - rho = r > 0.5 ? 1.0 : 1.1691 - v1 = r > 0.5 ? 0.0 : 0.1882 * cos_phi - v2 = r > 0.5 ? 0.0 : 0.1882 * sin_phi - p = r > 0.5 ? 1.0E-3 : 1.245 - - return prim2cons(SVector(rho, v1, v2, p), equations) + # Modified From Hennemann & Gassner JCP paper 2020 (Sec. 6.3) -> "medium blast wave" + # Set up polar coordinates + inicenter = SVector(0.0, 0.0) + x_norm = x[1] - inicenter[1] + y_norm = x[2] - inicenter[2] + r = sqrt(x_norm^2 + y_norm^2) + phi = atan(y_norm, x_norm) + sin_phi, cos_phi = sincos(phi) + + # Calculate primitive variables + rho = r > 0.5 ? 1.0 : 1.1691 + v1 = r > 0.5 ? 0.0 : 0.1882 * cos_phi + v2 = r > 0.5 ? 0.0 : 0.1882 * sin_phi + p = r > 0.5 ? 1.0E-3 : 1.245 + + return prim2cons(SVector(rho, v1, v2, p), equations) end initial_condition = initial_condition_blast_wave surface_flux = flux_lax_friedrichs -volume_flux = flux_ranocha +volume_flux = flux_ranocha basis = LobattoLegendreBasis(3) indicator_sc = IndicatorHennemannGassner(equations, basis, - alpha_max=0.5, - alpha_min=0.001, - alpha_smooth=true, - variable=density_pressure) + alpha_max = 0.5, + alpha_min = 0.001, + alpha_smooth = true, + variable = density_pressure) volume_integral = VolumeIntegralShockCapturingHG(indicator_sc; - volume_flux_dg=volume_flux, - volume_flux_fv=surface_flux) + volume_flux_dg = volume_flux, + volume_flux_fv = surface_flux) solver = DGSEM(basis, surface_flux, volume_integral) # Unstructured mesh with 48 cells of the square domain [-1, 1]^n mesh_file = joinpath(@__DIR__, "square_unstructured_1.inp") -isfile(mesh_file) || download("https://gist.githubusercontent.com/efaulhaber/a075f8ec39a67fa9fad8f6f84342cbca/raw/a7206a02ed3a5d3cadacd8d9694ac154f9151db7/square_unstructured_1.inp", - mesh_file) +isfile(mesh_file) || + download("https://gist.githubusercontent.com/efaulhaber/a075f8ec39a67fa9fad8f6f84342cbca/raw/a7206a02ed3a5d3cadacd8d9694ac154f9151db7/square_unstructured_1.inp", + mesh_file) -mesh = P4estMesh{2}(mesh_file, polydeg=3, initial_refinement_level=1) +mesh = P4estMesh{2}(mesh_file, polydeg = 3, initial_refinement_level = 1) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver, - boundary_conditions=Dict( - :all => BoundaryConditionDirichlet(initial_condition) - )) + boundary_conditions = Dict(:all => BoundaryConditionDirichlet(initial_condition))) ############################################################################### # ODE solvers, callbacks etc. @@ -70,40 +69,39 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=100, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 100, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) amr_indicator = IndicatorHennemannGassner(semi, - alpha_max=0.5, - alpha_min=0.001, - alpha_smooth=true, - variable=density_pressure) + alpha_max = 0.5, + alpha_min = 0.001, + alpha_smooth = true, + variable = density_pressure) amr_controller = ControllerThreeLevel(semi, amr_indicator, - base_level=1, - max_level =3, max_threshold=0.01) + base_level = 1, + max_level = 3, max_threshold = 0.01) amr_callback = AMRCallback(semi, amr_controller, - interval=5, - adapt_initial_condition=true, - adapt_initial_condition_only_refine=true) + interval = 5, + adapt_initial_condition = true, + adapt_initial_condition_only_refine = true) -stepsize_callback = StepsizeCallback(cfl=0.9) +stepsize_callback = StepsizeCallback(cfl = 0.9) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, save_solution, amr_callback, stepsize_callback) - ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/p4est_2d_dgsem/elixir_euler_double_mach_amr.jl b/examples/p4est_2d_dgsem/elixir_euler_double_mach_amr.jl index 70a0e10c296..92928146d7b 100644 --- a/examples/p4est_2d_dgsem/elixir_euler_double_mach_amr.jl +++ b/examples/p4est_2d_dgsem/elixir_euler_double_mach_amr.jl @@ -21,64 +21,66 @@ See Section IV c on the paper below for details. The Numerical Simulation of Two-Dimensional Fluid Flows with Strong Shocks. [DOI: 10.1016/0021-9991(84)90142-6](https://doi.org/10.1016/0021-9991(84)90142-6) """ -@inline function initial_condition_double_mach_reflection(x, t, equations::CompressibleEulerEquations2D) - - if x[1] < 1 / 6 + (x[2] + 20 * t) / sqrt(3) - phi = pi / 6 - sin_phi, cos_phi = sincos(phi) - - rho = 8.0 - v1 = 8.25 * cos_phi - v2 = -8.25 * sin_phi - p = 116.5 - else - rho = 1.4 - v1 = 0.0 - v2 = 0.0 - p = 1.0 - end - - prim = SVector(rho, v1, v2, p) - return prim2cons(prim, equations) +@inline function initial_condition_double_mach_reflection(x, t, + equations::CompressibleEulerEquations2D) + if x[1] < 1 / 6 + (x[2] + 20 * t) / sqrt(3) + phi = pi / 6 + sin_phi, cos_phi = sincos(phi) + + rho = 8.0 + v1 = 8.25 * cos_phi + v2 = -8.25 * sin_phi + p = 116.5 + else + rho = 1.4 + v1 = 0.0 + v2 = 0.0 + p = 1.0 + end + + prim = SVector(rho, v1, v2, p) + return prim2cons(prim, equations) end initial_condition = initial_condition_double_mach_reflection - boundary_condition_inflow = BoundaryConditionDirichlet(initial_condition_double_mach_reflection) # Supersonic outflow boundary condition. Solution is taken entirely from the internal state. # See `examples/p4est_2d_dgsem/elixir_euler_forward_step_amr.jl` for complete documentation. @inline function boundary_condition_outflow(u_inner, normal_direction::AbstractVector, x, t, - surface_flux_function, equations::CompressibleEulerEquations2D) - # NOTE: Only for the supersonic outflow is this strategy valid - # Calculate the boundary flux entirely from the internal solution state - return flux(u_inner, normal_direction, equations) + surface_flux_function, + equations::CompressibleEulerEquations2D) + # NOTE: Only for the supersonic outflow is this strategy valid + # Calculate the boundary flux entirely from the internal solution state + return flux(u_inner, normal_direction, equations) end # Special mixed boundary condition type for the :Bottom of the domain. # It is Dirichlet when x < 1/6 and a slip wall when x >= 1/6 -@inline function boundary_condition_mixed_dirichlet_wall(u_inner, normal_direction::AbstractVector, +@inline function boundary_condition_mixed_dirichlet_wall(u_inner, + normal_direction::AbstractVector, x, t, surface_flux_function, equations::CompressibleEulerEquations2D) - if x[1] < 1 / 6 - # From the BoundaryConditionDirichlet - # get the external value of the solution - u_boundary = initial_condition_double_mach_reflection(x, t, equations) - # Calculate boundary flux - flux = surface_flux_function(u_inner, u_boundary, normal_direction, equations) - else # x[1] >= 1 / 6 - # Use the free slip wall BC otherwise - flux = boundary_condition_slip_wall(u_inner, normal_direction, x, t, surface_flux_function, equations) - end - - return flux + if x[1] < 1 / 6 + # From the BoundaryConditionDirichlet + # get the external value of the solution + u_boundary = initial_condition_double_mach_reflection(x, t, equations) + # Calculate boundary flux + flux = surface_flux_function(u_inner, u_boundary, normal_direction, equations) + else # x[1] >= 1 / 6 + # Use the free slip wall BC otherwise + flux = boundary_condition_slip_wall(u_inner, normal_direction, x, t, + surface_flux_function, equations) + end + + return flux end -boundary_conditions = Dict( :Bottom => boundary_condition_mixed_dirichlet_wall, - :Top => boundary_condition_inflow, - :Right => boundary_condition_outflow, - :Left => boundary_condition_inflow ) +boundary_conditions = Dict(:Bottom => boundary_condition_mixed_dirichlet_wall, + :Top => boundary_condition_inflow, + :Right => boundary_condition_outflow, + :Left => boundary_condition_inflow) volume_flux = flux_ranocha surface_flux = flux_lax_friedrichs @@ -86,25 +88,27 @@ surface_flux = flux_lax_friedrichs polydeg = 4 basis = LobattoLegendreBasis(polydeg) shock_indicator = IndicatorHennemannGassner(equations, basis, - alpha_max=0.5, - alpha_min=0.001, - alpha_smooth=true, - variable=density_pressure) + alpha_max = 0.5, + alpha_min = 0.001, + alpha_smooth = true, + variable = density_pressure) volume_integral = VolumeIntegralShockCapturingHG(shock_indicator; - volume_flux_dg=volume_flux, - volume_flux_fv=surface_flux) -solver = DGSEM(polydeg=polydeg, surface_flux=surface_flux, volume_integral=volume_integral) + volume_flux_dg = volume_flux, + volume_flux_fv = surface_flux) +solver = DGSEM(polydeg = polydeg, surface_flux = surface_flux, + volume_integral = volume_integral) # Get the unstructured quad mesh from a file (downloads the file if not available locally) default_mesh_file = joinpath(@__DIR__, "abaqus_double_mach.inp") -isfile(default_mesh_file) || download("https://gist.githubusercontent.com/andrewwinters5000/a0806ef0d03cf5ea221af523167b6e32/raw/61ed0eb017eb432d996ed119a52fb041fe363e8c/abaqus_double_mach.inp", - default_mesh_file) +isfile(default_mesh_file) || + download("https://gist.githubusercontent.com/andrewwinters5000/a0806ef0d03cf5ea221af523167b6e32/raw/61ed0eb017eb432d996ed119a52fb041fe363e8c/abaqus_double_mach.inp", + default_mesh_file) mesh_file = default_mesh_file mesh = P4estMesh{2}(mesh_file) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver, - boundary_conditions=boundary_conditions) + boundary_conditions = boundary_conditions) ############################################################################### # ODE solvers, callbacks etc. @@ -115,27 +119,27 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval, - extra_analysis_integrals=(entropy,)) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval, + extra_analysis_integrals = (entropy,)) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=100, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 100, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) -amr_indicator = IndicatorLöhner(semi, variable=Trixi.density) +amr_indicator = IndicatorLöhner(semi, variable = Trixi.density) amr_controller = ControllerThreeLevel(semi, amr_indicator, - base_level=0, - med_level=3, med_threshold=0.05, - max_level=6, max_threshold=0.1) + base_level = 0, + med_level = 3, med_threshold = 0.05, + max_level = 6, max_threshold = 0.1) amr_callback = AMRCallback(semi, amr_controller, - interval=1, - adapt_initial_condition=true, - adapt_initial_condition_only_refine=true) + interval = 1, + adapt_initial_condition = true, + adapt_initial_condition_only_refine = true) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, @@ -143,11 +147,11 @@ callbacks = CallbackSet(summary_callback, amr_callback) # positivity limiter necessary for this example with strong shocks -stage_limiter! = PositivityPreservingLimiterZhangShu(thresholds=(5.0e-6, 5.0e-6), - variables=(Trixi.density, pressure)) +stage_limiter! = PositivityPreservingLimiterZhangShu(thresholds = (5.0e-6, 5.0e-6), + variables = (Trixi.density, pressure)) ############################################################################### # run the simulation sol = solve(ode, SSPRK43(stage_limiter!); - ode_default_options()..., callback=callbacks); + ode_default_options()..., callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/p4est_2d_dgsem/elixir_euler_forward_step_amr.jl b/examples/p4est_2d_dgsem/elixir_euler_forward_step_amr.jl index 667834ea108..0ec9fc222f2 100644 --- a/examples/p4est_2d_dgsem/elixir_euler_forward_step_amr.jl +++ b/examples/p4est_2d_dgsem/elixir_euler_forward_step_amr.jl @@ -20,19 +20,18 @@ See Section IV b on the paper below for details. [DOI: 10.1016/0021-9991(84)90142-6](https://doi.org/10.1016/0021-9991(84)90142-6) """ @inline function initial_condition_mach3_flow(x, t, equations::CompressibleEulerEquations2D) - # set the freestream flow parameters - rho_freestream = 1.4 - v1 = 3.0 - v2 = 0.0 - p_freestream = 1.0 - - prim = SVector(rho_freestream, v1, v2, p_freestream) - return prim2cons(prim, equations) + # set the freestream flow parameters + rho_freestream = 1.4 + v1 = 3.0 + v2 = 0.0 + p_freestream = 1.0 + + prim = SVector(rho_freestream, v1, v2, p_freestream) + return prim2cons(prim, equations) end initial_condition = initial_condition_mach3_flow - boundary_condition_inflow = BoundaryConditionDirichlet(initial_condition_mach3_flow) # Outflow boundary condition. @@ -46,46 +45,47 @@ boundary_condition_inflow = BoundaryConditionDirichlet(initial_condition_mach3_f # Inflow/Outflow Boundary Conditions with Application to FUN3D. # [NASA TM 20110022658](https://ntrs.nasa.gov/citations/20110022658) @inline function boundary_condition_outflow(u_inner, normal_direction::AbstractVector, x, t, - surface_flux_function, equations::CompressibleEulerEquations2D) - # # This would be for the general case where we need to check the magnitude of the local Mach number - # norm_ = norm(normal_direction) - # # Normalize the vector without using `normalize` since we need to multiply by the `norm_` later - # normal = normal_direction / norm_ - - # # Rotate the internal solution state - # u_local = Trixi.rotate_to_x(u_inner, normal, equations) - - # # Compute the primitive variables - # rho_local, v_normal, v_tangent, p_local = cons2prim(u_local, equations) - - # # Compute local Mach number - # a_local = sqrt( equations.gamma * p_local / rho_local ) - # Mach_local = abs( v_normal / a_local ) - # if Mach_local <= 1.0 - # p_local = # Set to the external reference pressure value (somehow? maybe stored in `equations`) - # end - - # # Create the `u_surface` solution state where the local pressure is possibly set from an external value - # prim = SVector(rho_local, v_normal, v_tangent, p_local) - # u_boundary = prim2cons(prim, equations) - # u_surface = Trixi.rotate_from_x(u_boundary, normal, equations) - - # Compute the flux using the appropriate mixture of internal / external solution states - # flux = Trixi.flux(u_surface, normal_direction, equations) - - # NOTE: Only for the supersonic outflow is this strategy valid - # Calculate the boundary flux entirely from the internal solution state - flux = Trixi.flux(u_inner, normal_direction, equations) - - return flux + surface_flux_function, + equations::CompressibleEulerEquations2D) + # # This would be for the general case where we need to check the magnitude of the local Mach number + # norm_ = norm(normal_direction) + # # Normalize the vector without using `normalize` since we need to multiply by the `norm_` later + # normal = normal_direction / norm_ + + # # Rotate the internal solution state + # u_local = Trixi.rotate_to_x(u_inner, normal, equations) + + # # Compute the primitive variables + # rho_local, v_normal, v_tangent, p_local = cons2prim(u_local, equations) + + # # Compute local Mach number + # a_local = sqrt( equations.gamma * p_local / rho_local ) + # Mach_local = abs( v_normal / a_local ) + # if Mach_local <= 1.0 + # p_local = # Set to the external reference pressure value (somehow? maybe stored in `equations`) + # end + + # # Create the `u_surface` solution state where the local pressure is possibly set from an external value + # prim = SVector(rho_local, v_normal, v_tangent, p_local) + # u_boundary = prim2cons(prim, equations) + # u_surface = Trixi.rotate_from_x(u_boundary, normal, equations) + + # Compute the flux using the appropriate mixture of internal / external solution states + # flux = Trixi.flux(u_surface, normal_direction, equations) + + # NOTE: Only for the supersonic outflow is this strategy valid + # Calculate the boundary flux entirely from the internal solution state + flux = Trixi.flux(u_inner, normal_direction, equations) + + return flux end -boundary_conditions = Dict( :Bottom => boundary_condition_slip_wall, - :Step_Front => boundary_condition_slip_wall, - :Step_Top => boundary_condition_slip_wall, - :Top => boundary_condition_slip_wall, - :Right => boundary_condition_outflow, - :Left => boundary_condition_inflow ) +boundary_conditions = Dict(:Bottom => boundary_condition_slip_wall, + :Step_Front => boundary_condition_slip_wall, + :Step_Top => boundary_condition_slip_wall, + :Top => boundary_condition_slip_wall, + :Right => boundary_condition_outflow, + :Left => boundary_condition_inflow) volume_flux = flux_ranocha surface_flux = flux_lax_friedrichs @@ -93,25 +93,27 @@ surface_flux = flux_lax_friedrichs polydeg = 4 basis = LobattoLegendreBasis(polydeg) shock_indicator = IndicatorHennemannGassner(equations, basis, - alpha_max=0.5, - alpha_min=0.001, - alpha_smooth=true, - variable=density_pressure) + alpha_max = 0.5, + alpha_min = 0.001, + alpha_smooth = true, + variable = density_pressure) volume_integral = VolumeIntegralShockCapturingHG(shock_indicator; - volume_flux_dg=volume_flux, - volume_flux_fv=surface_flux) -solver = DGSEM(polydeg=polydeg, surface_flux=surface_flux, volume_integral=volume_integral) + volume_flux_dg = volume_flux, + volume_flux_fv = surface_flux) +solver = DGSEM(polydeg = polydeg, surface_flux = surface_flux, + volume_integral = volume_integral) # Get the unstructured quad mesh from a file (downloads the file if not available locally) default_mesh_file = joinpath(@__DIR__, "abaqus_forward_step.inp") -isfile(default_mesh_file) || download("https://gist.githubusercontent.com/andrewwinters5000/b346ee6aa5446687f128eab8b37d52a7/raw/cd1e1d43bebd8d2631a07caec45585ec8456ca4c/abaqus_forward_step.inp", - default_mesh_file) +isfile(default_mesh_file) || + download("https://gist.githubusercontent.com/andrewwinters5000/b346ee6aa5446687f128eab8b37d52a7/raw/cd1e1d43bebd8d2631a07caec45585ec8456ca4c/abaqus_forward_step.inp", + default_mesh_file) mesh_file = default_mesh_file mesh = P4estMesh{2}(mesh_file) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver, - boundary_conditions=boundary_conditions) + boundary_conditions = boundary_conditions) ############################################################################### # ODE solvers, callbacks etc. @@ -122,27 +124,27 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 1000 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval, - extra_analysis_integrals=(entropy,)) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval, + extra_analysis_integrals = (entropy,)) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=2000, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 2000, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) -amr_indicator = IndicatorLöhner(semi, variable=Trixi.density) +amr_indicator = IndicatorLöhner(semi, variable = Trixi.density) amr_controller = ControllerThreeLevel(semi, amr_indicator, - base_level=0, - med_level=2, med_threshold=0.05, - max_level=5, max_threshold=0.1) + base_level = 0, + med_level = 2, med_threshold = 0.05, + max_level = 5, max_threshold = 0.1) amr_callback = AMRCallback(semi, amr_controller, - interval=5, - adapt_initial_condition=true, - adapt_initial_condition_only_refine=true) + interval = 5, + adapt_initial_condition = true, + adapt_initial_condition_only_refine = true) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, @@ -150,12 +152,12 @@ callbacks = CallbackSet(summary_callback, amr_callback) # positivity limiter necessary for this example with strong shocks -stage_limiter! = PositivityPreservingLimiterZhangShu(thresholds=(5.0e-6, 5.0e-6), - variables=(Trixi.density, pressure)) +stage_limiter! = PositivityPreservingLimiterZhangShu(thresholds = (5.0e-6, 5.0e-6), + variables = (Trixi.density, pressure)) ############################################################################### # run the simulation sol = solve(ode, SSPRK43(stage_limiter!); - maxiters=999999, ode_default_options()..., - callback=callbacks); + maxiters = 999999, ode_default_options()..., + callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/p4est_2d_dgsem/elixir_euler_free_stream.jl b/examples/p4est_2d_dgsem/elixir_euler_free_stream.jl index e88baa2223d..38307a7d781 100644 --- a/examples/p4est_2d_dgsem/elixir_euler_free_stream.jl +++ b/examples/p4est_2d_dgsem/elixir_euler_free_stream.jl @@ -10,21 +10,21 @@ equations = CompressibleEulerEquations2D(1.4) initial_condition = initial_condition_constant -solver = DGSEM(polydeg=3, surface_flux=flux_lax_friedrichs) +solver = DGSEM(polydeg = 3, surface_flux = flux_lax_friedrichs) # Mapping as described in https://arxiv.org/abs/2012.12040 but reduced to 2D function mapping(xi_, eta_) - # Transform input variables between -1 and 1 onto [0,3] - xi = 1.5 * xi_ + 1.5 - eta = 1.5 * eta_ + 1.5 + # Transform input variables between -1 and 1 onto [0,3] + xi = 1.5 * xi_ + 1.5 + eta = 1.5 * eta_ + 1.5 - y = eta + 3/8 * (cos(1.5 * pi * (2 * xi - 3)/3) * - cos(0.5 * pi * (2 * eta - 3)/3)) + y = eta + 3 / 8 * (cos(1.5 * pi * (2 * xi - 3) / 3) * + cos(0.5 * pi * (2 * eta - 3) / 3)) - x = xi + 3/8 * (cos(0.5 * pi * (2 * xi - 3)/3) * - cos(2 * pi * (2 * y - 3)/3)) + x = xi + 3 / 8 * (cos(0.5 * pi * (2 * xi - 3) / 3) * + cos(2 * pi * (2 * y - 3) / 3)) - return SVector(x, y) + return SVector(x, y) end ############################################################################### @@ -32,34 +32,34 @@ end # Unstructured mesh with 48 cells of the square domain [-1, 1]^n mesh_file = joinpath(@__DIR__, "square_unstructured_1.inp") -isfile(mesh_file) || download("https://gist.githubusercontent.com/efaulhaber/a075f8ec39a67fa9fad8f6f84342cbca/raw/a7206a02ed3a5d3cadacd8d9694ac154f9151db7/square_unstructured_1.inp", - mesh_file) +isfile(mesh_file) || + download("https://gist.githubusercontent.com/efaulhaber/a075f8ec39a67fa9fad8f6f84342cbca/raw/a7206a02ed3a5d3cadacd8d9694ac154f9151db7/square_unstructured_1.inp", + mesh_file) # Map the unstructured mesh with the mapping above -mesh = P4estMesh{2}(mesh_file, polydeg=3, mapping=mapping, initial_refinement_level=1) +mesh = P4estMesh{2}(mesh_file, polydeg = 3, mapping = mapping, initial_refinement_level = 1) # Refine bottom left quadrant of each tree to level 2 function refine_fn(p4est, which_tree, quadrant) - quadrant_obj = unsafe_load(quadrant) - if quadrant_obj.x == 0 && quadrant_obj.y == 0 && quadrant_obj.level < 3 - # return true (refine) - return Cint(1) - else - # return false (don't refine) - return Cint(0) - end + quadrant_obj = unsafe_load(quadrant) + if quadrant_obj.x == 0 && quadrant_obj.y == 0 && quadrant_obj.level < 3 + # return true (refine) + return Cint(1) + else + # return false (don't refine) + return Cint(0) + end end # Refine recursively until each bottom left quadrant of a tree has level 2. # The mesh will be rebalanced before the simulation starts. -refine_fn_c = @cfunction(refine_fn, Cint, (Ptr{Trixi.p4est_t}, Ptr{Trixi.p4est_topidx_t}, Ptr{Trixi.p4est_quadrant_t})) +refine_fn_c = @cfunction(refine_fn, Cint, + (Ptr{Trixi.p4est_t}, Ptr{Trixi.p4est_topidx_t}, + Ptr{Trixi.p4est_quadrant_t})) Trixi.refine_p4est!(mesh.p4est, true, refine_fn_c, C_NULL) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver, - boundary_conditions=Dict( - :all => BoundaryConditionDirichlet(initial_condition) - )) - + boundary_conditions = Dict(:all => BoundaryConditionDirichlet(initial_condition))) ############################################################################### # ODE solvers, callbacks etc. @@ -70,16 +70,16 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=100, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 100, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) -stepsize_callback = StepsizeCallback(cfl=2.0) +stepsize_callback = StepsizeCallback(cfl = 2.0) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, @@ -89,7 +89,7 @@ callbacks = CallbackSet(summary_callback, ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/p4est_2d_dgsem/elixir_euler_sedov.jl b/examples/p4est_2d_dgsem/elixir_euler_sedov.jl index d5d8e0c78bf..539ddb45395 100644 --- a/examples/p4est_2d_dgsem/elixir_euler_sedov.jl +++ b/examples/p4est_2d_dgsem/elixir_euler_sedov.jl @@ -14,25 +14,25 @@ The Sedov blast wave setup based on Flash - https://flash.rochester.edu/site/flashcode/user_support/flash_ug_devel/node187.html#SECTION010114000000000000000 """ function initial_condition_sedov_blast_wave(x, t, equations::CompressibleEulerEquations2D) - # Set up polar coordinates - inicenter = SVector(0.0, 0.0) - x_norm = x[1] - inicenter[1] - y_norm = x[2] - inicenter[2] - r = sqrt(x_norm^2 + y_norm^2) - - # Setup based on https://flash.rochester.edu/site/flashcode/user_support/flash_ug_devel/node187.html#SECTION010114000000000000000 - r0 = 0.21875 # = 3.5 * smallest dx (for domain length=4 and max-ref=6) - E = 1.0 - p0_inner = 3 * (equations.gamma - 1) * E / (3 * pi * r0^2) - p0_outer = 1.0e-5 # = true Sedov setup - - # Calculate primitive variables - rho = 1.0 - v1 = 0.0 - v2 = 0.0 - p = r > r0 ? p0_outer : p0_inner - - return prim2cons(SVector(rho, v1, v2, p), equations) + # Set up polar coordinates + inicenter = SVector(0.0, 0.0) + x_norm = x[1] - inicenter[1] + y_norm = x[2] - inicenter[2] + r = sqrt(x_norm^2 + y_norm^2) + + # Setup based on https://flash.rochester.edu/site/flashcode/user_support/flash_ug_devel/node187.html#SECTION010114000000000000000 + r0 = 0.21875 # = 3.5 * smallest dx (for domain length=4 and max-ref=6) + E = 1.0 + p0_inner = 3 * (equations.gamma - 1) * E / (3 * pi * r0^2) + p0_outer = 1.0e-5 # = true Sedov setup + + # Calculate primitive variables + rho = 1.0 + v1 = 0.0 + v2 = 0.0 + p = r > r0 ? p0_outer : p0_inner + + return prim2cons(SVector(rho, v1, v2, p), equations) end initial_condition = initial_condition_sedov_blast_wave @@ -43,26 +43,27 @@ volume_flux = flux_ranocha polydeg = 4 basis = LobattoLegendreBasis(polydeg) indicator_sc = IndicatorHennemannGassner(equations, basis, - alpha_max=1.0, - alpha_min=0.001, - alpha_smooth=true, - variable=density_pressure) + alpha_max = 1.0, + alpha_min = 0.001, + alpha_smooth = true, + variable = density_pressure) volume_integral = VolumeIntegralShockCapturingHG(indicator_sc; - volume_flux_dg=volume_flux, - volume_flux_fv=surface_flux) + volume_flux_dg = volume_flux, + volume_flux_fv = surface_flux) -solver = DGSEM(polydeg=polydeg, surface_flux=surface_flux, volume_integral=volume_integral) +solver = DGSEM(polydeg = polydeg, surface_flux = surface_flux, + volume_integral = volume_integral) ############################################################################### coordinates_min = (-1.0, -1.0) -coordinates_max = ( 1.0, 1.0) +coordinates_max = (1.0, 1.0) trees_per_dimension = (4, 4) mesh = P4estMesh(trees_per_dimension, - polydeg=4, initial_refinement_level=2, - coordinates_min=coordinates_min, coordinates_max=coordinates_max, - periodicity=true) + polydeg = 4, initial_refinement_level = 2, + coordinates_min = coordinates_min, coordinates_max = coordinates_max, + periodicity = true) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver) @@ -75,15 +76,15 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 300 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=300, - save_initial_solution=true, - save_final_solution=true) +save_solution = SaveSolutionCallback(interval = 300, + save_initial_solution = true, + save_final_solution = true) -stepsize_callback = StepsizeCallback(cfl=0.5) +stepsize_callback = StepsizeCallback(cfl = 0.5) callbacks = CallbackSet(summary_callback, analysis_callback, @@ -94,7 +95,7 @@ callbacks = CallbackSet(summary_callback, ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/p4est_2d_dgsem/elixir_euler_shockcapturing_ec.jl b/examples/p4est_2d_dgsem/elixir_euler_shockcapturing_ec.jl index 6ef551c486f..0cb18526f8d 100644 --- a/examples/p4est_2d_dgsem/elixir_euler_shockcapturing_ec.jl +++ b/examples/p4est_2d_dgsem/elixir_euler_shockcapturing_ec.jl @@ -14,30 +14,30 @@ volume_flux = flux_ranocha polydeg = 4 basis = LobattoLegendreBasis(polydeg) indicator_sc = IndicatorHennemannGassner(equations, basis, - alpha_max=1.0, - alpha_min=0.001, - alpha_smooth=true, - variable=density_pressure) + alpha_max = 1.0, + alpha_min = 0.001, + alpha_smooth = true, + variable = density_pressure) volume_integral = VolumeIntegralShockCapturingHG(indicator_sc; - volume_flux_dg=volume_flux, - volume_flux_fv=surface_flux) + volume_flux_dg = volume_flux, + volume_flux_fv = surface_flux) -solver = DGSEM(polydeg=polydeg, surface_flux=surface_flux, volume_integral=volume_integral) +solver = DGSEM(polydeg = polydeg, surface_flux = surface_flux, + volume_integral = volume_integral) ############################################################################### coordinates_min = (-1.0, -1.0) -coordinates_max = ( 1.0, 1.0) +coordinates_max = (1.0, 1.0) trees_per_dimension = (4, 4) mesh = P4estMesh(trees_per_dimension, - polydeg=4, initial_refinement_level=2, - coordinates_min=coordinates_min, coordinates_max=coordinates_max, - periodicity=true) + polydeg = 4, initial_refinement_level = 2, + coordinates_min = coordinates_min, coordinates_max = coordinates_max, + periodicity = true) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver) - ############################################################################### # ODE solvers, callbacks etc. @@ -47,16 +47,16 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=100, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 100, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) -stepsize_callback = StepsizeCallback(cfl=1.0) +stepsize_callback = StepsizeCallback(cfl = 1.0) callbacks = CallbackSet(summary_callback, analysis_callback, @@ -66,7 +66,7 @@ callbacks = CallbackSet(summary_callback, ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/p4est_2d_dgsem/elixir_euler_source_terms_nonconforming_unstructured_flag.jl b/examples/p4est_2d_dgsem/elixir_euler_source_terms_nonconforming_unstructured_flag.jl index d9a322b065a..09d018309a6 100644 --- a/examples/p4est_2d_dgsem/elixir_euler_source_terms_nonconforming_unstructured_flag.jl +++ b/examples/p4est_2d_dgsem/elixir_euler_source_terms_nonconforming_unstructured_flag.jl @@ -14,18 +14,16 @@ source_terms = source_terms_convergence_test # BCs must be passed as Dict boundary_condition = BoundaryConditionDirichlet(initial_condition) -boundary_conditions = Dict( - :all => boundary_condition -) +boundary_conditions = Dict(:all => boundary_condition) -solver = DGSEM(polydeg=3, surface_flux=flux_lax_friedrichs) +solver = DGSEM(polydeg = 3, surface_flux = flux_lax_friedrichs) # Deformed rectangle that looks like a waving flag, # lower and upper faces are sinus curves, left and right are vertical lines. f1(s) = SVector(-1.0, s - 1.0) -f2(s) = SVector( 1.0, s + 1.0) +f2(s) = SVector(1.0, s + 1.0) f3(s) = SVector(s, -1.0 + sin(0.5 * pi * s)) -f4(s) = SVector(s, 1.0 + sin(0.5 * pi * s)) +f4(s) = SVector(s, 1.0 + sin(0.5 * pi * s)) faces = (f1, f2, f3, f4) Trixi.validate_faces(faces) @@ -34,34 +32,36 @@ mapping_flag = Trixi.transfinite_mapping(faces) # Get the uncurved mesh from a file (downloads the file if not available locally) # Unstructured mesh with 24 cells of the square domain [-1, 1]^n mesh_file = joinpath(@__DIR__, "square_unstructured_2.inp") -isfile(mesh_file) || download("https://gist.githubusercontent.com/efaulhaber/63ff2ea224409e55ee8423b3a33e316a/raw/7db58af7446d1479753ae718930741c47a3b79b7/square_unstructured_2.inp", - mesh_file) +isfile(mesh_file) || + download("https://gist.githubusercontent.com/efaulhaber/63ff2ea224409e55ee8423b3a33e316a/raw/7db58af7446d1479753ae718930741c47a3b79b7/square_unstructured_2.inp", + mesh_file) -mesh = P4estMesh{2}(mesh_file, polydeg=3, - mapping=mapping_flag, - initial_refinement_level=1) +mesh = P4estMesh{2}(mesh_file, polydeg = 3, + mapping = mapping_flag, + initial_refinement_level = 1) # Refine bottom left quadrant of each tree to level 2 function refine_fn(p4est, which_tree, quadrant) - quadrant_obj = unsafe_load(quadrant) - if quadrant_obj.x == 0 && quadrant_obj.y == 0 && quadrant_obj.level < 2 - # return true (refine) - return Cint(1) - else - # return false (don't refine) - return Cint(0) - end + quadrant_obj = unsafe_load(quadrant) + if quadrant_obj.x == 0 && quadrant_obj.y == 0 && quadrant_obj.level < 2 + # return true (refine) + return Cint(1) + else + # return false (don't refine) + return Cint(0) + end end # Refine recursively until each bottom left quadrant of a tree has level 2 # The mesh will be rebalanced before the simulation starts -refine_fn_c = @cfunction(refine_fn, Cint, (Ptr{Trixi.p4est_t}, Ptr{Trixi.p4est_topidx_t}, Ptr{Trixi.p4est_quadrant_t})) +refine_fn_c = @cfunction(refine_fn, Cint, + (Ptr{Trixi.p4est_t}, Ptr{Trixi.p4est_topidx_t}, + Ptr{Trixi.p4est_quadrant_t})) Trixi.refine_p4est!(mesh.p4est, true, refine_fn_c, C_NULL) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver, - source_terms=source_terms, - boundary_conditions=boundary_conditions) - + source_terms = source_terms, + boundary_conditions = boundary_conditions) ############################################################################### # ODE solvers, callbacks etc. @@ -72,19 +72,19 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_restart = SaveRestartCallback(interval=100, - save_final_restart=true) +save_restart = SaveRestartCallback(interval = 100, + save_final_restart = true) -save_solution = SaveSolutionCallback(interval=100, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 100, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) -stepsize_callback = StepsizeCallback(cfl=0.8) +stepsize_callback = StepsizeCallback(cfl = 0.8) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, @@ -93,7 +93,7 @@ callbacks = CallbackSet(summary_callback, ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/p4est_2d_dgsem/elixir_euler_supersonic_cylinder.jl b/examples/p4est_2d_dgsem/elixir_euler_supersonic_cylinder.jl index 366be700f9f..36c5624ba97 100644 --- a/examples/p4est_2d_dgsem/elixir_euler_supersonic_cylinder.jl +++ b/examples/p4est_2d_dgsem/elixir_euler_supersonic_cylinder.jl @@ -23,14 +23,14 @@ using Trixi equations = CompressibleEulerEquations2D(1.4) @inline function initial_condition_mach3_flow(x, t, equations::CompressibleEulerEquations2D) - # set the freestream flow parameters - rho_freestream = 1.4 - v1 = 3.0 - v2 = 0.0 - p_freestream = 1.0 - - prim = SVector(rho_freestream, v1, v2, p_freestream) - return prim2cons(prim, equations) + # set the freestream flow parameters + rho_freestream = 1.4 + v1 = 3.0 + v2 = 0.0 + p_freestream = 1.0 + + prim = SVector(rho_freestream, v1, v2, p_freestream) + return prim2cons(prim, equations) end initial_condition = initial_condition_mach3_flow @@ -38,30 +38,32 @@ initial_condition = initial_condition_mach3_flow # Supersonic inflow boundary condition. # Calculate the boundary flux entirely from the external solution state, i.e., set # external solution state values for everything entering the domain. -@inline function boundary_condition_supersonic_inflow(u_inner, normal_direction::AbstractVector, x, t, - surface_flux_function, equations::CompressibleEulerEquations2D) - u_boundary = initial_condition_mach3_flow(x, t, equations) - flux = Trixi.flux(u_boundary, normal_direction, equations) - - return flux +@inline function boundary_condition_supersonic_inflow(u_inner, + normal_direction::AbstractVector, + x, t, surface_flux_function, + equations::CompressibleEulerEquations2D) + u_boundary = initial_condition_mach3_flow(x, t, equations) + flux = Trixi.flux(u_boundary, normal_direction, equations) + + return flux end - # Supersonic outflow boundary condition. # Calculate the boundary flux entirely from the internal solution state. Analogous to supersonic inflow # except all the solution state values are set from the internal solution as everything leaves the domain @inline function boundary_condition_outflow(u_inner, normal_direction::AbstractVector, x, t, - surface_flux_function, equations::CompressibleEulerEquations2D) - flux = Trixi.flux(u_inner, normal_direction, equations) + surface_flux_function, + equations::CompressibleEulerEquations2D) + flux = Trixi.flux(u_inner, normal_direction, equations) - return flux + return flux end -boundary_conditions = Dict( :Bottom => boundary_condition_slip_wall, - :Circle => boundary_condition_slip_wall, - :Top => boundary_condition_slip_wall, - :Right => boundary_condition_outflow, - :Left => boundary_condition_supersonic_inflow ) +boundary_conditions = Dict(:Bottom => boundary_condition_slip_wall, + :Circle => boundary_condition_slip_wall, + :Top => boundary_condition_slip_wall, + :Right => boundary_condition_outflow, + :Left => boundary_condition_supersonic_inflow) volume_flux = flux_ranocha_turbo surface_flux = flux_lax_friedrichs @@ -69,25 +71,27 @@ surface_flux = flux_lax_friedrichs polydeg = 3 basis = LobattoLegendreBasis(polydeg) shock_indicator = IndicatorHennemannGassner(equations, basis, - alpha_max=0.5, - alpha_min=0.001, - alpha_smooth=true, - variable=density_pressure) + alpha_max = 0.5, + alpha_min = 0.001, + alpha_smooth = true, + variable = density_pressure) volume_integral = VolumeIntegralShockCapturingHG(shock_indicator; - volume_flux_dg=volume_flux, - volume_flux_fv=surface_flux) -solver = DGSEM(polydeg=polydeg, surface_flux=surface_flux, volume_integral=volume_integral) + volume_flux_dg = volume_flux, + volume_flux_fv = surface_flux) +solver = DGSEM(polydeg = polydeg, surface_flux = surface_flux, + volume_integral = volume_integral) # Get the unstructured quad mesh from a file (downloads the file if not available locally) default_mesh_file = joinpath(@__DIR__, "abaqus_cylinder_in_channel.inp") -isfile(default_mesh_file) || download("https://gist.githubusercontent.com/andrewwinters5000/a08f78f6b185b63c3baeff911a63f628/raw/addac716ea0541f588b9d2bd3f92f643eb27b88f/abaqus_cylinder_in_channel.inp", - default_mesh_file) +isfile(default_mesh_file) || + download("https://gist.githubusercontent.com/andrewwinters5000/a08f78f6b185b63c3baeff911a63f628/raw/addac716ea0541f588b9d2bd3f92f643eb27b88f/abaqus_cylinder_in_channel.inp", + default_mesh_file) mesh_file = default_mesh_file mesh = P4estMesh{2}(mesh_file) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver, - boundary_conditions=boundary_conditions) + boundary_conditions = boundary_conditions) ############################################################################### # ODE solvers @@ -100,26 +104,26 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 1000 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=1000, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 1000, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) -amr_indicator = IndicatorLöhner(semi, variable=Trixi.density) +amr_indicator = IndicatorLöhner(semi, variable = Trixi.density) amr_controller = ControllerThreeLevel(semi, amr_indicator, - base_level=0, - med_level=3, med_threshold=0.05, - max_level=5, max_threshold=0.1) + base_level = 0, + med_level = 3, med_threshold = 0.05, + max_level = 5, max_threshold = 0.1) amr_callback = AMRCallback(semi, amr_controller, - interval=1, - adapt_initial_condition=true, - adapt_initial_condition_only_refine=true) + interval = 1, + adapt_initial_condition = true, + adapt_initial_condition_only_refine = true) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, @@ -128,11 +132,11 @@ callbacks = CallbackSet(summary_callback, # positivity limiter necessary for this example with strong shocks. Very sensitive # to the order of the limiter variables, pressure must come first. -stage_limiter! = PositivityPreservingLimiterZhangShu(thresholds=(5.0e-7, 1.0e-6), - variables=(pressure, Trixi.density)) +stage_limiter! = PositivityPreservingLimiterZhangShu(thresholds = (5.0e-7, 1.0e-6), + variables = (pressure, Trixi.density)) ############################################################################### # run the simulation sol = solve(ode, SSPRK43(stage_limiter!); - ode_default_options()..., callback=callbacks); + ode_default_options()..., callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/p4est_2d_dgsem/elixir_euler_wall_bc_amr.jl b/examples/p4est_2d_dgsem/elixir_euler_wall_bc_amr.jl index 7c7896ce372..8b8d05bade8 100644 --- a/examples/p4est_2d_dgsem/elixir_euler_wall_bc_amr.jl +++ b/examples/p4est_2d_dgsem/elixir_euler_wall_bc_amr.jl @@ -9,45 +9,46 @@ using Trixi equations = CompressibleEulerEquations2D(1.4) @inline function uniform_flow_state(x, t, equations::CompressibleEulerEquations2D) - # set the freestream flow parameters - rho_freestream = 1.0 - u_freestream = 0.3 - p_freestream = inv(equations.gamma) - - theta = pi / 90.0 # analogous with a two degree angle of attack - si, co = sincos(theta) - v1 = u_freestream * co - v2 = u_freestream * si - - prim = SVector(rho_freestream, v1, v2, p_freestream) - return prim2cons(prim, equations) + # set the freestream flow parameters + rho_freestream = 1.0 + u_freestream = 0.3 + p_freestream = inv(equations.gamma) + + theta = pi / 90.0 # analogous with a two degree angle of attack + si, co = sincos(theta) + v1 = u_freestream * co + v2 = u_freestream * si + + prim = SVector(rho_freestream, v1, v2, p_freestream) + return prim2cons(prim, equations) end initial_condition = uniform_flow_state boundary_condition_uniform_flow = BoundaryConditionDirichlet(uniform_flow_state) -boundary_conditions = Dict( :Body => boundary_condition_uniform_flow, - :Button1 => boundary_condition_slip_wall, - :Button2 => boundary_condition_slip_wall, - :Eye1 => boundary_condition_slip_wall, - :Eye2 => boundary_condition_slip_wall, - :Smile => boundary_condition_slip_wall, - :Bowtie => boundary_condition_slip_wall ) +boundary_conditions = Dict(:Body => boundary_condition_uniform_flow, + :Button1 => boundary_condition_slip_wall, + :Button2 => boundary_condition_slip_wall, + :Eye1 => boundary_condition_slip_wall, + :Eye2 => boundary_condition_slip_wall, + :Smile => boundary_condition_slip_wall, + :Bowtie => boundary_condition_slip_wall) volume_flux = flux_ranocha -solver = DGSEM(polydeg=5, surface_flux=flux_lax_friedrichs, - volume_integral=VolumeIntegralFluxDifferencing(volume_flux)) +solver = DGSEM(polydeg = 5, surface_flux = flux_lax_friedrichs, + volume_integral = VolumeIntegralFluxDifferencing(volume_flux)) # Get the unstructured quad mesh from a file (downloads the file if not available locally) default_mesh_file = joinpath(@__DIR__, "abaqus_gingerbread_man.inp") -isfile(default_mesh_file) || download("https://gist.githubusercontent.com/andrewwinters5000/0e9e990a04b5105d1d2e3096a6e41272/raw/0d924b1d7e7d3cc1070a6cc22fe1d501687aa6dd/abaqus_gingerbread_man.inp", - default_mesh_file) +isfile(default_mesh_file) || + download("https://gist.githubusercontent.com/andrewwinters5000/0e9e990a04b5105d1d2e3096a6e41272/raw/0d924b1d7e7d3cc1070a6cc22fe1d501687aa6dd/abaqus_gingerbread_man.inp", + default_mesh_file) mesh_file = default_mesh_file mesh = P4estMesh{2}(mesh_file) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver, - boundary_conditions=boundary_conditions) + boundary_conditions = boundary_conditions) ############################################################################### # ODE solvers, callbacks etc. @@ -58,36 +59,35 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval, - extra_analysis_integrals=(entropy,)) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval, + extra_analysis_integrals = (entropy,)) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=100, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 100, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) -amr_indicator = IndicatorLöhner(semi, variable=density) +amr_indicator = IndicatorLöhner(semi, variable = density) amr_controller = ControllerThreeLevel(semi, amr_indicator, - base_level=0, - med_level=1, med_threshold=0.05, - max_level=3, max_threshold=0.1) + base_level = 0, + med_level = 1, med_threshold = 0.05, + max_level = 3, max_threshold = 0.1) amr_callback = AMRCallback(semi, amr_controller, - interval=5, - adapt_initial_condition=true, - adapt_initial_condition_only_refine=true) + interval = 5, + adapt_initial_condition = true, + adapt_initial_condition_only_refine = true) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, save_solution, amr_callback) - ############################################################################### # run the simulation -sol = solve(ode, RDPK3SpFSAL49(); abstol=1.0e-7, reltol=1.0e-7, - ode_default_options()..., callback=callbacks); +sol = solve(ode, RDPK3SpFSAL49(); abstol = 1.0e-7, reltol = 1.0e-7, + ode_default_options()..., callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/p4est_2d_dgsem/elixir_eulergravity_convergence.jl b/examples/p4est_2d_dgsem/elixir_eulergravity_convergence.jl index b34c73d2a4e..d55a59ca5ce 100644 --- a/examples/p4est_2d_dgsem/elixir_eulergravity_convergence.jl +++ b/examples/p4est_2d_dgsem/elixir_eulergravity_convergence.jl @@ -2,10 +2,8 @@ using OrdinaryDiffEq using Trixi - initial_condition = initial_condition_eoc_test_coupled_euler_gravity - ############################################################################### # semidiscretization of the compressible Euler equations gamma = 2.0 @@ -18,13 +16,13 @@ coordinates_min = (0.0, 0.0) coordinates_max = (2.0, 2.0) trees_per_dimension = (1, 1) -mesh = P4estMesh(trees_per_dimension, polydeg=1, - coordinates_min=coordinates_min, coordinates_max=coordinates_max, - initial_refinement_level=2) - -semi_euler = SemidiscretizationHyperbolic(mesh, equations_euler, initial_condition, solver_euler, - source_terms=source_terms_eoc_test_coupled_euler_gravity) +mesh = P4estMesh(trees_per_dimension, polydeg = 1, + coordinates_min = coordinates_min, coordinates_max = coordinates_max, + initial_refinement_level = 2) +semi_euler = SemidiscretizationHyperbolic(mesh, equations_euler, initial_condition, + solver_euler, + source_terms = source_terms_eoc_test_coupled_euler_gravity) ############################################################################### # semidiscretization of the hyperbolic diffusion equations @@ -32,24 +30,23 @@ equations_gravity = HyperbolicDiffusionEquations2D() solver_gravity = DGSEM(polydeg, flux_lax_friedrichs) -semi_gravity = SemidiscretizationHyperbolic(mesh, equations_gravity, initial_condition, solver_gravity, - source_terms=source_terms_harmonic) - +semi_gravity = SemidiscretizationHyperbolic(mesh, equations_gravity, initial_condition, + solver_gravity, + source_terms = source_terms_harmonic) ############################################################################### # combining both semidiscretizations for Euler + self-gravity -parameters = ParametersEulerGravity(background_density=2.0, # aka rho0 +parameters = ParametersEulerGravity(background_density = 2.0, # aka rho0 # rho0 is (ab)used to add a "+8π" term to the source terms # for the manufactured solution - gravitational_constant=1.0, # aka G - cfl=1.1, - resid_tol=1.0e-10, - n_iterations_max=1000, - timestep_gravity=timestep_gravity_erk52_3Sstar!) + gravitational_constant = 1.0, # aka G + cfl = 1.1, + resid_tol = 1.0e-10, + n_iterations_max = 1000, + timestep_gravity = timestep_gravity_erk52_3Sstar!) semi = SemidiscretizationEulerGravity(semi_euler, semi_gravity, parameters) - ############################################################################### # ODE solvers, callbacks etc. tspan = (0.0, 0.5) @@ -57,31 +54,30 @@ ode = semidiscretize(semi, tspan); summary_callback = SummaryCallback() -stepsize_callback = StepsizeCallback(cfl=0.8) +stepsize_callback = StepsizeCallback(cfl = 0.8) -save_solution = SaveSolutionCallback(interval=10, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 10, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) -save_restart = SaveRestartCallback(interval=100, - save_final_restart=true) +save_restart = SaveRestartCallback(interval = 100, + save_final_restart = true) analysis_interval = 100 -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -analysis_callback = AnalysisCallback(semi_euler, interval=analysis_interval, - save_analysis=true) +analysis_callback = AnalysisCallback(semi_euler, interval = analysis_interval, + save_analysis = true) callbacks = CallbackSet(summary_callback, stepsize_callback, save_restart, save_solution, analysis_callback, alive_callback) - ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary println("Number of gravity subcycles: ", semi.gravity_counter.ncalls_since_readout) diff --git a/examples/p4est_2d_dgsem/elixir_linearizedeuler_gaussian_source.jl b/examples/p4est_2d_dgsem/elixir_linearizedeuler_gaussian_source.jl index ba2ec827778..364e0296449 100644 --- a/examples/p4est_2d_dgsem/elixir_linearizedeuler_gaussian_source.jl +++ b/examples/p4est_2d_dgsem/elixir_linearizedeuler_gaussian_source.jl @@ -8,20 +8,22 @@ using Trixi # Oscillating Gaussian-shaped source terms function source_terms_gauss(u, x, t, equations::LinearizedEulerEquations2D) - r = 0.1 - A = 1.0 - f = 2.0 + r = 0.1 + A = 1.0 + f = 2.0 - # Velocity sources - s2 = 0.0 - s3 = 0.0 - # Density and pressure source - s1 = s4 = exp(-(x[1]^2 + x[2]^2) / (2 * r^2)) * A * sin(2 * pi * f * t) + # Velocity sources + s2 = 0.0 + s3 = 0.0 + # Density and pressure source + s1 = s4 = exp(-(x[1]^2 + x[2]^2) / (2 * r^2)) * A * sin(2 * pi * f * t) - return SVector(s1, s2, s3, s4) + return SVector(s1, s2, s3, s4) end -initial_condition_zero(x, t, equations::LinearizedEulerEquations2D) = SVector(0.0, 0.0, 0.0, 0.0) +function initial_condition_zero(x, t, equations::LinearizedEulerEquations2D) + SVector(0.0, 0.0, 0.0, 0.0) +end ############################################################################### # semidiscretization of the linearized Euler equations @@ -30,28 +32,27 @@ initial_condition_zero(x, t, equations::LinearizedEulerEquations2D) = SVector(0. c = cospi(2 * 30.0 / 360.0) s = sinpi(2 * 30.0 / 360.0) rot_mat = Trixi.SMatrix{2, 2}([c -s; s c]) -mapping(xi, eta) = rot_mat * SVector(3.0*xi, 3.0*eta) +mapping(xi, eta) = rot_mat * SVector(3.0 * xi, 3.0 * eta) # Mean density and speed of sound are slightly off from 1.0 to allow proper verification of # curved LEE implementation using this elixir (some things in the LEE cancel if both are 1.0) -equations = LinearizedEulerEquations2D(v_mean_global=Tuple(rot_mat * SVector(-0.5, 0.25)), - c_mean_global=1.02, rho_mean_global=1.01) +equations = LinearizedEulerEquations2D(v_mean_global = Tuple(rot_mat * SVector(-0.5, 0.25)), + c_mean_global = 1.02, rho_mean_global = 1.01) initial_condition = initial_condition_zero # Create DG solver with polynomial degree = 3 and upwind flux as surface flux -solver = DGSEM(polydeg=3, surface_flux=flux_godunov) +solver = DGSEM(polydeg = 3, surface_flux = flux_godunov) # Create a uniformly refined mesh with periodic boundaries trees_per_dimension = (4, 4) -mesh = P4estMesh(trees_per_dimension, polydeg=1, - mapping=mapping, - periodicity=true, initial_refinement_level=2) +mesh = P4estMesh(trees_per_dimension, polydeg = 1, + mapping = mapping, + periodicity = true, initial_refinement_level = 2) # A semidiscretization collects data structures and functions for the spatial discretization semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver, - source_terms=source_terms_gauss) - + source_terms = source_terms_gauss) ############################################################################### # ODE solvers, callbacks etc. @@ -65,25 +66,25 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() # The AnalysisCallback allows to analyse the solution in regular intervals and prints the results -analysis_callback = AnalysisCallback(semi, interval=100) +analysis_callback = AnalysisCallback(semi, interval = 100) # The SaveSolutionCallback allows to save the solution to a file in regular intervals -save_solution = SaveSolutionCallback(interval=100) +save_solution = SaveSolutionCallback(interval = 100) # The StepsizeCallback handles the re-calculation of the maximum Δt after each time step -stepsize_callback = StepsizeCallback(cfl=0.5) +stepsize_callback = StepsizeCallback(cfl = 0.5) # Create a CallbackSet to collect all callbacks such that they can be passed to the ODE solver -callbacks = CallbackSet(summary_callback, analysis_callback, save_solution, stepsize_callback) - +callbacks = CallbackSet(summary_callback, analysis_callback, save_solution, + stepsize_callback) ############################################################################### # run the simulation # OrdinaryDiffEq's `solve` method evolves the solution in time and executes the passed callbacks -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); # Print the timer summary summary_callback() diff --git a/examples/p4est_2d_dgsem/elixir_mhd_alfven_wave.jl b/examples/p4est_2d_dgsem/elixir_mhd_alfven_wave.jl index 66bce781f60..93db7bfdbaf 100644 --- a/examples/p4est_2d_dgsem/elixir_mhd_alfven_wave.jl +++ b/examples/p4est_2d_dgsem/elixir_mhd_alfven_wave.jl @@ -2,28 +2,27 @@ using OrdinaryDiffEq using Trixi - ############################################################################### # semidiscretization of the compressible ideal GLM-MHD equations -gamma = 5/3 +gamma = 5 / 3 equations = IdealGlmMhdEquations2D(gamma) initial_condition = initial_condition_convergence_test # Get the DG approximation space volume_flux = (flux_central, flux_nonconservative_powell) -solver = DGSEM(polydeg=4, surface_flux=(flux_hll, flux_nonconservative_powell), - volume_integral=VolumeIntegralFluxDifferencing(volume_flux)) +solver = DGSEM(polydeg = 4, surface_flux = (flux_hll, flux_nonconservative_powell), + volume_integral = VolumeIntegralFluxDifferencing(volume_flux)) -coordinates_min = (0.0 , 0.0 ) +coordinates_min = (0.0, 0.0) coordinates_max = (sqrt(2.0), sqrt(2.0)) trees_per_dimension = (8, 8) mesh = P4estMesh(trees_per_dimension, - polydeg=3, initial_refinement_level=0, - coordinates_min=coordinates_min, coordinates_max=coordinates_max, - periodicity=true) + polydeg = 3, initial_refinement_level = 0, + coordinates_min = coordinates_min, coordinates_max = coordinates_max, + periodicity = true) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver) @@ -36,14 +35,14 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) cfl = 0.9 -stepsize_callback = StepsizeCallback(cfl=cfl) +stepsize_callback = StepsizeCallback(cfl = cfl) -glm_speed_callback = GlmSpeedCallback(glm_scale=0.5, cfl=cfl) +glm_speed_callback = GlmSpeedCallback(glm_scale = 0.5, cfl = cfl) callbacks = CallbackSet(summary_callback, analysis_callback, @@ -54,7 +53,7 @@ callbacks = CallbackSet(summary_callback, ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/p4est_2d_dgsem/elixir_mhd_rotor.jl b/examples/p4est_2d_dgsem/elixir_mhd_rotor.jl index 58915a8f6a7..380db487356 100644 --- a/examples/p4est_2d_dgsem/elixir_mhd_rotor.jl +++ b/examples/p4est_2d_dgsem/elixir_mhd_rotor.jl @@ -16,74 +16,74 @@ The classical MHD rotor test case. Here, the setup is taken from [doi: 10.1365/s13291-018-0178-9](https://doi.org/10.1365/s13291-018-0178-9) """ function initial_condition_rotor(x, t, equations::IdealGlmMhdEquations2D) - # setup taken from Derigs et al. DMV article (2018) - # domain must be [0, 1] x [0, 1], γ = 1.4 - dx = x[1] - 0.5 - dy = x[2] - 0.5 - r = sqrt(dx^2 + dy^2) - f = (0.115 - r)/0.015 - if r <= 0.1 - rho = 10.0 - v1 = -20.0*dy - v2 = 20.0*dx - elseif r >= 0.115 - rho = 1.0 - v1 = 0.0 - v2 = 0.0 - else - rho = 1.0 + 9.0*f - v1 = -20.0*f*dy - v2 = 20.0*f*dx - end - v3 = 0.0 - p = 1.0 - B1 = 5.0/sqrt(4.0*pi) - B2 = 0.0 - B3 = 0.0 - psi = 0.0 - return prim2cons(SVector(rho, v1, v2, v3, p, B1, B2, B3, psi), equations) + # setup taken from Derigs et al. DMV article (2018) + # domain must be [0, 1] x [0, 1], γ = 1.4 + dx = x[1] - 0.5 + dy = x[2] - 0.5 + r = sqrt(dx^2 + dy^2) + f = (0.115 - r) / 0.015 + if r <= 0.1 + rho = 10.0 + v1 = -20.0 * dy + v2 = 20.0 * dx + elseif r >= 0.115 + rho = 1.0 + v1 = 0.0 + v2 = 0.0 + else + rho = 1.0 + 9.0 * f + v1 = -20.0 * f * dy + v2 = 20.0 * f * dx + end + v3 = 0.0 + p = 1.0 + B1 = 5.0 / sqrt(4.0 * pi) + B2 = 0.0 + B3 = 0.0 + psi = 0.0 + return prim2cons(SVector(rho, v1, v2, v3, p, B1, B2, B3, psi), equations) end initial_condition = initial_condition_rotor surface_flux = (flux_lax_friedrichs, flux_nonconservative_powell) -volume_flux = (flux_hindenlang_gassner, flux_nonconservative_powell) +volume_flux = (flux_hindenlang_gassner, flux_nonconservative_powell) polydeg = 4 basis = LobattoLegendreBasis(polydeg) indicator_sc = IndicatorHennemannGassner(equations, basis, - alpha_max=0.5, - alpha_min=0.001, - alpha_smooth=true, - variable=density_pressure) + alpha_max = 0.5, + alpha_min = 0.001, + alpha_smooth = true, + variable = density_pressure) volume_integral = VolumeIntegralShockCapturingHG(indicator_sc; - volume_flux_dg=volume_flux, - volume_flux_fv=surface_flux) + volume_flux_dg = volume_flux, + volume_flux_fv = surface_flux) solver = DGSEM(basis, surface_flux, volume_integral) # Affine type mapping to take the [-1,1]^2 domain from the mesh file # and put it onto the rotor domain [0,1]^2 and then warp it with a mapping # as described in https://arxiv.org/abs/2012.12040 function mapping_twist(xi, eta) - y = 0.5 * (eta + 1.0) + 0.05 * cos(1.5 * pi * (2.0 * xi - 1.0)) * cos(0.5 * pi * (2.0 * eta - 1.0)) - x = 0.5 * (xi + 1.0) + 0.05 * cos(0.5 * pi * (2.0 * xi - 1.0)) * cos(2.0 * pi * y) - return SVector(x, y) + y = 0.5 * (eta + 1.0) + + 0.05 * cos(1.5 * pi * (2.0 * xi - 1.0)) * cos(0.5 * pi * (2.0 * eta - 1.0)) + x = 0.5 * (xi + 1.0) + 0.05 * cos(0.5 * pi * (2.0 * xi - 1.0)) * cos(2.0 * pi * y) + return SVector(x, y) end - mesh_file = joinpath(@__DIR__, "square_unstructured_2.inp") -isfile(mesh_file) || download("https://gist.githubusercontent.com/efaulhaber/63ff2ea224409e55ee8423b3a33e316a/raw/7db58af7446d1479753ae718930741c47a3b79b7/square_unstructured_2.inp", - mesh_file) +isfile(mesh_file) || + download("https://gist.githubusercontent.com/efaulhaber/63ff2ea224409e55ee8423b3a33e316a/raw/7db58af7446d1479753ae718930741c47a3b79b7/square_unstructured_2.inp", + mesh_file) mesh = P4estMesh{2}(mesh_file, - polydeg=4, - mapping=mapping_twist, - initial_refinement_level=1) + polydeg = 4, + mapping = mapping_twist, + initial_refinement_level = 1) boundary_condition = BoundaryConditionDirichlet(initial_condition) -boundary_conditions = Dict( :all => boundary_condition ) +boundary_conditions = Dict(:all => boundary_condition) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver, - boundary_conditions=boundary_conditions) - + boundary_conditions = boundary_conditions) ############################################################################### # ODE solvers, callbacks etc. @@ -94,31 +94,31 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=100, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 100, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) amr_indicator = IndicatorLöhner(semi, - variable=density_pressure) + variable = density_pressure) amr_controller = ControllerThreeLevel(semi, amr_indicator, - base_level=1, - med_level =3, med_threshold=0.05, - max_level =5, max_threshold=0.1) + base_level = 1, + med_level = 3, med_threshold = 0.05, + max_level = 5, max_threshold = 0.1) amr_callback = AMRCallback(semi, amr_controller, - interval=5, - adapt_initial_condition=true, - adapt_initial_condition_only_refine=true) + interval = 5, + adapt_initial_condition = true, + adapt_initial_condition_only_refine = true) cfl = 0.5 -stepsize_callback = StepsizeCallback(cfl=cfl) +stepsize_callback = StepsizeCallback(cfl = cfl) -glm_speed_callback = GlmSpeedCallback(glm_scale=0.5, cfl=cfl) +glm_speed_callback = GlmSpeedCallback(glm_scale = 0.5, cfl = cfl) callbacks = CallbackSet(summary_callback, analysis_callback, @@ -131,7 +131,7 @@ callbacks = CallbackSet(summary_callback, ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/p4est_2d_dgsem/elixir_navierstokes_convergence.jl b/examples/p4est_2d_dgsem/elixir_navierstokes_convergence.jl index b0c6086ad63..7aa14e25750 100644 --- a/examples/p4est_2d_dgsem/elixir_navierstokes_convergence.jl +++ b/examples/p4est_2d_dgsem/elixir_navierstokes_convergence.jl @@ -8,174 +8,182 @@ prandtl_number() = 0.72 mu() = 0.01 equations = CompressibleEulerEquations2D(1.4) -equations_parabolic = CompressibleNavierStokesDiffusion2D(equations, mu=mu(), Prandtl=prandtl_number(), - gradient_variables=GradientVariablesPrimitive()) +equations_parabolic = CompressibleNavierStokesDiffusion2D(equations, mu = mu(), + Prandtl = prandtl_number(), + gradient_variables = GradientVariablesPrimitive()) # Create DG solver with polynomial degree = 3 and (local) Lax-Friedrichs/Rusanov flux as surface flux -solver = DGSEM(polydeg=3, surface_flux=flux_lax_friedrichs, - volume_integral=VolumeIntegralWeakForm()) +solver = DGSEM(polydeg = 3, surface_flux = flux_lax_friedrichs, + volume_integral = VolumeIntegralWeakForm()) coordinates_min = (-1.0, -1.0) # minimum coordinates (min(x), min(y)) -coordinates_max = ( 1.0, 1.0) # maximum coordinates (max(x), max(y)) +coordinates_max = (1.0, 1.0) # maximum coordinates (max(x), max(y)) trees_per_dimension = (4, 4) mesh = P4estMesh(trees_per_dimension, - polydeg=3, initial_refinement_level=2, - coordinates_min=coordinates_min, coordinates_max=coordinates_max, - periodicity=(true, false)) + polydeg = 3, initial_refinement_level = 2, + coordinates_min = coordinates_min, coordinates_max = coordinates_max, + periodicity = (true, false)) # Note: the initial condition cannot be specialized to `CompressibleNavierStokesDiffusion2D` # since it is called by both the parabolic solver (which passes in `CompressibleNavierStokesDiffusion2D`) # and by the initial condition (which passes in `CompressibleEulerEquations2D`). # This convergence test setup was originally derived by Andrew Winters (@andrewwinters5000) function initial_condition_navier_stokes_convergence_test(x, t, equations) - # Amplitude and shift - A = 0.5 - c = 2.0 + # Amplitude and shift + A = 0.5 + c = 2.0 - # convenience values for trig. functions - pi_x = pi * x[1] - pi_y = pi * x[2] - pi_t = pi * t + # convenience values for trig. functions + pi_x = pi * x[1] + pi_y = pi * x[2] + pi_t = pi * t - rho = c + A * sin(pi_x) * cos(pi_y) * cos(pi_t) - v1 = sin(pi_x) * log(x[2] + 2.0) * (1.0 - exp(-A * (x[2] - 1.0)) ) * cos(pi_t) - v2 = v1 - p = rho^2 + rho = c + A * sin(pi_x) * cos(pi_y) * cos(pi_t) + v1 = sin(pi_x) * log(x[2] + 2.0) * (1.0 - exp(-A * (x[2] - 1.0))) * cos(pi_t) + v2 = v1 + p = rho^2 - return prim2cons(SVector(rho, v1, v2, p), equations) + return prim2cons(SVector(rho, v1, v2, p), equations) end @inline function source_terms_navier_stokes_convergence_test(u, x, t, equations) - y = x[2] - - # TODO: parabolic - # we currently need to hardcode these parameters until we fix the "combined equation" issue - # see also https://github.com/trixi-framework/Trixi.jl/pull/1160 - inv_gamma_minus_one = inv(equations.gamma - 1) - Pr = prandtl_number() - mu_ = mu() - - # Same settings as in `initial_condition` - # Amplitude and shift - A = 0.5 - c = 2.0 - - # convenience values for trig. functions - pi_x = pi * x[1] - pi_y = pi * x[2] - pi_t = pi * t - - # compute the manufactured solution and all necessary derivatives - rho = c + A * sin(pi_x) * cos(pi_y) * cos(pi_t) - rho_t = -pi * A * sin(pi_x) * cos(pi_y) * sin(pi_t) - rho_x = pi * A * cos(pi_x) * cos(pi_y) * cos(pi_t) - rho_y = -pi * A * sin(pi_x) * sin(pi_y) * cos(pi_t) - rho_xx = -pi * pi * A * sin(pi_x) * cos(pi_y) * cos(pi_t) - rho_yy = -pi * pi * A * sin(pi_x) * cos(pi_y) * cos(pi_t) - - v1 = sin(pi_x) * log(y + 2.0) * (1.0 - exp(-A * (y - 1.0))) * cos(pi_t) - v1_t = -pi * sin(pi_x) * log(y + 2.0) * (1.0 - exp(-A * (y - 1.0))) * sin(pi_t) - v1_x = pi * cos(pi_x) * log(y + 2.0) * (1.0 - exp(-A * (y - 1.0))) * cos(pi_t) - v1_y = sin(pi_x) * (A * log(y + 2.0) * exp(-A * (y - 1.0)) + (1.0 - exp(-A * (y - 1.0))) / (y + 2.0)) * cos(pi_t) - v1_xx = -pi * pi * sin(pi_x) * log(y + 2.0) * (1.0 - exp(-A * (y - 1.0))) * cos(pi_t) - v1_xy = pi * cos(pi_x) * (A * log(y + 2.0) * exp(-A * (y - 1.0)) + (1.0 - exp(-A * (y - 1.0))) / (y + 2.0)) * cos(pi_t) - v1_yy = (sin(pi_x) * ( 2.0 * A * exp(-A * (y - 1.0)) / (y + 2.0) - - A * A * log(y + 2.0) * exp(-A * (y - 1.0)) - - (1.0 - exp(-A * (y - 1.0))) / ((y + 2.0) * (y + 2.0))) * cos(pi_t)) - v2 = v1 - v2_t = v1_t - v2_x = v1_x - v2_y = v1_y - v2_xx = v1_xx - v2_xy = v1_xy - v2_yy = v1_yy - - p = rho * rho - p_t = 2.0 * rho * rho_t - p_x = 2.0 * rho * rho_x - p_y = 2.0 * rho * rho_y - p_xx = 2.0 * rho * rho_xx + 2.0 * rho_x * rho_x - p_yy = 2.0 * rho * rho_yy + 2.0 * rho_y * rho_y - - # Note this simplifies slightly because the ansatz assumes that v1 = v2 - E = p * inv_gamma_minus_one + 0.5 * rho * (v1^2 + v2^2) - E_t = p_t * inv_gamma_minus_one + rho_t * v1^2 + 2.0 * rho * v1 * v1_t - E_x = p_x * inv_gamma_minus_one + rho_x * v1^2 + 2.0 * rho * v1 * v1_x - E_y = p_y * inv_gamma_minus_one + rho_y * v1^2 + 2.0 * rho * v1 * v1_y - - # Some convenience constants - T_const = equations.gamma * inv_gamma_minus_one / Pr - inv_rho_cubed = 1.0 / (rho^3) - - # compute the source terms - # density equation - du1 = rho_t + rho_x * v1 + rho * v1_x + rho_y * v2 + rho * v2_y - - # x-momentum equation - du2 = ( rho_t * v1 + rho * v1_t + p_x + rho_x * v1^2 - + 2.0 * rho * v1 * v1_x - + rho_y * v1 * v2 - + rho * v1_y * v2 - + rho * v1 * v2_y - # stress tensor from x-direction - - 4.0 / 3.0 * v1_xx * mu_ - + 2.0 / 3.0 * v2_xy * mu_ - - v1_yy * mu_ - - v2_xy * mu_ ) - # y-momentum equation - du3 = ( rho_t * v2 + rho * v2_t + p_y + rho_x * v1 * v2 - + rho * v1_x * v2 - + rho * v1 * v2_x - + rho_y * v2^2 - + 2.0 * rho * v2 * v2_y - # stress tensor from y-direction - - v1_xy * mu_ - - v2_xx * mu_ - - 4.0 / 3.0 * v2_yy * mu_ - + 2.0 / 3.0 * v1_xy * mu_ ) - # total energy equation - du4 = ( E_t + v1_x * (E + p) + v1 * (E_x + p_x) - + v2_y * (E + p) + v2 * (E_y + p_y) - # stress tensor and temperature gradient terms from x-direction - - 4.0 / 3.0 * v1_xx * v1 * mu_ - + 2.0 / 3.0 * v2_xy * v1 * mu_ - - 4.0 / 3.0 * v1_x * v1_x * mu_ - + 2.0 / 3.0 * v2_y * v1_x * mu_ - - v1_xy * v2 * mu_ - - v2_xx * v2 * mu_ - - v1_y * v2_x * mu_ - - v2_x * v2_x * mu_ - - T_const * inv_rho_cubed * ( p_xx * rho * rho - - 2.0 * p_x * rho * rho_x - + 2.0 * p * rho_x * rho_x - - p * rho * rho_xx ) * mu_ - # stress tensor and temperature gradient terms from y-direction - - v1_yy * v1 * mu_ - - v2_xy * v1 * mu_ - - v1_y * v1_y * mu_ - - v2_x * v1_y * mu_ - - 4.0 / 3.0 * v2_yy * v2 * mu_ - + 2.0 / 3.0 * v1_xy * v2 * mu_ - - 4.0 / 3.0 * v2_y * v2_y * mu_ - + 2.0 / 3.0 * v1_x * v2_y * mu_ - - T_const * inv_rho_cubed * ( p_yy * rho * rho - - 2.0 * p_y * rho * rho_y - + 2.0 * p * rho_y * rho_y - - p * rho * rho_yy ) * mu_ ) - - return SVector(du1, du2, du3, du4) + y = x[2] + + # TODO: parabolic + # we currently need to hardcode these parameters until we fix the "combined equation" issue + # see also https://github.com/trixi-framework/Trixi.jl/pull/1160 + inv_gamma_minus_one = inv(equations.gamma - 1) + Pr = prandtl_number() + mu_ = mu() + + # Same settings as in `initial_condition` + # Amplitude and shift + A = 0.5 + c = 2.0 + + # convenience values for trig. functions + pi_x = pi * x[1] + pi_y = pi * x[2] + pi_t = pi * t + + # compute the manufactured solution and all necessary derivatives + rho = c + A * sin(pi_x) * cos(pi_y) * cos(pi_t) + rho_t = -pi * A * sin(pi_x) * cos(pi_y) * sin(pi_t) + rho_x = pi * A * cos(pi_x) * cos(pi_y) * cos(pi_t) + rho_y = -pi * A * sin(pi_x) * sin(pi_y) * cos(pi_t) + rho_xx = -pi * pi * A * sin(pi_x) * cos(pi_y) * cos(pi_t) + rho_yy = -pi * pi * A * sin(pi_x) * cos(pi_y) * cos(pi_t) + + v1 = sin(pi_x) * log(y + 2.0) * (1.0 - exp(-A * (y - 1.0))) * cos(pi_t) + v1_t = -pi * sin(pi_x) * log(y + 2.0) * (1.0 - exp(-A * (y - 1.0))) * sin(pi_t) + v1_x = pi * cos(pi_x) * log(y + 2.0) * (1.0 - exp(-A * (y - 1.0))) * cos(pi_t) + v1_y = sin(pi_x) * + (A * log(y + 2.0) * exp(-A * (y - 1.0)) + + (1.0 - exp(-A * (y - 1.0))) / (y + 2.0)) * cos(pi_t) + v1_xx = -pi * pi * sin(pi_x) * log(y + 2.0) * (1.0 - exp(-A * (y - 1.0))) * cos(pi_t) + v1_xy = pi * cos(pi_x) * + (A * log(y + 2.0) * exp(-A * (y - 1.0)) + + (1.0 - exp(-A * (y - 1.0))) / (y + 2.0)) * cos(pi_t) + v1_yy = (sin(pi_x) * + (2.0 * A * exp(-A * (y - 1.0)) / (y + 2.0) - + A * A * log(y + 2.0) * exp(-A * (y - 1.0)) - + (1.0 - exp(-A * (y - 1.0))) / ((y + 2.0) * (y + 2.0))) * cos(pi_t)) + v2 = v1 + v2_t = v1_t + v2_x = v1_x + v2_y = v1_y + v2_xx = v1_xx + v2_xy = v1_xy + v2_yy = v1_yy + + p = rho * rho + p_t = 2.0 * rho * rho_t + p_x = 2.0 * rho * rho_x + p_y = 2.0 * rho * rho_y + p_xx = 2.0 * rho * rho_xx + 2.0 * rho_x * rho_x + p_yy = 2.0 * rho * rho_yy + 2.0 * rho_y * rho_y + + # Note this simplifies slightly because the ansatz assumes that v1 = v2 + E = p * inv_gamma_minus_one + 0.5 * rho * (v1^2 + v2^2) + E_t = p_t * inv_gamma_minus_one + rho_t * v1^2 + 2.0 * rho * v1 * v1_t + E_x = p_x * inv_gamma_minus_one + rho_x * v1^2 + 2.0 * rho * v1 * v1_x + E_y = p_y * inv_gamma_minus_one + rho_y * v1^2 + 2.0 * rho * v1 * v1_y + + # Some convenience constants + T_const = equations.gamma * inv_gamma_minus_one / Pr + inv_rho_cubed = 1.0 / (rho^3) + + # compute the source terms + # density equation + du1 = rho_t + rho_x * v1 + rho * v1_x + rho_y * v2 + rho * v2_y + + # x-momentum equation + du2 = (rho_t * v1 + rho * v1_t + p_x + rho_x * v1^2 + + 2.0 * rho * v1 * v1_x + + rho_y * v1 * v2 + + rho * v1_y * v2 + + rho * v1 * v2_y - + # stress tensor from x-direction + 4.0 / 3.0 * v1_xx * mu_ + + 2.0 / 3.0 * v2_xy * mu_ - + v1_yy * mu_ - + v2_xy * mu_) + # y-momentum equation + du3 = (rho_t * v2 + rho * v2_t + p_y + rho_x * v1 * v2 + + rho * v1_x * v2 + + rho * v1 * v2_x + + rho_y * v2^2 + + 2.0 * rho * v2 * v2_y - + # stress tensor from y-direction + v1_xy * mu_ - + v2_xx * mu_ - + 4.0 / 3.0 * v2_yy * mu_ + + 2.0 / 3.0 * v1_xy * mu_) + # total energy equation + du4 = (E_t + v1_x * (E + p) + v1 * (E_x + p_x) + + v2_y * (E + p) + v2 * (E_y + p_y) - + # stress tensor and temperature gradient terms from x-direction + 4.0 / 3.0 * v1_xx * v1 * mu_ + + 2.0 / 3.0 * v2_xy * v1 * mu_ - + 4.0 / 3.0 * v1_x * v1_x * mu_ + + 2.0 / 3.0 * v2_y * v1_x * mu_ - + v1_xy * v2 * mu_ - + v2_xx * v2 * mu_ - + v1_y * v2_x * mu_ - + v2_x * v2_x * mu_ - + T_const * inv_rho_cubed * + (p_xx * rho * rho - + 2.0 * p_x * rho * rho_x + + 2.0 * p * rho_x * rho_x - + p * rho * rho_xx) * mu_ - + # stress tensor and temperature gradient terms from y-direction + v1_yy * v1 * mu_ - + v2_xy * v1 * mu_ - + v1_y * v1_y * mu_ - + 4.0 / 3.0 * v2_yy * v2 * mu_ + + 2.0 / 3.0 * v1_xy * v2 * mu_ - + 4.0 / 3.0 * v2_y * v2_y * mu_ + + 2.0 / 3.0 * v1_x * v2_y * mu_ - + T_const * inv_rho_cubed * + (p_yy * rho * rho - + 2.0 * p_y * rho * rho_y + + 2.0 * p * rho_y * rho_y - + p * rho * rho_yy) * mu_) + + return SVector(du1, du2, du3, du4) end initial_condition = initial_condition_navier_stokes_convergence_test # BC types velocity_bc_top_bottom = NoSlip() do x, t, equations - u = initial_condition_navier_stokes_convergence_test(x, t, equations) - return SVector(u[2], u[3]) + u = initial_condition_navier_stokes_convergence_test(x, t, equations) + return SVector(u[2], u[3]) end heat_bc_top_bottom = Adiabatic((x, t, equations) -> 0.0) -boundary_condition_top_bottom = BoundaryConditionNavierStokesWall(velocity_bc_top_bottom, heat_bc_top_bottom) +boundary_condition_top_bottom = BoundaryConditionNavierStokesWall(velocity_bc_top_bottom, + heat_bc_top_bottom) # define inviscid boundary conditions boundary_conditions = Dict(:y_neg => boundary_condition_slip_wall, @@ -185,9 +193,11 @@ boundary_conditions = Dict(:y_neg => boundary_condition_slip_wall, boundary_conditions_parabolic = Dict(:y_neg => boundary_condition_top_bottom, :y_pos => boundary_condition_top_bottom) -semi = SemidiscretizationHyperbolicParabolic(mesh, (equations, equations_parabolic), initial_condition, solver; - boundary_conditions=(boundary_conditions, boundary_conditions_parabolic), - source_terms=source_terms_navier_stokes_convergence_test) +semi = SemidiscretizationHyperbolicParabolic(mesh, (equations, equations_parabolic), + initial_condition, solver; + boundary_conditions = (boundary_conditions, + boundary_conditions_parabolic), + source_terms = source_terms_navier_stokes_convergence_test) # ############################################################################### # # ODE solvers, callbacks etc. @@ -197,16 +207,15 @@ tspan = (0.0, 0.5) ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() -alive_callback = AliveCallback(alive_interval=10) +alive_callback = AliveCallback(alive_interval = 10) analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) callbacks = CallbackSet(summary_callback, alive_callback, analysis_callback) ############################################################################### # run the simulation time_int_tol = 1e-8 -sol = solve(ode, RDPK3SpFSAL49(); abstol=time_int_tol, reltol=time_int_tol, dt = 1e-5, - ode_default_options()..., callback=callbacks) +sol = solve(ode, RDPK3SpFSAL49(); abstol = time_int_tol, reltol = time_int_tol, dt = 1e-5, + ode_default_options()..., callback = callbacks) summary_callback() # print the timer summary - diff --git a/examples/p4est_2d_dgsem/elixir_navierstokes_convergence_nonperiodic.jl b/examples/p4est_2d_dgsem/elixir_navierstokes_convergence_nonperiodic.jl index 935f132ba4b..b4177fe8538 100644 --- a/examples/p4est_2d_dgsem/elixir_navierstokes_convergence_nonperiodic.jl +++ b/examples/p4est_2d_dgsem/elixir_navierstokes_convergence_nonperiodic.jl @@ -8,171 +8,182 @@ prandtl_number() = 0.72 mu() = 0.01 equations = CompressibleEulerEquations2D(1.4) -equations_parabolic = CompressibleNavierStokesDiffusion2D(equations, mu=mu(), Prandtl=prandtl_number(), - gradient_variables=GradientVariablesPrimitive()) +equations_parabolic = CompressibleNavierStokesDiffusion2D(equations, mu = mu(), + Prandtl = prandtl_number(), + gradient_variables = GradientVariablesPrimitive()) # Create DG solver with polynomial degree = 3 and (local) Lax-Friedrichs/Rusanov flux as surface flux -solver = DGSEM(polydeg=3, surface_flux=flux_lax_friedrichs, - volume_integral=VolumeIntegralWeakForm()) +solver = DGSEM(polydeg = 3, surface_flux = flux_lax_friedrichs, + volume_integral = VolumeIntegralWeakForm()) coordinates_min = (-1.0, -1.0) # minimum coordinates (min(x), min(y)) -coordinates_max = ( 1.0, 1.0) # maximum coordinates (max(x), max(y)) +coordinates_max = (1.0, 1.0) # maximum coordinates (max(x), max(y)) trees_per_dimension = (4, 4) mesh = P4estMesh(trees_per_dimension, - polydeg=3, initial_refinement_level=2, - coordinates_min=coordinates_min, coordinates_max=coordinates_max, - periodicity=(false, false)) + polydeg = 3, initial_refinement_level = 2, + coordinates_min = coordinates_min, coordinates_max = coordinates_max, + periodicity = (false, false)) # Note: the initial condition cannot be specialized to `CompressibleNavierStokesDiffusion2D` # since it is called by both the parabolic solver (which passes in `CompressibleNavierStokesDiffusion2D`) # and by the initial condition (which passes in `CompressibleEulerEquations2D`). # This convergence test setup was originally derived by Andrew Winters (@andrewwinters5000) function initial_condition_navier_stokes_convergence_test(x, t, equations) - # Amplitude and shift - A = 0.5 - c = 2.0 + # Amplitude and shift + A = 0.5 + c = 2.0 - # convenience values for trig. functions - pi_x = pi * x[1] - pi_y = pi * x[2] - pi_t = pi * t + # convenience values for trig. functions + pi_x = pi * x[1] + pi_y = pi * x[2] + pi_t = pi * t - rho = c + A * sin(pi_x) * cos(pi_y) * cos(pi_t) - v1 = sin(pi_x) * log(x[2] + 2.0) * (1.0 - exp(-A * (x[2] - 1.0)) ) * cos(pi_t) - v2 = v1 - p = rho^2 + rho = c + A * sin(pi_x) * cos(pi_y) * cos(pi_t) + v1 = sin(pi_x) * log(x[2] + 2.0) * (1.0 - exp(-A * (x[2] - 1.0))) * cos(pi_t) + v2 = v1 + p = rho^2 - return prim2cons(SVector(rho, v1, v2, p), equations) + return prim2cons(SVector(rho, v1, v2, p), equations) end @inline function source_terms_navier_stokes_convergence_test(u, x, t, equations) - y = x[2] - - # TODO: parabolic - # we currently need to hardcode these parameters until we fix the "combined equation" issue - # see also https://github.com/trixi-framework/Trixi.jl/pull/1160 - inv_gamma_minus_one = inv(equations.gamma - 1) - Pr = prandtl_number() - mu_ = mu() - - # Same settings as in `initial_condition` - # Amplitude and shift - A = 0.5 - c = 2.0 - - # convenience values for trig. functions - pi_x = pi * x[1] - pi_y = pi * x[2] - pi_t = pi * t - - # compute the manufactured solution and all necessary derivatives - rho = c + A * sin(pi_x) * cos(pi_y) * cos(pi_t) - rho_t = -pi * A * sin(pi_x) * cos(pi_y) * sin(pi_t) - rho_x = pi * A * cos(pi_x) * cos(pi_y) * cos(pi_t) - rho_y = -pi * A * sin(pi_x) * sin(pi_y) * cos(pi_t) - rho_xx = -pi * pi * A * sin(pi_x) * cos(pi_y) * cos(pi_t) - rho_yy = -pi * pi * A * sin(pi_x) * cos(pi_y) * cos(pi_t) - - v1 = sin(pi_x) * log(y + 2.0) * (1.0 - exp(-A * (y - 1.0))) * cos(pi_t) - v1_t = -pi * sin(pi_x) * log(y + 2.0) * (1.0 - exp(-A * (y - 1.0))) * sin(pi_t) - v1_x = pi * cos(pi_x) * log(y + 2.0) * (1.0 - exp(-A * (y - 1.0))) * cos(pi_t) - v1_y = sin(pi_x) * (A * log(y + 2.0) * exp(-A * (y - 1.0)) + (1.0 - exp(-A * (y - 1.0))) / (y + 2.0)) * cos(pi_t) - v1_xx = -pi * pi * sin(pi_x) * log(y + 2.0) * (1.0 - exp(-A * (y - 1.0))) * cos(pi_t) - v1_xy = pi * cos(pi_x) * (A * log(y + 2.0) * exp(-A * (y - 1.0)) + (1.0 - exp(-A * (y - 1.0))) / (y + 2.0)) * cos(pi_t) - v1_yy = (sin(pi_x) * ( 2.0 * A * exp(-A * (y - 1.0)) / (y + 2.0) - - A * A * log(y + 2.0) * exp(-A * (y - 1.0)) - - (1.0 - exp(-A * (y - 1.0))) / ((y + 2.0) * (y + 2.0))) * cos(pi_t)) - v2 = v1 - v2_t = v1_t - v2_x = v1_x - v2_y = v1_y - v2_xx = v1_xx - v2_xy = v1_xy - v2_yy = v1_yy - - p = rho * rho - p_t = 2.0 * rho * rho_t - p_x = 2.0 * rho * rho_x - p_y = 2.0 * rho * rho_y - p_xx = 2.0 * rho * rho_xx + 2.0 * rho_x * rho_x - p_yy = 2.0 * rho * rho_yy + 2.0 * rho_y * rho_y - - # Note this simplifies slightly because the ansatz assumes that v1 = v2 - E = p * inv_gamma_minus_one + 0.5 * rho * (v1^2 + v2^2) - E_t = p_t * inv_gamma_minus_one + rho_t * v1^2 + 2.0 * rho * v1 * v1_t - E_x = p_x * inv_gamma_minus_one + rho_x * v1^2 + 2.0 * rho * v1 * v1_x - E_y = p_y * inv_gamma_minus_one + rho_y * v1^2 + 2.0 * rho * v1 * v1_y - - # Some convenience constants - T_const = equations.gamma * inv_gamma_minus_one / Pr - inv_rho_cubed = 1.0 / (rho^3) - - # compute the source terms - # density equation - du1 = rho_t + rho_x * v1 + rho * v1_x + rho_y * v2 + rho * v2_y - - # x-momentum equation - du2 = ( rho_t * v1 + rho * v1_t + p_x + rho_x * v1^2 - + 2.0 * rho * v1 * v1_x - + rho_y * v1 * v2 - + rho * v1_y * v2 - + rho * v1 * v2_y - # stress tensor from x-direction - - 4.0 / 3.0 * v1_xx * mu_ - + 2.0 / 3.0 * v2_xy * mu_ - - v1_yy * mu_ - - v2_xy * mu_ ) - # y-momentum equation - du3 = ( rho_t * v2 + rho * v2_t + p_y + rho_x * v1 * v2 - + rho * v1_x * v2 - + rho * v1 * v2_x - + rho_y * v2^2 - + 2.0 * rho * v2 * v2_y - # stress tensor from y-direction - - v1_xy * mu_ - - v2_xx * mu_ - - 4.0 / 3.0 * v2_yy * mu_ - + 2.0 / 3.0 * v1_xy * mu_ ) - # total energy equation - du4 = ( E_t + v1_x * (E + p) + v1 * (E_x + p_x) - + v2_y * (E + p) + v2 * (E_y + p_y) - # stress tensor and temperature gradient terms from x-direction - - 4.0 / 3.0 * v1_xx * v1 * mu_ - + 2.0 / 3.0 * v2_xy * v1 * mu_ - - 4.0 / 3.0 * v1_x * v1_x * mu_ - + 2.0 / 3.0 * v2_y * v1_x * mu_ - - v1_xy * v2 * mu_ - - v2_xx * v2 * mu_ - - v1_y * v2_x * mu_ - - v2_x * v2_x * mu_ - - T_const * inv_rho_cubed * ( p_xx * rho * rho - - 2.0 * p_x * rho * rho_x - + 2.0 * p * rho_x * rho_x - - p * rho * rho_xx ) * mu_ - # stress tensor and temperature gradient terms from y-direction - - v1_yy * v1 * mu_ - - v2_xy * v1 * mu_ - - v1_y * v1_y * mu_ - - v2_x * v1_y * mu_ - - 4.0 / 3.0 * v2_yy * v2 * mu_ - + 2.0 / 3.0 * v1_xy * v2 * mu_ - - 4.0 / 3.0 * v2_y * v2_y * mu_ - + 2.0 / 3.0 * v1_x * v2_y * mu_ - - T_const * inv_rho_cubed * ( p_yy * rho * rho - - 2.0 * p_y * rho * rho_y - + 2.0 * p * rho_y * rho_y - - p * rho * rho_yy ) * mu_ ) - - return SVector(du1, du2, du3, du4) + y = x[2] + + # TODO: parabolic + # we currently need to hardcode these parameters until we fix the "combined equation" issue + # see also https://github.com/trixi-framework/Trixi.jl/pull/1160 + inv_gamma_minus_one = inv(equations.gamma - 1) + Pr = prandtl_number() + mu_ = mu() + + # Same settings as in `initial_condition` + # Amplitude and shift + A = 0.5 + c = 2.0 + + # convenience values for trig. functions + pi_x = pi * x[1] + pi_y = pi * x[2] + pi_t = pi * t + + # compute the manufactured solution and all necessary derivatives + rho = c + A * sin(pi_x) * cos(pi_y) * cos(pi_t) + rho_t = -pi * A * sin(pi_x) * cos(pi_y) * sin(pi_t) + rho_x = pi * A * cos(pi_x) * cos(pi_y) * cos(pi_t) + rho_y = -pi * A * sin(pi_x) * sin(pi_y) * cos(pi_t) + rho_xx = -pi * pi * A * sin(pi_x) * cos(pi_y) * cos(pi_t) + rho_yy = -pi * pi * A * sin(pi_x) * cos(pi_y) * cos(pi_t) + + v1 = sin(pi_x) * log(y + 2.0) * (1.0 - exp(-A * (y - 1.0))) * cos(pi_t) + v1_t = -pi * sin(pi_x) * log(y + 2.0) * (1.0 - exp(-A * (y - 1.0))) * sin(pi_t) + v1_x = pi * cos(pi_x) * log(y + 2.0) * (1.0 - exp(-A * (y - 1.0))) * cos(pi_t) + v1_y = sin(pi_x) * + (A * log(y + 2.0) * exp(-A * (y - 1.0)) + + (1.0 - exp(-A * (y - 1.0))) / (y + 2.0)) * cos(pi_t) + v1_xx = -pi * pi * sin(pi_x) * log(y + 2.0) * (1.0 - exp(-A * (y - 1.0))) * cos(pi_t) + v1_xy = pi * cos(pi_x) * + (A * log(y + 2.0) * exp(-A * (y - 1.0)) + + (1.0 - exp(-A * (y - 1.0))) / (y + 2.0)) * cos(pi_t) + v1_yy = (sin(pi_x) * + (2.0 * A * exp(-A * (y - 1.0)) / (y + 2.0) - + A * A * log(y + 2.0) * exp(-A * (y - 1.0)) - + (1.0 - exp(-A * (y - 1.0))) / ((y + 2.0) * (y + 2.0))) * cos(pi_t)) + v2 = v1 + v2_t = v1_t + v2_x = v1_x + v2_y = v1_y + v2_xx = v1_xx + v2_xy = v1_xy + v2_yy = v1_yy + + p = rho * rho + p_t = 2.0 * rho * rho_t + p_x = 2.0 * rho * rho_x + p_y = 2.0 * rho * rho_y + p_xx = 2.0 * rho * rho_xx + 2.0 * rho_x * rho_x + p_yy = 2.0 * rho * rho_yy + 2.0 * rho_y * rho_y + + # Note this simplifies slightly because the ansatz assumes that v1 = v2 + E = p * inv_gamma_minus_one + 0.5 * rho * (v1^2 + v2^2) + E_t = p_t * inv_gamma_minus_one + rho_t * v1^2 + 2.0 * rho * v1 * v1_t + E_x = p_x * inv_gamma_minus_one + rho_x * v1^2 + 2.0 * rho * v1 * v1_x + E_y = p_y * inv_gamma_minus_one + rho_y * v1^2 + 2.0 * rho * v1 * v1_y + + # Some convenience constants + T_const = equations.gamma * inv_gamma_minus_one / Pr + inv_rho_cubed = 1.0 / (rho^3) + + # compute the source terms + # density equation + du1 = rho_t + rho_x * v1 + rho * v1_x + rho_y * v2 + rho * v2_y + + # x-momentum equation + du2 = (rho_t * v1 + rho * v1_t + p_x + rho_x * v1^2 + + 2.0 * rho * v1 * v1_x + + rho_y * v1 * v2 + + rho * v1_y * v2 + + rho * v1 * v2_y - + # stress tensor from x-direction + 4.0 / 3.0 * v1_xx * mu_ + + 2.0 / 3.0 * v2_xy * mu_ - + v1_yy * mu_ - + v2_xy * mu_) + # y-momentum equation + du3 = (rho_t * v2 + rho * v2_t + p_y + rho_x * v1 * v2 + + rho * v1_x * v2 + + rho * v1 * v2_x + + rho_y * v2^2 + + 2.0 * rho * v2 * v2_y - + # stress tensor from y-direction + v1_xy * mu_ - + v2_xx * mu_ - + 4.0 / 3.0 * v2_yy * mu_ + + 2.0 / 3.0 * v1_xy * mu_) + # total energy equation + du4 = (E_t + v1_x * (E + p) + v1 * (E_x + p_x) + + v2_y * (E + p) + v2 * (E_y + p_y) - + # stress tensor and temperature gradient terms from x-direction + 4.0 / 3.0 * v1_xx * v1 * mu_ + + 2.0 / 3.0 * v2_xy * v1 * mu_ - + 4.0 / 3.0 * v1_x * v1_x * mu_ + + 2.0 / 3.0 * v2_y * v1_x * mu_ - + v1_xy * v2 * mu_ - + v2_xx * v2 * mu_ - + v1_y * v2_x * mu_ - + v2_x * v2_x * mu_ - + T_const * inv_rho_cubed * + (p_xx * rho * rho - + 2.0 * p_x * rho * rho_x + + 2.0 * p * rho_x * rho_x - + p * rho * rho_xx) * mu_ - + # stress tensor and temperature gradient terms from y-direction + v1_yy * v1 * mu_ - + v2_xy * v1 * mu_ - + v1_y * v1_y * mu_ - + v2_x * v1_y * mu_ - + 4.0 / 3.0 * v2_yy * v2 * mu_ + + 2.0 / 3.0 * v1_xy * v2 * mu_ - + 4.0 / 3.0 * v2_y * v2_y * mu_ + + 2.0 / 3.0 * v1_x * v2_y * mu_ - + T_const * inv_rho_cubed * + (p_yy * rho * rho - + 2.0 * p_y * rho * rho_y + + 2.0 * p * rho_y * rho_y - + p * rho * rho_yy) * mu_) + + return SVector(du1, du2, du3, du4) end initial_condition = initial_condition_navier_stokes_convergence_test # BC types -velocity_bc_top_bottom = NoSlip((x, t, equations) -> initial_condition_navier_stokes_convergence_test(x, t, equations)[2:3]) +velocity_bc_top_bottom = NoSlip((x, t, equations) -> initial_condition_navier_stokes_convergence_test(x, + t, + equations)[2:3]) heat_bc_top_bottom = Adiabatic((x, t, equations) -> 0.0) -boundary_condition_top_bottom = BoundaryConditionNavierStokesWall(velocity_bc_top_bottom, heat_bc_top_bottom) +boundary_condition_top_bottom = BoundaryConditionNavierStokesWall(velocity_bc_top_bottom, + heat_bc_top_bottom) boundary_condition_left_right = BoundaryConditionDirichlet(initial_condition_navier_stokes_convergence_test) @@ -188,9 +199,11 @@ boundary_conditions_parabolic = Dict(:x_neg => boundary_condition_left_right, :y_neg => boundary_condition_top_bottom, :y_pos => boundary_condition_top_bottom) -semi = SemidiscretizationHyperbolicParabolic(mesh, (equations, equations_parabolic), initial_condition, solver; - boundary_conditions=(boundary_conditions, boundary_conditions_parabolic), - source_terms=source_terms_navier_stokes_convergence_test) +semi = SemidiscretizationHyperbolicParabolic(mesh, (equations, equations_parabolic), + initial_condition, solver; + boundary_conditions = (boundary_conditions, + boundary_conditions_parabolic), + source_terms = source_terms_navier_stokes_convergence_test) # ############################################################################### # # ODE solvers, callbacks etc. @@ -200,16 +213,15 @@ tspan = (0.0, 0.5) ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() -alive_callback = AliveCallback(alive_interval=10) +alive_callback = AliveCallback(alive_interval = 10) analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) callbacks = CallbackSet(summary_callback, alive_callback, analysis_callback) ############################################################################### # run the simulation time_int_tol = 1e-8 -sol = solve(ode, RDPK3SpFSAL49(); abstol=time_int_tol, reltol=time_int_tol, dt = 1e-5, - ode_default_options()..., callback=callbacks) +sol = solve(ode, RDPK3SpFSAL49(); abstol = time_int_tol, reltol = time_int_tol, dt = 1e-5, + ode_default_options()..., callback = callbacks) summary_callback() # print the timer summary - diff --git a/examples/p4est_2d_dgsem/elixir_navierstokes_lid_driven_cavity.jl b/examples/p4est_2d_dgsem/elixir_navierstokes_lid_driven_cavity.jl index 051f4defe54..e6566edb18a 100644 --- a/examples/p4est_2d_dgsem/elixir_navierstokes_lid_driven_cavity.jl +++ b/examples/p4est_2d_dgsem/elixir_navierstokes_lid_driven_cavity.jl @@ -9,28 +9,28 @@ prandtl_number() = 0.72 mu() = 0.001 equations = CompressibleEulerEquations2D(1.4) -equations_parabolic = CompressibleNavierStokesDiffusion2D(equations, mu=mu(), - Prandtl=prandtl_number()) +equations_parabolic = CompressibleNavierStokesDiffusion2D(equations, mu = mu(), + Prandtl = prandtl_number()) # Create DG solver with polynomial degree = 3 and (local) Lax-Friedrichs/Rusanov flux as surface flux -solver = DGSEM(polydeg=3, surface_flux=flux_lax_friedrichs) +solver = DGSEM(polydeg = 3, surface_flux = flux_lax_friedrichs) coordinates_min = (-1.0, -1.0) # minimum coordinates (min(x), min(y)) -coordinates_max = ( 1.0, 1.0) # maximum coordinates (max(x), max(y)) +coordinates_max = (1.0, 1.0) # maximum coordinates (max(x), max(y)) # Create a uniformly refined mesh trees_per_dimension = (4, 4) mesh = P4estMesh(trees_per_dimension, - polydeg=3, initial_refinement_level=2, - coordinates_min=coordinates_min, coordinates_max=coordinates_max, - periodicity=(false, false)) + polydeg = 3, initial_refinement_level = 2, + coordinates_min = coordinates_min, coordinates_max = coordinates_max, + periodicity = (false, false)) function initial_condition_cavity(x, t, equations::CompressibleEulerEquations2D) - Ma = 0.1 - rho = 1.0 - u, v = 0.0, 0.0 - p = 1.0 / (Ma^2 * equations.gamma) - return prim2cons(SVector(rho, u, v, p), equations) + Ma = 0.1 + rho = 1.0 + u, v = 0.0, 0.0 + p = 1.0 / (Ma^2 * equations.gamma) + return prim2cons(SVector(rho, u, v, p), equations) end initial_condition = initial_condition_cavity @@ -42,21 +42,21 @@ boundary_condition_lid = BoundaryConditionNavierStokesWall(velocity_bc_lid, heat boundary_condition_cavity = BoundaryConditionNavierStokesWall(velocity_bc_cavity, heat_bc) # define periodic boundary conditions everywhere -boundary_conditions = Dict( :x_neg => boundary_condition_slip_wall, - :y_neg => boundary_condition_slip_wall, - :y_pos => boundary_condition_slip_wall, - :x_pos => boundary_condition_slip_wall) +boundary_conditions = Dict(:x_neg => boundary_condition_slip_wall, + :y_neg => boundary_condition_slip_wall, + :y_pos => boundary_condition_slip_wall, + :x_pos => boundary_condition_slip_wall) -boundary_conditions_parabolic = Dict( :x_neg => boundary_condition_cavity, - :y_neg => boundary_condition_cavity, - :y_pos => boundary_condition_lid, - :x_pos => boundary_condition_cavity) +boundary_conditions_parabolic = Dict(:x_neg => boundary_condition_cavity, + :y_neg => boundary_condition_cavity, + :y_pos => boundary_condition_lid, + :x_pos => boundary_condition_cavity) # A semidiscretization collects data structures and functions for the spatial discretization semi = SemidiscretizationHyperbolicParabolic(mesh, (equations, equations_parabolic), initial_condition, solver; - boundary_conditions=(boundary_conditions, - boundary_conditions_parabolic)) + boundary_conditions = (boundary_conditions, + boundary_conditions_parabolic)) ############################################################################### # ODE solvers, callbacks etc. @@ -66,17 +66,15 @@ tspan = (0.0, 25.0) ode = semidiscretize(semi, tspan); summary_callback = SummaryCallback() -alive_callback = AliveCallback(alive_interval=100) +alive_callback = AliveCallback(alive_interval = 100) analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) callbacks = CallbackSet(summary_callback, alive_callback) ############################################################################### # run the simulation time_int_tol = 1e-8 -sol = solve(ode, RDPK3SpFSAL49(); abstol=time_int_tol, reltol=time_int_tol, - ode_default_options()..., callback=callbacks) +sol = solve(ode, RDPK3SpFSAL49(); abstol = time_int_tol, reltol = time_int_tol, + ode_default_options()..., callback = callbacks) summary_callback() # print the timer summary - - diff --git a/examples/p4est_2d_dgsem/elixir_shallowwater_source_terms.jl b/examples/p4est_2d_dgsem/elixir_shallowwater_source_terms.jl index b185a8ce39d..c7922fd3b75 100644 --- a/examples/p4est_2d_dgsem/elixir_shallowwater_source_terms.jl +++ b/examples/p4est_2d_dgsem/elixir_shallowwater_source_terms.jl @@ -5,17 +5,17 @@ using Trixi ############################################################################### # semidiscretization of the shallow water equations -equations = ShallowWaterEquations2D(gravity_constant=9.81) +equations = ShallowWaterEquations2D(gravity_constant = 9.81) initial_condition = initial_condition_convergence_test # MMS EOC test - ############################################################################### # Get the DG approximation space volume_flux = (flux_wintermeyer_etal, flux_nonconservative_wintermeyer_etal) -solver = DGSEM(polydeg=3, surface_flux=(flux_lax_friedrichs, flux_nonconservative_fjordholm_etal), - volume_integral=VolumeIntegralFluxDifferencing(volume_flux)) +solver = DGSEM(polydeg = 3, + surface_flux = (flux_lax_friedrichs, flux_nonconservative_fjordholm_etal), + volume_integral = VolumeIntegralFluxDifferencing(volume_flux)) ############################################################################### # Get the P4estMesh and setup a periodic mesh @@ -25,14 +25,13 @@ coordinates_max = (sqrt(2.0), sqrt(2.0)) # maximum coordinates (max(x), max(y)) # Create P4estMesh with 8 x 8 trees and 16 x 16 elements trees_per_dimension = (8, 8) -mesh = P4estMesh(trees_per_dimension, polydeg=3, - coordinates_min=coordinates_min, coordinates_max=coordinates_max, - initial_refinement_level=1) +mesh = P4estMesh(trees_per_dimension, polydeg = 3, + coordinates_min = coordinates_min, coordinates_max = coordinates_max, + initial_refinement_level = 1) # A semidiscretization collects data structures and functions for the spatial discretization semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver, - source_terms=source_terms_convergence_test) - + source_terms = source_terms_convergence_test) ############################################################################### # ODE solvers, callbacks etc. @@ -44,13 +43,13 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 500 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=200, - save_initial_solution=true, - save_final_solution=true) +save_solution = SaveSolutionCallback(interval = 200, + save_initial_solution = true, + save_final_solution = true) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, save_solution) @@ -58,6 +57,6 @@ callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, sav # run the simulation # use a Runge-Kutta method with automatic (error based) time step size control -sol = solve(ode, RDPK3SpFSAL49(); abstol=1.0e-8, reltol=1.0e-8, - ode_default_options()..., callback=callbacks); +sol = solve(ode, RDPK3SpFSAL49(); abstol = 1.0e-8, reltol = 1.0e-8, + ode_default_options()..., callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/p4est_3d_dgsem/elixir_advection_amr.jl b/examples/p4est_3d_dgsem/elixir_advection_amr.jl index 0473fd2b23a..d56ecc233ff 100644 --- a/examples/p4est_3d_dgsem/elixir_advection_amr.jl +++ b/examples/p4est_3d_dgsem/elixir_advection_amr.jl @@ -11,23 +11,21 @@ advection_velocity = (0.2, -0.7, 0.5) equations = LinearScalarAdvectionEquation3D(advection_velocity) initial_condition = initial_condition_gauss -solver = DGSEM(polydeg=3, surface_flux=flux_lax_friedrichs) +solver = DGSEM(polydeg = 3, surface_flux = flux_lax_friedrichs) coordinates_min = (-5.0, -5.0, -5.0) -coordinates_max = ( 5.0, 5.0, 5.0) +coordinates_max = (5.0, 5.0, 5.0) trees_per_dimension = (1, 1, 1) # Note that it is not necessary to use mesh polydeg lower than the solver polydeg # on a Cartesian mesh. # See https://doi.org/10.1007/s10915-018-00897-9, Section 6. -mesh = P4estMesh(trees_per_dimension, polydeg=1, - coordinates_min=coordinates_min, coordinates_max=coordinates_max, - initial_refinement_level=4) - +mesh = P4estMesh(trees_per_dimension, polydeg = 1, + coordinates_min = coordinates_min, coordinates_max = coordinates_max, + initial_refinement_level = 4) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver) - ############################################################################### # ODE solvers, callbacks etc. @@ -37,26 +35,26 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval, - extra_analysis_integrals=(entropy,)) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval, + extra_analysis_integrals = (entropy,)) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=100, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 100, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) -amr_controller = ControllerThreeLevel(semi, IndicatorMax(semi, variable=first), - base_level=4, - med_level=5, med_threshold=0.1, - max_level=6, max_threshold=0.6) +amr_controller = ControllerThreeLevel(semi, IndicatorMax(semi, variable = first), + base_level = 4, + med_level = 5, med_threshold = 0.1, + max_level = 6, max_threshold = 0.6) amr_callback = AMRCallback(semi, amr_controller, - interval=5, - adapt_initial_condition=true, - adapt_initial_condition_only_refine=true) + interval = 5, + adapt_initial_condition = true, + adapt_initial_condition_only_refine = true) -stepsize_callback = StepsizeCallback(cfl=1.2) +stepsize_callback = StepsizeCallback(cfl = 1.2) callbacks = CallbackSet(summary_callback, analysis_callback, @@ -68,7 +66,7 @@ callbacks = CallbackSet(summary_callback, ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/p4est_3d_dgsem/elixir_advection_amr_unstructured_curved.jl b/examples/p4est_3d_dgsem/elixir_advection_amr_unstructured_curved.jl index fb87c361c18..cd280cf5bf6 100644 --- a/examples/p4est_3d_dgsem/elixir_advection_amr_unstructured_curved.jl +++ b/examples/p4est_3d_dgsem/elixir_advection_amr_unstructured_curved.jl @@ -12,54 +12,55 @@ equations = LinearScalarAdvectionEquation3D(advection_velocity) # Solver with polydeg=4 to ensure free stream preservation (FSP) on non-conforming meshes. # The polydeg of the solver must be at least twice as big as the polydeg of the mesh. # See https://doi.org/10.1007/s10915-018-00897-9, Section 6. -solver = DGSEM(polydeg=4, surface_flux=flux_lax_friedrichs) +solver = DGSEM(polydeg = 4, surface_flux = flux_lax_friedrichs) initial_condition = initial_condition_gauss boundary_condition = BoundaryConditionDirichlet(initial_condition) -boundary_conditions = Dict( - :all => boundary_condition -) +boundary_conditions = Dict(:all => boundary_condition) # Mapping as described in https://arxiv.org/abs/2012.12040 but with less warping. # The mapping will be interpolated at tree level, and then refined without changing # the geometry interpolant. The original mapping applied to this unstructured mesh # causes some Jacobians to be negative, which makes the mesh invalid. function mapping(xi, eta, zeta) - # Don't transform input variables between -1 and 1 onto [0,3] to obtain curved boundaries - # xi = 1.5 * xi_ + 1.5 - # eta = 1.5 * eta_ + 1.5 - # zeta = 1.5 * zeta_ + 1.5 - - y = eta + 1/4 * (cos(1.5 * pi * (2 * xi - 3)/3) * - cos(0.5 * pi * (2 * eta - 3)/3) * - cos(0.5 * pi * (2 * zeta - 3)/3)) - - x = xi + 1/4 * (cos(0.5 * pi * (2 * xi - 3)/3) * - cos(2 * pi * (2 * y - 3)/3) * - cos(0.5 * pi * (2 * zeta - 3)/3)) - - z = zeta + 1/4 * (cos(0.5 * pi * (2 * x - 3)/3) * - cos(pi * (2 * y - 3)/3) * - cos(0.5 * pi * (2 * zeta - 3)/3)) - - # Transform the weird deformed cube to be approximately the size of [-5,5]^3 to match IC - return SVector(5 * x, 5 * y, 5 * z) + # Don't transform input variables between -1 and 1 onto [0,3] to obtain curved boundaries + # xi = 1.5 * xi_ + 1.5 + # eta = 1.5 * eta_ + 1.5 + # zeta = 1.5 * zeta_ + 1.5 + + y = eta + + 1 / 4 * (cos(1.5 * pi * (2 * xi - 3) / 3) * + cos(0.5 * pi * (2 * eta - 3) / 3) * + cos(0.5 * pi * (2 * zeta - 3) / 3)) + + x = xi + + 1 / 4 * (cos(0.5 * pi * (2 * xi - 3) / 3) * + cos(2 * pi * (2 * y - 3) / 3) * + cos(0.5 * pi * (2 * zeta - 3) / 3)) + + z = zeta + + 1 / 4 * (cos(0.5 * pi * (2 * x - 3) / 3) * + cos(pi * (2 * y - 3) / 3) * + cos(0.5 * pi * (2 * zeta - 3) / 3)) + + # Transform the weird deformed cube to be approximately the size of [-5,5]^3 to match IC + return SVector(5 * x, 5 * y, 5 * z) end # Unstructured mesh with 48 cells of the cube domain [-1, 1]^3 mesh_file = joinpath(@__DIR__, "cube_unstructured_2.inp") -isfile(mesh_file) || download("https://gist.githubusercontent.com/efaulhaber/b8df0033798e4926dec515fc045e8c2c/raw/b9254cde1d1fb64b6acc8416bc5ccdd77a240227/cube_unstructured_2.inp", - mesh_file) +isfile(mesh_file) || + download("https://gist.githubusercontent.com/efaulhaber/b8df0033798e4926dec515fc045e8c2c/raw/b9254cde1d1fb64b6acc8416bc5ccdd77a240227/cube_unstructured_2.inp", + mesh_file) # Mesh polydeg of 2 (half the solver polydeg) to ensure FSP (see above). -mesh = P4estMesh{3}(mesh_file, polydeg=2, - mapping=mapping, - initial_refinement_level=1) - - -semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver, boundary_conditions=boundary_conditions) +mesh = P4estMesh{3}(mesh_file, polydeg = 2, + mapping = mapping, + initial_refinement_level = 1) +semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver, + boundary_conditions = boundary_conditions) ############################################################################### # ODE solvers, callbacks etc. @@ -70,29 +71,29 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval, - extra_analysis_integrals=(entropy,)) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval, + extra_analysis_integrals = (entropy,)) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_restart = SaveRestartCallback(interval=100, - save_final_restart=true) +save_restart = SaveRestartCallback(interval = 100, + save_final_restart = true) -save_solution = SaveSolutionCallback(interval=100, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 100, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) -amr_controller = ControllerThreeLevel(semi, IndicatorMax(semi, variable=first), - base_level=1, - med_level=2, med_threshold=0.1, - max_level=3, max_threshold=0.6) +amr_controller = ControllerThreeLevel(semi, IndicatorMax(semi, variable = first), + base_level = 1, + med_level = 2, med_threshold = 0.1, + max_level = 3, max_threshold = 0.6) amr_callback = AMRCallback(semi, amr_controller, - interval=5, - adapt_initial_condition=true, - adapt_initial_condition_only_refine=true) + interval = 5, + adapt_initial_condition = true, + adapt_initial_condition_only_refine = true) -stepsize_callback = StepsizeCallback(cfl=1.2) +stepsize_callback = StepsizeCallback(cfl = 1.2) callbacks = CallbackSet(summary_callback, analysis_callback, @@ -105,7 +106,7 @@ callbacks = CallbackSet(summary_callback, ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/p4est_3d_dgsem/elixir_advection_basic.jl b/examples/p4est_3d_dgsem/elixir_advection_basic.jl index a165d1ff132..02ffa5c7aff 100644 --- a/examples/p4est_3d_dgsem/elixir_advection_basic.jl +++ b/examples/p4est_3d_dgsem/elixir_advection_basic.jl @@ -11,19 +11,20 @@ advection_velocity = (0.2, -0.7, 0.5) equations = LinearScalarAdvectionEquation3D(advection_velocity) # Create DG solver with polynomial degree = 3 and (local) Lax-Friedrichs/Rusanov flux as surface flux -solver = DGSEM(polydeg=3, surface_flux=flux_lax_friedrichs) +solver = DGSEM(polydeg = 3, surface_flux = flux_lax_friedrichs) coordinates_min = (-1.0, -1.0, -1.0) # minimum coordinates (min(x), min(y), min(z)) -coordinates_max = ( 1.0, 1.0, 1.0) # maximum coordinates (max(x), max(y), max(z)) +coordinates_max = (1.0, 1.0, 1.0) # maximum coordinates (max(x), max(y), max(z)) # Create P4estMesh with 8 x 8 x 8 elements (note `refinement_level=1`) trees_per_dimension = (4, 4, 4) -mesh = P4estMesh(trees_per_dimension, polydeg=3, - coordinates_min=coordinates_min, coordinates_max=coordinates_max, - initial_refinement_level=1) +mesh = P4estMesh(trees_per_dimension, polydeg = 3, + coordinates_min = coordinates_min, coordinates_max = coordinates_max, + initial_refinement_level = 1) # A semidiscretization collects data structures and functions for the spatial discretization -semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition_convergence_test, solver) +semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition_convergence_test, + solver) ############################################################################### # ODE solvers, callbacks etc. @@ -37,30 +38,30 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() # The AnalysisCallback allows to analyse the solution in regular intervals and prints the results -analysis_callback = AnalysisCallback(semi, interval=100) +analysis_callback = AnalysisCallback(semi, interval = 100) # The SaveRestartCallback allows to save a file from which a Trixi.jl simulation can be restarted -save_restart = SaveRestartCallback(interval=100, - save_final_restart=true) +save_restart = SaveRestartCallback(interval = 100, + save_final_restart = true) # The SaveSolutionCallback allows to save the solution to a file in regular intervals -save_solution = SaveSolutionCallback(interval=100, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 100, + solution_variables = cons2prim) # The StepsizeCallback handles the re-calculation of the maximum Δt after each time step -stepsize_callback = StepsizeCallback(cfl=1.2) +stepsize_callback = StepsizeCallback(cfl = 1.2) # Create a CallbackSet to collect all callbacks such that they can be passed to the ODE solver -callbacks = CallbackSet(summary_callback, analysis_callback, save_restart, save_solution, stepsize_callback) - +callbacks = CallbackSet(summary_callback, analysis_callback, save_restart, save_solution, + stepsize_callback) ############################################################################### # run the simulation # OrdinaryDiffEq's `solve` method evolves the solution in time and executes the passed callbacks -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); # Print the timer summary summary_callback() diff --git a/examples/p4est_3d_dgsem/elixir_advection_cubed_sphere.jl b/examples/p4est_3d_dgsem/elixir_advection_cubed_sphere.jl index 07a8b36bb4c..cd641ca4af7 100644 --- a/examples/p4est_3d_dgsem/elixir_advection_cubed_sphere.jl +++ b/examples/p4est_3d_dgsem/elixir_advection_cubed_sphere.jl @@ -9,21 +9,20 @@ advection_velocity = (0.2, -0.7, 0.5) equations = LinearScalarAdvectionEquation3D(advection_velocity) # Create DG solver with polynomial degree = 3 and (local) Lax-Friedrichs/Rusanov flux as surface flux -solver = DGSEM(polydeg=3, surface_flux=flux_lax_friedrichs) +solver = DGSEM(polydeg = 3, surface_flux = flux_lax_friedrichs) initial_condition = initial_condition_convergence_test boundary_condition = BoundaryConditionDirichlet(initial_condition) -boundary_conditions = Dict( - :inside => boundary_condition, - :outside => boundary_condition, -) +boundary_conditions = Dict(:inside => boundary_condition, + :outside => boundary_condition) mesh = Trixi.P4estMeshCubedSphere(5, 3, 0.5, 0.5, - polydeg=3, initial_refinement_level=0) + polydeg = 3, initial_refinement_level = 0) # A semidiscretization collects data structures and functions for the spatial discretization -semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver, boundary_conditions=boundary_conditions) +semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver, + boundary_conditions = boundary_conditions) ############################################################################### # ODE solvers, callbacks etc. @@ -37,26 +36,26 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() # The AnalysisCallback allows to analyse the solution in regular intervals and prints the results -analysis_callback = AnalysisCallback(semi, interval=100) +analysis_callback = AnalysisCallback(semi, interval = 100) # The SaveSolutionCallback allows to save the solution to a file in regular intervals -save_solution = SaveSolutionCallback(interval=100, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 100, + solution_variables = cons2prim) # The StepsizeCallback handles the re-calculation of the maximum Δt after each time step -stepsize_callback = StepsizeCallback(cfl=1.2) +stepsize_callback = StepsizeCallback(cfl = 1.2) # Create a CallbackSet to collect all callbacks such that they can be passed to the ODE solver -callbacks = CallbackSet(summary_callback, analysis_callback, save_solution, stepsize_callback) - +callbacks = CallbackSet(summary_callback, analysis_callback, save_solution, + stepsize_callback) ############################################################################### # run the simulation # OrdinaryDiffEq's `solve` method evolves the solution in time and executes the passed callbacks -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); # Print the timer summary summary_callback() diff --git a/examples/p4est_3d_dgsem/elixir_advection_nonconforming.jl b/examples/p4est_3d_dgsem/elixir_advection_nonconforming.jl index 93ff17c7842..34b0e95834d 100644 --- a/examples/p4est_3d_dgsem/elixir_advection_nonconforming.jl +++ b/examples/p4est_3d_dgsem/elixir_advection_nonconforming.jl @@ -2,7 +2,6 @@ using OrdinaryDiffEq using Trixi - ############################################################################### # semidiscretization of the linear advection equation @@ -10,39 +9,42 @@ advection_velocity = (0.2, -0.7, 0.5) equations = LinearScalarAdvectionEquation3D(advection_velocity) # Create DG solver with polynomial degree = 3 and (local) Lax-Friedrichs/Rusanov flux as surface flux -solver = DGSEM(polydeg=3, surface_flux=flux_lax_friedrichs) +solver = DGSEM(polydeg = 3, surface_flux = flux_lax_friedrichs) coordinates_min = (-1.0, -1.0, -1.0) # minimum coordinates (min(x), min(y), min(z)) -coordinates_max = ( 1.0, 1.0, 1.0) # maximum coordinates (max(x), max(y), max(z)) +coordinates_max = (1.0, 1.0, 1.0) # maximum coordinates (max(x), max(y), max(z)) trees_per_dimension = (1, 1, 1) # Note that it is not necessary to use mesh polydeg lower than the solver polydeg # on a Cartesian mesh. # See https://doi.org/10.1007/s10915-018-00897-9, Section 6. -mesh = P4estMesh(trees_per_dimension, polydeg=3, - coordinates_min=coordinates_min, coordinates_max=coordinates_max, - initial_refinement_level=2) +mesh = P4estMesh(trees_per_dimension, polydeg = 3, + coordinates_min = coordinates_min, coordinates_max = coordinates_max, + initial_refinement_level = 2) # Refine bottom left quadrant of each tree to level 3 function refine_fn(p8est, which_tree, quadrant) - quadrant_obj = unsafe_load(quadrant) - if quadrant_obj.x == 0 && quadrant_obj.y == 0 && quadrant_obj.z == 0 && quadrant_obj.level < 3 - # return true (refine) - return Cint(1) - else - # return false (don't refine) - return Cint(0) - end + quadrant_obj = unsafe_load(quadrant) + if quadrant_obj.x == 0 && quadrant_obj.y == 0 && quadrant_obj.z == 0 && + quadrant_obj.level < 3 + # return true (refine) + return Cint(1) + else + # return false (don't refine) + return Cint(0) + end end # Refine recursively until each bottom left quadrant of a tree has level 3 # The mesh will be rebalanced before the simulation starts -refine_fn_c = @cfunction(refine_fn, Cint, (Ptr{Trixi.p8est_t}, Ptr{Trixi.p4est_topidx_t}, Ptr{Trixi.p8est_quadrant_t})) +refine_fn_c = @cfunction(refine_fn, Cint, + (Ptr{Trixi.p8est_t}, Ptr{Trixi.p4est_topidx_t}, + Ptr{Trixi.p8est_quadrant_t})) Trixi.refine_p4est!(mesh.p4est, true, refine_fn_c, C_NULL) # A semidiscretization collects data structures and functions for the spatial discretization -semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition_convergence_test, solver) - +semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition_convergence_test, + solver) ############################################################################### # ODE solvers, callbacks etc. @@ -56,26 +58,26 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() # The AnalysisCallback allows to analyse the solution in regular intervals and prints the results -analysis_callback = AnalysisCallback(semi, interval=100) +analysis_callback = AnalysisCallback(semi, interval = 100) # The SaveSolutionCallback allows to save the solution to a file in regular intervals -save_solution = SaveSolutionCallback(interval=100, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 100, + solution_variables = cons2prim) # The StepsizeCallback handles the re-calculation of the maximum Δt after each time step -stepsize_callback = StepsizeCallback(cfl=1.6) +stepsize_callback = StepsizeCallback(cfl = 1.6) # Create a CallbackSet to collect all callbacks such that they can be passed to the ODE solver -callbacks = CallbackSet(summary_callback, analysis_callback, save_solution, stepsize_callback) - +callbacks = CallbackSet(summary_callback, analysis_callback, save_solution, + stepsize_callback) ############################################################################### # run the simulation # OrdinaryDiffEq's `solve` method evolves the solution in time and executes the passed callbacks -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); # Print the timer summary summary_callback() diff --git a/examples/p4est_3d_dgsem/elixir_advection_restart.jl b/examples/p4est_3d_dgsem/elixir_advection_restart.jl index 26d10cf8826..cd97d69d692 100644 --- a/examples/p4est_3d_dgsem/elixir_advection_restart.jl +++ b/examples/p4est_3d_dgsem/elixir_advection_restart.jl @@ -6,8 +6,7 @@ using Trixi # create a restart file trixi_include(@__MODULE__, joinpath(@__DIR__, "elixir_advection_basic.jl"), - trees_per_dimension=(2, 2, 2)) - + trees_per_dimension = (2, 2, 2)) ############################################################################### # adapt the parameters that have changed compared to "elixir_advection_extended.jl" @@ -18,7 +17,8 @@ trixi_include(@__MODULE__, joinpath(@__DIR__, "elixir_advection_basic.jl"), restart_filename = joinpath("out", "restart_000010.h5") mesh = load_mesh(restart_filename) -semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition_convergence_test, solver) +semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition_convergence_test, + solver) tspan = (load_time(restart_filename), 2.0) dt = load_dt(restart_filename) @@ -27,14 +27,13 @@ ode = semidiscretize(semi, tspan, restart_filename); # Do not overwrite the initial snapshot written by elixir_advection_extended.jl. save_solution.condition.save_initial_solution = false -integrator = init(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=dt, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +integrator = init(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = dt, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); # Get the last time index and work with that. load_timestep!(integrator, restart_filename) - ############################################################################### # run the simulation diff --git a/examples/p4est_3d_dgsem/elixir_advection_unstructured_curved.jl b/examples/p4est_3d_dgsem/elixir_advection_unstructured_curved.jl index 85fd0b9a2cf..6df9ac0b16a 100644 --- a/examples/p4est_3d_dgsem/elixir_advection_unstructured_curved.jl +++ b/examples/p4est_3d_dgsem/elixir_advection_unstructured_curved.jl @@ -10,51 +10,54 @@ advection_velocity = (0.2, -0.7, 0.5) equations = LinearScalarAdvectionEquation3D(advection_velocity) # Create DG solver with polynomial degree = 3 and (local) Lax-Friedrichs/Rusanov flux as surface flux -solver = DGSEM(polydeg=3, surface_flux=flux_lax_friedrichs) +solver = DGSEM(polydeg = 3, surface_flux = flux_lax_friedrichs) initial_condition = initial_condition_convergence_test boundary_condition = BoundaryConditionDirichlet(initial_condition) -boundary_conditions = Dict( - :all => boundary_condition -) +boundary_conditions = Dict(:all => boundary_condition) # Mapping as described in https://arxiv.org/abs/2012.12040 but with less warping. # The mapping will be interpolated at tree level, and then refined without changing # the geometry interpolant. The original mapping applied to this unstructured mesh # causes some Jacobians to be negative, which makes the mesh invalid. function mapping(xi, eta, zeta) - # Don't transform input variables between -1 and 1 onto [0,3] to obtain curved boundaries - # xi = 1.5 * xi_ + 1.5 - # eta = 1.5 * eta_ + 1.5 - # zeta = 1.5 * zeta_ + 1.5 - - y = eta + 1/6 * (cos(1.5 * pi * (2 * xi - 3)/3) * - cos(0.5 * pi * (2 * eta - 3)/3) * - cos(0.5 * pi * (2 * zeta - 3)/3)) - - x = xi + 1/6 * (cos(0.5 * pi * (2 * xi - 3)/3) * - cos(2 * pi * (2 * y - 3)/3) * - cos(0.5 * pi * (2 * zeta - 3)/3)) - - z = zeta + 1/6 * (cos(0.5 * pi * (2 * x - 3)/3) * - cos(pi * (2 * y - 3)/3) * - cos(0.5 * pi * (2 * zeta - 3)/3)) - - return SVector(x, y, z) + # Don't transform input variables between -1 and 1 onto [0,3] to obtain curved boundaries + # xi = 1.5 * xi_ + 1.5 + # eta = 1.5 * eta_ + 1.5 + # zeta = 1.5 * zeta_ + 1.5 + + y = eta + + 1 / 6 * (cos(1.5 * pi * (2 * xi - 3) / 3) * + cos(0.5 * pi * (2 * eta - 3) / 3) * + cos(0.5 * pi * (2 * zeta - 3) / 3)) + + x = xi + + 1 / 6 * (cos(0.5 * pi * (2 * xi - 3) / 3) * + cos(2 * pi * (2 * y - 3) / 3) * + cos(0.5 * pi * (2 * zeta - 3) / 3)) + + z = zeta + + 1 / 6 * (cos(0.5 * pi * (2 * x - 3) / 3) * + cos(pi * (2 * y - 3) / 3) * + cos(0.5 * pi * (2 * zeta - 3) / 3)) + + return SVector(x, y, z) end # Unstructured mesh with 68 cells of the cube domain [-1, 1]^3 mesh_file = joinpath(@__DIR__, "cube_unstructured_1.inp") -isfile(mesh_file) || download("https://gist.githubusercontent.com/efaulhaber/d45c8ac1e248618885fa7cc31a50ab40/raw/37fba24890ab37cfa49c39eae98b44faf4502882/cube_unstructured_1.inp", - mesh_file) +isfile(mesh_file) || + download("https://gist.githubusercontent.com/efaulhaber/d45c8ac1e248618885fa7cc31a50ab40/raw/37fba24890ab37cfa49c39eae98b44faf4502882/cube_unstructured_1.inp", + mesh_file) -mesh = P4estMesh{3}(mesh_file, polydeg=3, - mapping=mapping, - initial_refinement_level=2) +mesh = P4estMesh{3}(mesh_file, polydeg = 3, + mapping = mapping, + initial_refinement_level = 2) # A semidiscretization collects data structures and functions for the spatial discretization -semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver, boundary_conditions=boundary_conditions) +semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver, + boundary_conditions = boundary_conditions) ############################################################################### # ODE solvers, callbacks etc. @@ -68,32 +71,32 @@ summary_callback = SummaryCallback() # The AnalysisCallback allows to analyse the solution in regular intervals and prints the results analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) # The SaveRestartCallback allows to save a file from which a Trixi.jl simulation can be restarted -save_restart = SaveRestartCallback(interval=100, - save_final_restart=true) +save_restart = SaveRestartCallback(interval = 100, + save_final_restart = true) # The SaveSolutionCallback allows to save the solution to a file in regular intervals -save_solution = SaveSolutionCallback(interval=100, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 100, + solution_variables = cons2prim) # The StepsizeCallback handles the re-calculation of the maximum Δt after each time step -stepsize_callback = StepsizeCallback(cfl=1.2) +stepsize_callback = StepsizeCallback(cfl = 1.2) # Create a CallbackSet to collect all callbacks such that they can be passed to the ODE solver -callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, save_restart, save_solution, stepsize_callback) - +callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, save_restart, + save_solution, stepsize_callback) ############################################################################### # run the simulation # OrdinaryDiffEq's `solve` method evolves the solution in time and executes the passed callbacks -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); # Print the timer summary summary_callback() diff --git a/examples/p4est_3d_dgsem/elixir_euler_baroclinic_instability.jl b/examples/p4est_3d_dgsem/elixir_euler_baroclinic_instability.jl index 27c8ceb130c..0274a89aec7 100644 --- a/examples/p4est_3d_dgsem/elixir_euler_baroclinic_instability.jl +++ b/examples/p4est_3d_dgsem/elixir_euler_baroclinic_instability.jl @@ -22,190 +22,194 @@ equations = CompressibleEulerEquations3D(gamma) # Initial condition for an idealized baroclinic instability test # https://doi.org/10.1002/qj.2241, Section 3.2 and Appendix A -function initial_condition_baroclinic_instability(x, t, equations::CompressibleEulerEquations3D) - lon, lat, r = cartesian_to_sphere(x) - radius_earth = 6.371229e6 - # Make sure that the r is not smaller than radius_earth - z = max(r - radius_earth, 0.0) +function initial_condition_baroclinic_instability(x, t, + equations::CompressibleEulerEquations3D) + lon, lat, r = cartesian_to_sphere(x) + radius_earth = 6.371229e6 + # Make sure that the r is not smaller than radius_earth + z = max(r - radius_earth, 0.0) - # Unperturbed basic state - rho, u, p = basic_state_baroclinic_instability_longitudinal_velocity(lon, lat, z) + # Unperturbed basic state + rho, u, p = basic_state_baroclinic_instability_longitudinal_velocity(lon, lat, z) - # Stream function type perturbation - u_perturbation, v_perturbation = perturbation_stream_function(lon, lat, z) + # Stream function type perturbation + u_perturbation, v_perturbation = perturbation_stream_function(lon, lat, z) - u += u_perturbation - v = v_perturbation + u += u_perturbation + v = v_perturbation - # Convert spherical velocity to Cartesian - v1 = -sin(lon) * u - sin(lat) * cos(lon) * v - v2 = cos(lon) * u - sin(lat) * sin(lon) * v - v3 = cos(lat) * v + # Convert spherical velocity to Cartesian + v1 = -sin(lon) * u - sin(lat) * cos(lon) * v + v2 = cos(lon) * u - sin(lat) * sin(lon) * v + v3 = cos(lat) * v - return prim2cons(SVector(rho, v1, v2, v3, p), equations) + return prim2cons(SVector(rho, v1, v2, v3, p), equations) end # Steady state for RHS correction below function steady_state_baroclinic_instability(x, t, equations::CompressibleEulerEquations3D) - lon, lat, r = cartesian_to_sphere(x) - radius_earth = 6.371229e6 - # Make sure that the r is not smaller than radius_earth - z = max(r - radius_earth, 0.0) + lon, lat, r = cartesian_to_sphere(x) + radius_earth = 6.371229e6 + # Make sure that the r is not smaller than radius_earth + z = max(r - radius_earth, 0.0) - # Unperturbed basic state - rho, u, p = basic_state_baroclinic_instability_longitudinal_velocity(lon, lat, z) + # Unperturbed basic state + rho, u, p = basic_state_baroclinic_instability_longitudinal_velocity(lon, lat, z) - # Convert spherical velocity to Cartesian - v1 = -sin(lon) * u - v2 = cos(lon) * u - v3 = 0.0 + # Convert spherical velocity to Cartesian + v1 = -sin(lon) * u + v2 = cos(lon) * u + v3 = 0.0 - return prim2cons(SVector(rho, v1, v2, v3, p), equations) + return prim2cons(SVector(rho, v1, v2, v3, p), equations) end function cartesian_to_sphere(x) - r = norm(x) - lambda = atan(x[2], x[1]) - if lambda < 0 - lambda += 2 * pi - end - phi = asin(x[3] / r) - - return lambda, phi, r + r = norm(x) + lambda = atan(x[2], x[1]) + if lambda < 0 + lambda += 2 * pi + end + phi = asin(x[3] / r) + + return lambda, phi, r end # Unperturbed balanced steady-state. # Returns primitive variables with only the velocity in longitudinal direction (rho, u, p). # The other velocity components are zero. function basic_state_baroclinic_instability_longitudinal_velocity(lon, lat, z) - # Parameters from Table 1 in the paper - # Corresponding names in the paper are commented - radius_earth = 6.371229e6 # a - half_width_parameter = 2 # b - gravitational_acceleration = 9.80616 # g - k = 3 # k - surface_pressure = 1e5 # p₀ - gas_constant = 287 # R - surface_equatorial_temperature = 310.0 # T₀ᴱ - surface_polar_temperature = 240.0 # T₀ᴾ - lapse_rate = 0.005 # Γ - angular_velocity = 7.29212e-5 # Ω - - # Distance to the center of the Earth - r = z + radius_earth - - # In the paper: T₀ - temperature0 = 0.5 * (surface_equatorial_temperature + surface_polar_temperature) - # In the paper: A, B, C, H - const_a = 1 / lapse_rate - const_b = (temperature0 - surface_polar_temperature) / - (temperature0 * surface_polar_temperature) - const_c = 0.5 * (k + 2) * (surface_equatorial_temperature - surface_polar_temperature) / - (surface_equatorial_temperature * surface_polar_temperature) - const_h = gas_constant * temperature0 / gravitational_acceleration - - # In the paper: (r - a) / bH - scaled_z = z / (half_width_parameter * const_h) - - # Temporary variables - temp1 = exp(lapse_rate/temperature0 * z) - temp2 = exp(-scaled_z^2) - - # In the paper: ̃τ₁, ̃τ₂ - tau1 = const_a * lapse_rate / temperature0 * temp1 + const_b * (1 - 2 * scaled_z^2) * temp2 - tau2 = const_c * (1 - 2 * scaled_z^2) * temp2 - - # In the paper: ∫τ₁(r') dr', ∫τ₂(r') dr' - inttau1 = const_a * (temp1 - 1) + const_b * z * temp2 - inttau2 = const_c * z * temp2 - - # Temporary variables - temp3 = r/radius_earth * cos(lat) - temp4 = temp3^k - k/(k + 2) * temp3^(k+2) - - # In the paper: T - temperature = 1 / ((r/radius_earth)^2 * (tau1 - tau2 * temp4)) - - # In the paper: U, u (zonal wind, first component of spherical velocity) - big_u = gravitational_acceleration/radius_earth * k * temperature * inttau2 * (temp3^(k-1) - temp3^(k+1)) - temp5 = radius_earth * cos(lat) - u = -angular_velocity * temp5 + sqrt(angular_velocity^2 * temp5^2 + temp5 * big_u) - - # Hydrostatic pressure - p = surface_pressure * exp(-gravitational_acceleration/gas_constant * (inttau1 - inttau2 * temp4)) - - # Density (via ideal gas law) - rho = p / (gas_constant * temperature) - - return rho, u, p + # Parameters from Table 1 in the paper + # Corresponding names in the paper are commented + radius_earth = 6.371229e6 # a + half_width_parameter = 2 # b + gravitational_acceleration = 9.80616 # g + k = 3 # k + surface_pressure = 1e5 # p₀ + gas_constant = 287 # R + surface_equatorial_temperature = 310.0 # T₀ᴱ + surface_polar_temperature = 240.0 # T₀ᴾ + lapse_rate = 0.005 # Γ + angular_velocity = 7.29212e-5 # Ω + + # Distance to the center of the Earth + r = z + radius_earth + + # In the paper: T₀ + temperature0 = 0.5 * (surface_equatorial_temperature + surface_polar_temperature) + # In the paper: A, B, C, H + const_a = 1 / lapse_rate + const_b = (temperature0 - surface_polar_temperature) / + (temperature0 * surface_polar_temperature) + const_c = 0.5 * (k + 2) * (surface_equatorial_temperature - surface_polar_temperature) / + (surface_equatorial_temperature * surface_polar_temperature) + const_h = gas_constant * temperature0 / gravitational_acceleration + + # In the paper: (r - a) / bH + scaled_z = z / (half_width_parameter * const_h) + + # Temporary variables + temp1 = exp(lapse_rate / temperature0 * z) + temp2 = exp(-scaled_z^2) + + # In the paper: ̃τ₁, ̃τ₂ + tau1 = const_a * lapse_rate / temperature0 * temp1 + + const_b * (1 - 2 * scaled_z^2) * temp2 + tau2 = const_c * (1 - 2 * scaled_z^2) * temp2 + + # In the paper: ∫τ₁(r') dr', ∫τ₂(r') dr' + inttau1 = const_a * (temp1 - 1) + const_b * z * temp2 + inttau2 = const_c * z * temp2 + + # Temporary variables + temp3 = r / radius_earth * cos(lat) + temp4 = temp3^k - k / (k + 2) * temp3^(k + 2) + + # In the paper: T + temperature = 1 / ((r / radius_earth)^2 * (tau1 - tau2 * temp4)) + + # In the paper: U, u (zonal wind, first component of spherical velocity) + big_u = gravitational_acceleration / radius_earth * k * temperature * inttau2 * + (temp3^(k - 1) - temp3^(k + 1)) + temp5 = radius_earth * cos(lat) + u = -angular_velocity * temp5 + sqrt(angular_velocity^2 * temp5^2 + temp5 * big_u) + + # Hydrostatic pressure + p = surface_pressure * + exp(-gravitational_acceleration / gas_constant * (inttau1 - inttau2 * temp4)) + + # Density (via ideal gas law) + rho = p / (gas_constant * temperature) + + return rho, u, p end # Perturbation as in Equations 25 and 26 of the paper (analytical derivative) function perturbation_stream_function(lon, lat, z) - # Parameters from Table 1 in the paper - # Corresponding names in the paper are commented - perturbation_radius = 1/6 # d₀ / a - perturbed_wind_amplitude = 1.0 # Vₚ - perturbation_lon = pi/9 # Longitude of perturbation location - perturbation_lat = 2 * pi/9 # Latitude of perturbation location - pertz = 15000 # Perturbation height cap - - # Great circle distance (d in the paper) divided by a (radius of the Earth) - # because we never actually need d without dividing by a - great_circle_distance_by_a = acos(sin(perturbation_lat) * sin(lat) + - cos(perturbation_lat) * cos(lat) * - cos(lon - perturbation_lon)) - - # In the first case, the vertical taper function is per definition zero. - # In the second case, the stream function is per definition zero. - if z > pertz || great_circle_distance_by_a > perturbation_radius - return 0.0, 0.0 - end - - # Vertical tapering of stream function - perttaper = 1.0 - 3 * z^2 / pertz^2 + 2 * z^3 / pertz^3 - - # sin/cos(pi * d / (2 * d_0)) in the paper - sin_, cos_ = sincos(0.5 * pi * great_circle_distance_by_a / perturbation_radius) - - # Common factor for both u and v - factor = 16 / (3 * sqrt(3)) * perturbed_wind_amplitude * perttaper * cos_^3 * sin_ - - u_perturbation = -factor * (-sin(perturbation_lat) * cos(lat) + - cos(perturbation_lat) * sin(lat) * cos(lon - perturbation_lon) - ) / sin(great_circle_distance_by_a) - - v_perturbation = factor * cos(perturbation_lat) * sin(lon - perturbation_lon) / - sin(great_circle_distance_by_a) - - return u_perturbation, v_perturbation -end + # Parameters from Table 1 in the paper + # Corresponding names in the paper are commented + perturbation_radius = 1 / 6 # d₀ / a + perturbed_wind_amplitude = 1.0 # Vₚ + perturbation_lon = pi / 9 # Longitude of perturbation location + perturbation_lat = 2 * pi / 9 # Latitude of perturbation location + pertz = 15000 # Perturbation height cap + + # Great circle distance (d in the paper) divided by a (radius of the Earth) + # because we never actually need d without dividing by a + great_circle_distance_by_a = acos(sin(perturbation_lat) * sin(lat) + + cos(perturbation_lat) * cos(lat) * + cos(lon - perturbation_lon)) + + # In the first case, the vertical taper function is per definition zero. + # In the second case, the stream function is per definition zero. + if z > pertz || great_circle_distance_by_a > perturbation_radius + return 0.0, 0.0 + end + + # Vertical tapering of stream function + perttaper = 1.0 - 3 * z^2 / pertz^2 + 2 * z^3 / pertz^3 + + # sin/cos(pi * d / (2 * d_0)) in the paper + sin_, cos_ = sincos(0.5 * pi * great_circle_distance_by_a / perturbation_radius) + # Common factor for both u and v + factor = 16 / (3 * sqrt(3)) * perturbed_wind_amplitude * perttaper * cos_^3 * sin_ -@inline function source_terms_baroclinic_instability(u, x, t, equations::CompressibleEulerEquations3D) - radius_earth = 6.371229e6 # a - gravitational_acceleration = 9.80616 # g - angular_velocity = 7.29212e-5 # Ω + u_perturbation = -factor * (-sin(perturbation_lat) * cos(lat) + + cos(perturbation_lat) * sin(lat) * cos(lon - perturbation_lon)) / + sin(great_circle_distance_by_a) - r = norm(x) - # Make sure that r is not smaller than radius_earth - z = max(r - radius_earth, 0.0) - r = z + radius_earth + v_perturbation = factor * cos(perturbation_lat) * sin(lon - perturbation_lon) / + sin(great_circle_distance_by_a) - du1 = zero(eltype(u)) + return u_perturbation, v_perturbation +end + +@inline function source_terms_baroclinic_instability(u, x, t, + equations::CompressibleEulerEquations3D) + radius_earth = 6.371229e6 # a + gravitational_acceleration = 9.80616 # g + angular_velocity = 7.29212e-5 # Ω + + r = norm(x) + # Make sure that r is not smaller than radius_earth + z = max(r - radius_earth, 0.0) + r = z + radius_earth - # Gravity term - temp = -gravitational_acceleration * radius_earth^2 / r^3 - du2 = temp * u[1] * x[1] - du3 = temp * u[1] * x[2] - du4 = temp * u[1] * x[3] - du5 = temp * (u[2] * x[1] + u[3] * x[2] + u[4] * x[3]) + du1 = zero(eltype(u)) - # Coriolis term, -2Ω × ρv = -2 * angular_velocity * (0, 0, 1) × u[2:4] - du2 -= -2 * angular_velocity * u[3] - du3 -= 2 * angular_velocity * u[2] + # Gravity term + temp = -gravitational_acceleration * radius_earth^2 / r^3 + du2 = temp * u[1] * x[1] + du3 = temp * u[1] * x[2] + du4 = temp * u[1] * x[3] + du5 = temp * (u[2] * x[1] + u[3] * x[2] + u[4] * x[3]) - return SVector(du1, du2, du3, du4, du5) + # Coriolis term, -2Ω × ρv = -2 * angular_velocity * (0, 0, 1) × u[2:4] + du2 -= -2 * angular_velocity * u[3] + du3 -= 2 * angular_velocity * u[2] + + return SVector(du1, du2, du3, du4, du5) end ############################################################################### @@ -213,26 +217,24 @@ end initial_condition = initial_condition_baroclinic_instability -boundary_conditions = Dict( - :inside => boundary_condition_slip_wall, - :outside => boundary_condition_slip_wall, -) +boundary_conditions = Dict(:inside => boundary_condition_slip_wall, + :outside => boundary_condition_slip_wall) # This is a good estimate for the speed of sound in this example. # Other values between 300 and 400 should work as well. surface_flux = FluxLMARS(340) -volume_flux = flux_kennedy_gruber -solver = DGSEM(polydeg=5, surface_flux=surface_flux, volume_integral=VolumeIntegralFluxDifferencing(volume_flux)) +volume_flux = flux_kennedy_gruber +solver = DGSEM(polydeg = 5, surface_flux = surface_flux, + volume_integral = VolumeIntegralFluxDifferencing(volume_flux)) # For optimal results, use (16, 8) here trees_per_cube_face = (8, 4) mesh = Trixi.P4estMeshCubedSphere(trees_per_cube_face..., 6.371229e6, 30000.0, - polydeg=5, initial_refinement_level=0) + polydeg = 5, initial_refinement_level = 0) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver, - source_terms=source_terms_baroclinic_instability, - boundary_conditions=boundary_conditions) - + source_terms = source_terms_baroclinic_instability, + boundary_conditions = boundary_conditions) ############################################################################### # ODE solvers, callbacks etc. @@ -250,20 +252,20 @@ tspan = (0.0, 10 * 24 * 60 * 60.0) # time in seconds for 10 days u_steady_state = compute_coefficients(steady_state_baroclinic_instability, tspan[1], semi) # Use a `let` block for performance (otherwise du_steady_state will be a global variable) let du_steady_state = similar(u_steady_state) - # Save RHS of the steady state - Trixi.rhs!(du_steady_state, u_steady_state, semi, tspan[1]) - - global function corrected_rhs!(du, u, semi, t) - # Normal RHS evaluation - Trixi.rhs!(du, u, semi, t) - # Correct by subtracting the steady-state RHS - Trixi.@trixi_timeit Trixi.timer() "rhs correction" begin - # Use Trixi.@threaded for threaded performance - Trixi.@threaded for i in eachindex(du) - du[i] -= du_steady_state[i] - end + # Save RHS of the steady state + Trixi.rhs!(du_steady_state, u_steady_state, semi, tspan[1]) + + global function corrected_rhs!(du, u, semi, t) + # Normal RHS evaluation + Trixi.rhs!(du, u, semi, t) + # Correct by subtracting the steady-state RHS + Trixi.@trixi_timeit Trixi.timer() "rhs correction" begin + # Use Trixi.@threaded for threaded performance + Trixi.@threaded for i in eachindex(du) + du[i] -= du_steady_state[i] + end + end end - end end u0 = compute_coefficients(tspan[1], semi) ode = ODEProblem(corrected_rhs!, u0, tspan, semi) @@ -271,27 +273,27 @@ ode = ODEProblem(corrected_rhs!, u0, tspan, semi) summary_callback = SummaryCallback() analysis_interval = 5000 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=5000, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 5000, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, save_solution) - ############################################################################### # run the simulation # Use a Runge-Kutta method with automatic (error based) time step size control # Enable threading of the RK method for better performance on multiple threads -sol = solve(ode, RDPK3SpFSAL49(thread=OrdinaryDiffEq.True()); abstol=1.0e-6, reltol=1.0e-6, - ode_default_options()..., callback=callbacks); +sol = solve(ode, RDPK3SpFSAL49(thread = OrdinaryDiffEq.True()); abstol = 1.0e-6, + reltol = 1.0e-6, + ode_default_options()..., callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/p4est_3d_dgsem/elixir_euler_circular_wind_nonconforming.jl b/examples/p4est_3d_dgsem/elixir_euler_circular_wind_nonconforming.jl index 63e937620f0..34a43a5b534 100644 --- a/examples/p4est_3d_dgsem/elixir_euler_circular_wind_nonconforming.jl +++ b/examples/p4est_3d_dgsem/elixir_euler_circular_wind_nonconforming.jl @@ -14,78 +14,77 @@ using LinearAlgebra gamma = 1.4 equations = CompressibleEulerEquations3D(gamma) - function initial_condition_circular_wind(x, t, equations::CompressibleEulerEquations3D) - radius_earth = 6.371229e6 - p = 1e5 - rho = 1.0 - v1 = -10 * x[2] / radius_earth - v2 = 10 * x[1] / radius_earth - v3 = 0.0 - - return prim2cons(SVector(rho, v1, v2, v3, p), equations) + radius_earth = 6.371229e6 + p = 1e5 + rho = 1.0 + v1 = -10 * x[2] / radius_earth + v2 = 10 * x[1] / radius_earth + v3 = 0.0 + + return prim2cons(SVector(rho, v1, v2, v3, p), equations) end -@inline function source_terms_circular_wind(u, x, t, equations::CompressibleEulerEquations3D) - radius_earth = 6.371229e6 - rho = 1.0 +@inline function source_terms_circular_wind(u, x, t, + equations::CompressibleEulerEquations3D) + radius_earth = 6.371229e6 + rho = 1.0 - du1 = 0.0 - du2 = -rho * (10 / radius_earth) * (10 * x[1] / radius_earth) - du3 = -rho * (10 / radius_earth) * (10 * x[2] / radius_earth) - du4 = 0.0 - du5 = 0.0 + du1 = 0.0 + du2 = -rho * (10 / radius_earth) * (10 * x[1] / radius_earth) + du3 = -rho * (10 / radius_earth) * (10 * x[2] / radius_earth) + du4 = 0.0 + du5 = 0.0 - return SVector(du1, du2, du3, du4, du5) + return SVector(du1, du2, du3, du4, du5) end - -function indicator_test(u::AbstractArray{<:Any,5}, +function indicator_test(u::AbstractArray{<:Any, 5}, mesh, equations, dg::DGSEM, cache; kwargs...) - alpha = zeros(Int, nelements(dg, cache)) - - for element in eachelement(dg, cache) - for k in eachnode(dg), j in eachnode(dg), i in eachnode(dg) - x = Trixi.get_node_coords(cache.elements.node_coordinates, equations, dg, i, j, k, element) - lambda, phi, r = cart_to_sphere(x) - if 0.22 < lambda < 3.3 && 0.45 < phi < 1.3 - alpha[element] = 1 - end + alpha = zeros(Int, nelements(dg, cache)) + + for element in eachelement(dg, cache) + for k in eachnode(dg), j in eachnode(dg), i in eachnode(dg) + x = Trixi.get_node_coords(cache.elements.node_coordinates, equations, dg, i, j, + k, element) + lambda, phi, r = cart_to_sphere(x) + if 0.22 < lambda < 3.3 && 0.45 < phi < 1.3 + alpha[element] = 1 + end + end end - end - return alpha + return alpha end function cart_to_sphere(x) - r = norm(x) - lambda = atan(x[2], x[1]) - if lambda < 0 - lambda += 2 * pi - end - phi = asin(x[3] / r) - - return lambda, phi, r + r = norm(x) + lambda = atan(x[2], x[1]) + if lambda < 0 + lambda += 2 * pi + end + phi = asin(x[3] / r) + + return lambda, phi, r end -function Trixi.get_element_variables!(element_variables, indicator::typeof(indicator_test), ::AMRCallback) - return nothing +function Trixi.get_element_variables!(element_variables, indicator::typeof(indicator_test), + ::AMRCallback) + return nothing end initial_condition = initial_condition_circular_wind -boundary_conditions = Dict( - :inside => boundary_condition_slip_wall, - :outside => boundary_condition_slip_wall -) +boundary_conditions = Dict(:inside => boundary_condition_slip_wall, + :outside => boundary_condition_slip_wall) # The speed of sound in this example is 374 m/s. surface_flux = FluxLMARS(374) # Note that a free stream is not preserved if N < 2 * N_geo, where N is the # polydeg of the solver and N_geo is the polydeg of the mesh. # However, the FSP error is negligible in this example. -solver = DGSEM(polydeg=4, surface_flux=surface_flux) +solver = DGSEM(polydeg = 4, surface_flux = surface_flux) # Other mesh configurations to run this simulation on. # The cylinder allows to use a structured mesh, the face of the cubed sphere @@ -113,12 +112,11 @@ solver = DGSEM(polydeg=4, surface_flux=surface_flux) trees_per_cube_face = (6, 2) mesh = Trixi.P4estMeshCubedSphere(trees_per_cube_face..., 6.371229e6, 30000.0, - polydeg=4, initial_refinement_level=0) + polydeg = 4, initial_refinement_level = 0) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver, - source_terms=source_terms_circular_wind, - boundary_conditions=boundary_conditions) - + source_terms = source_terms_circular_wind, + boundary_conditions = boundary_conditions) ############################################################################### # ODE solvers, callbacks etc. @@ -129,22 +127,22 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 5000 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=5000, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 5000, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) amr_controller = ControllerThreeLevel(semi, indicator_test, - base_level=0, - max_level=1, max_threshold=0.6) + base_level = 0, + max_level = 1, max_threshold = 0.6) amr_callback = AMRCallback(semi, amr_controller, - interval=0, # Only initial refinement - adapt_initial_condition=true, - adapt_initial_condition_only_refine=true) + interval = 0, # Only initial refinement + adapt_initial_condition = true, + adapt_initial_condition_only_refine = true) callbacks = CallbackSet(summary_callback, analysis_callback, @@ -152,13 +150,13 @@ callbacks = CallbackSet(summary_callback, save_solution, amr_callback) - ############################################################################### # run the simulation # Use a Runge-Kutta method with automatic (error based) time step size control # Enable threading of the RK method for better performance on multiple threads -sol = solve(ode, RDPK3SpFSAL49(thread=OrdinaryDiffEq.True()); abstol=1.0e-6, reltol=1.0e-6, - ode_default_options()..., callback=callbacks); +sol = solve(ode, RDPK3SpFSAL49(thread = OrdinaryDiffEq.True()); abstol = 1.0e-6, + reltol = 1.0e-6, + ode_default_options()..., callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/p4est_3d_dgsem/elixir_euler_ec.jl b/examples/p4est_3d_dgsem/elixir_euler_ec.jl index 463a26fca53..d9d774a7ffc 100644 --- a/examples/p4est_3d_dgsem/elixir_euler_ec.jl +++ b/examples/p4est_3d_dgsem/elixir_euler_ec.jl @@ -6,56 +6,59 @@ using Trixi ############################################################################### # semidiscretization of the compressible Euler equations -equations = CompressibleEulerEquations3D(5/3) +equations = CompressibleEulerEquations3D(5 / 3) initial_condition = initial_condition_weak_blast_wave -boundary_conditions = Dict( - :all => boundary_condition_slip_wall -) +boundary_conditions = Dict(:all => boundary_condition_slip_wall) # Get the DG approximation space volume_flux = flux_ranocha -solver = DGSEM(polydeg=5, surface_flux=flux_ranocha, - volume_integral=VolumeIntegralFluxDifferencing(volume_flux)) +solver = DGSEM(polydeg = 5, surface_flux = flux_ranocha, + volume_integral = VolumeIntegralFluxDifferencing(volume_flux)) # Get the curved quad mesh from a file # Mapping as described in https://arxiv.org/abs/2012.12040 function mapping(xi_, eta_, zeta_) - # Transform input variables between -1 and 1 onto [0,3] - xi = 1.5 * xi_ + 1.5 - eta = 1.5 * eta_ + 1.5 - zeta = 1.5 * zeta_ + 1.5 - - y = eta + 3/8 * (cos(1.5 * pi * (2 * xi - 3)/3) * - cos(0.5 * pi * (2 * eta - 3)/3) * - cos(0.5 * pi * (2 * zeta - 3)/3)) - - x = xi + 3/8 * (cos(0.5 * pi * (2 * xi - 3)/3) * - cos(2 * pi * (2 * y - 3)/3) * - cos(0.5 * pi * (2 * zeta - 3)/3)) - - z = zeta + 3/8 * (cos(0.5 * pi * (2 * x - 3)/3) * - cos(pi * (2 * y - 3)/3) * - cos(0.5 * pi * (2 * zeta - 3)/3)) - - return SVector(x, y, z) + # Transform input variables between -1 and 1 onto [0,3] + xi = 1.5 * xi_ + 1.5 + eta = 1.5 * eta_ + 1.5 + zeta = 1.5 * zeta_ + 1.5 + + y = eta + + 3 / 8 * (cos(1.5 * pi * (2 * xi - 3) / 3) * + cos(0.5 * pi * (2 * eta - 3) / 3) * + cos(0.5 * pi * (2 * zeta - 3) / 3)) + + x = xi + + 3 / 8 * (cos(0.5 * pi * (2 * xi - 3) / 3) * + cos(2 * pi * (2 * y - 3) / 3) * + cos(0.5 * pi * (2 * zeta - 3) / 3)) + + z = zeta + + 3 / 8 * (cos(0.5 * pi * (2 * x - 3) / 3) * + cos(pi * (2 * y - 3) / 3) * + cos(0.5 * pi * (2 * zeta - 3) / 3)) + + return SVector(x, y, z) end # Unstructured mesh with 48 cells of the cube domain [-1, 1]^3 mesh_file = joinpath(@__DIR__, "cube_unstructured_2.inp") -isfile(mesh_file) || download("https://gist.githubusercontent.com/efaulhaber/b8df0033798e4926dec515fc045e8c2c/raw/b9254cde1d1fb64b6acc8416bc5ccdd77a240227/cube_unstructured_2.inp", - mesh_file) +isfile(mesh_file) || + download("https://gist.githubusercontent.com/efaulhaber/b8df0033798e4926dec515fc045e8c2c/raw/b9254cde1d1fb64b6acc8416bc5ccdd77a240227/cube_unstructured_2.inp", + mesh_file) -mesh = P4estMesh{3}(mesh_file, polydeg=5, - mapping=mapping, - initial_refinement_level=0) +mesh = P4estMesh{3}(mesh_file, polydeg = 5, + mapping = mapping, + initial_refinement_level = 0) # create the semidiscretization object -semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver, boundary_conditions=boundary_conditions) +semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver, + boundary_conditions = boundary_conditions) ############################################################################### # ODE solvers, callbacks etc. @@ -66,15 +69,15 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=100, - save_initial_solution=true, - save_final_solution=true) +save_solution = SaveSolutionCallback(interval = 100, + save_initial_solution = true, + save_final_solution = true) -stepsize_callback = StepsizeCallback(cfl=1.0) +stepsize_callback = StepsizeCallback(cfl = 1.0) callbacks = CallbackSet(summary_callback, analysis_callback, @@ -85,7 +88,7 @@ callbacks = CallbackSet(summary_callback, ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/p4est_3d_dgsem/elixir_euler_free_stream.jl b/examples/p4est_3d_dgsem/elixir_euler_free_stream.jl index 3450adfe861..24a781ca59e 100644 --- a/examples/p4est_3d_dgsem/elixir_euler_free_stream.jl +++ b/examples/p4est_3d_dgsem/elixir_euler_free_stream.jl @@ -10,70 +10,75 @@ equations = CompressibleEulerEquations3D(1.4) initial_condition = initial_condition_constant -boundary_conditions = Dict( - :all => BoundaryConditionDirichlet(initial_condition) -) +boundary_conditions = Dict(:all => BoundaryConditionDirichlet(initial_condition)) # Solver with polydeg=4 to ensure free stream preservation (FSP) on non-conforming meshes. # The polydeg of the solver must be at least twice as big as the polydeg of the mesh. # See https://doi.org/10.1007/s10915-018-00897-9, Section 6. -solver = DGSEM(polydeg=4, surface_flux=flux_lax_friedrichs, - volume_integral=VolumeIntegralWeakForm()) +solver = DGSEM(polydeg = 4, surface_flux = flux_lax_friedrichs, + volume_integral = VolumeIntegralWeakForm()) # Mapping as described in https://arxiv.org/abs/2012.12040 but with less warping. # The mapping will be interpolated at tree level, and then refined without changing # the geometry interpolant. This can yield problematic geometries if the unrefined mesh # is not fine enough. function mapping(xi_, eta_, zeta_) - # Transform input variables between -1 and 1 onto [0,3] - xi = 1.5 * xi_ + 1.5 - eta = 1.5 * eta_ + 1.5 - zeta = 1.5 * zeta_ + 1.5 - - y = eta + 1/6 * (cos(1.5 * pi * (2 * xi - 3)/3) * - cos(0.5 * pi * (2 * eta - 3)/3) * - cos(0.5 * pi * (2 * zeta - 3)/3)) - - x = xi + 1/6 * (cos(0.5 * pi * (2 * xi - 3)/3) * - cos(2 * pi * (2 * y - 3)/3) * - cos(0.5 * pi * (2 * zeta - 3)/3)) - - z = zeta + 1/6 * (cos(0.5 * pi * (2 * x - 3)/3) * - cos(pi * (2 * y - 3)/3) * - cos(0.5 * pi * (2 * zeta - 3)/3)) - - return SVector(x, y, z) + # Transform input variables between -1 and 1 onto [0,3] + xi = 1.5 * xi_ + 1.5 + eta = 1.5 * eta_ + 1.5 + zeta = 1.5 * zeta_ + 1.5 + + y = eta + + 1 / 6 * (cos(1.5 * pi * (2 * xi - 3) / 3) * + cos(0.5 * pi * (2 * eta - 3) / 3) * + cos(0.5 * pi * (2 * zeta - 3) / 3)) + + x = xi + + 1 / 6 * (cos(0.5 * pi * (2 * xi - 3) / 3) * + cos(2 * pi * (2 * y - 3) / 3) * + cos(0.5 * pi * (2 * zeta - 3) / 3)) + + z = zeta + + 1 / 6 * (cos(0.5 * pi * (2 * x - 3) / 3) * + cos(pi * (2 * y - 3) / 3) * + cos(0.5 * pi * (2 * zeta - 3) / 3)) + + return SVector(x, y, z) end # Unstructured mesh with 68 cells of the cube domain [-1, 1]^3 mesh_file = joinpath(@__DIR__, "cube_unstructured_1.inp") -isfile(mesh_file) || download("https://gist.githubusercontent.com/efaulhaber/d45c8ac1e248618885fa7cc31a50ab40/raw/37fba24890ab37cfa49c39eae98b44faf4502882/cube_unstructured_1.inp", - mesh_file) +isfile(mesh_file) || + download("https://gist.githubusercontent.com/efaulhaber/d45c8ac1e248618885fa7cc31a50ab40/raw/37fba24890ab37cfa49c39eae98b44faf4502882/cube_unstructured_1.inp", + mesh_file) # Mesh polydeg of 2 (half the solver polydeg) to ensure FSP (see above). -mesh = P4estMesh{3}(mesh_file, polydeg=2, - mapping=mapping, - initial_refinement_level=0) +mesh = P4estMesh{3}(mesh_file, polydeg = 2, + mapping = mapping, + initial_refinement_level = 0) # Refine bottom left quadrant of each second tree to level 2 function refine_fn(p8est, which_tree, quadrant) - quadrant_obj = unsafe_load(quadrant) - if iseven(convert(Int, which_tree)) && quadrant_obj.x == 0 && quadrant_obj.y == 0 && quadrant_obj.z == 0 && quadrant_obj.level < 2 - # return true (refine) - return Cint(1) - else - # return false (don't refine) - return Cint(0) - end + quadrant_obj = unsafe_load(quadrant) + if iseven(convert(Int, which_tree)) && quadrant_obj.x == 0 && quadrant_obj.y == 0 && + quadrant_obj.z == 0 && quadrant_obj.level < 2 + # return true (refine) + return Cint(1) + else + # return false (don't refine) + return Cint(0) + end end # Refine recursively until each bottom left quadrant of every second tree has level 2. # The mesh will be rebalanced before the simulation starts. -refine_fn_c = @cfunction(refine_fn, Cint, (Ptr{Trixi.p8est_t}, Ptr{Trixi.p4est_topidx_t}, Ptr{Trixi.p8est_quadrant_t})) +refine_fn_c = @cfunction(refine_fn, Cint, + (Ptr{Trixi.p8est_t}, Ptr{Trixi.p4est_topidx_t}, + Ptr{Trixi.p8est_quadrant_t})) Trixi.refine_p4est!(mesh.p4est, true, refine_fn_c, C_NULL) -semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver, boundary_conditions=boundary_conditions) - +semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver, + boundary_conditions = boundary_conditions) ############################################################################### # ODE solvers, callbacks etc. @@ -84,27 +89,26 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=100, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 100, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) -stepsize_callback = StepsizeCallback(cfl=1.2) +stepsize_callback = StepsizeCallback(cfl = 1.2) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, save_solution, stepsize_callback) - ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/p4est_3d_dgsem/elixir_euler_free_stream_extruded.jl b/examples/p4est_3d_dgsem/elixir_euler_free_stream_extruded.jl index 630a269b4a1..f56fe3a429d 100644 --- a/examples/p4est_3d_dgsem/elixir_euler_free_stream_extruded.jl +++ b/examples/p4est_3d_dgsem/elixir_euler_free_stream_extruded.jl @@ -10,12 +10,10 @@ equations = CompressibleEulerEquations3D(1.4) initial_condition = initial_condition_constant -boundary_conditions = Dict( - :all => BoundaryConditionDirichlet(initial_condition) -) +boundary_conditions = Dict(:all => BoundaryConditionDirichlet(initial_condition)) -solver = DGSEM(polydeg=3, surface_flux=flux_lax_friedrichs, - volume_integral=VolumeIntegralWeakForm()) +solver = DGSEM(polydeg = 3, surface_flux = flux_lax_friedrichs, + volume_integral = VolumeIntegralWeakForm()) # Mapping as described in https://arxiv.org/abs/2012.12040 but reduced to 2D. # This particular mesh is unstructured in the yz-plane, but extruded in x-direction. @@ -23,47 +21,52 @@ solver = DGSEM(polydeg=3, surface_flux=flux_lax_friedrichs, # in x-direction to ensure free stream preservation on a non-conforming mesh. # See https://doi.org/10.1007/s10915-018-00897-9, Section 6. function mapping(xi, eta_, zeta_) - # Transform input variables between -1 and 1 onto [0,3] - eta = 1.5 * eta_ + 1.5 - zeta = 1.5 * zeta_ + 1.5 + # Transform input variables between -1 and 1 onto [0,3] + eta = 1.5 * eta_ + 1.5 + zeta = 1.5 * zeta_ + 1.5 - z = zeta + 1/6 * (cos(1.5 * pi * (2 * eta - 3)/3) * - cos(0.5 * pi * (2 * zeta - 3)/3)) + z = zeta + + 1 / 6 * (cos(1.5 * pi * (2 * eta - 3) / 3) * + cos(0.5 * pi * (2 * zeta - 3) / 3)) - y = eta + 1/6 * (cos(0.5 * pi * (2 * eta - 3)/3) * - cos(2 * pi * (2 * z - 3)/3)) + y = eta + 1 / 6 * (cos(0.5 * pi * (2 * eta - 3) / 3) * + cos(2 * pi * (2 * z - 3) / 3)) - return SVector(xi, y, z) + return SVector(xi, y, z) end # Unstructured mesh with 48 cells of the cube domain [-1, 1]^3 mesh_file = joinpath(@__DIR__, "cube_unstructured_2.inp") -isfile(mesh_file) || download("https://gist.githubusercontent.com/efaulhaber/b8df0033798e4926dec515fc045e8c2c/raw/b9254cde1d1fb64b6acc8416bc5ccdd77a240227/cube_unstructured_2.inp", - mesh_file) +isfile(mesh_file) || + download("https://gist.githubusercontent.com/efaulhaber/b8df0033798e4926dec515fc045e8c2c/raw/b9254cde1d1fb64b6acc8416bc5ccdd77a240227/cube_unstructured_2.inp", + mesh_file) -mesh = P4estMesh{3}(mesh_file, polydeg=3, - mapping=mapping, - initial_refinement_level=0) +mesh = P4estMesh{3}(mesh_file, polydeg = 3, + mapping = mapping, + initial_refinement_level = 0) # Refine quadrants in y-direction of each tree at one edge to level 2 function refine_fn(p8est, which_tree, quadrant) - quadrant_obj = unsafe_load(quadrant) - if convert(Int, which_tree) < 4 && quadrant_obj.x == 0 && quadrant_obj.y == 0 && quadrant_obj.level < 2 - # return true (refine) - return Cint(1) - else - # return false (don't refine) - return Cint(0) - end + quadrant_obj = unsafe_load(quadrant) + if convert(Int, which_tree) < 4 && quadrant_obj.x == 0 && quadrant_obj.y == 0 && + quadrant_obj.level < 2 + # return true (refine) + return Cint(1) + else + # return false (don't refine) + return Cint(0) + end end # Refine recursively until each desired quadrant has level 2. # The mesh will be rebalanced before the simulation starts. -refine_fn_c = @cfunction(refine_fn, Cint, (Ptr{Trixi.p8est_t}, Ptr{Trixi.p4est_topidx_t}, Ptr{Trixi.p8est_quadrant_t})) +refine_fn_c = @cfunction(refine_fn, Cint, + (Ptr{Trixi.p8est_t}, Ptr{Trixi.p4est_topidx_t}, + Ptr{Trixi.p8est_quadrant_t})) Trixi.refine_p4est!(mesh.p4est, true, refine_fn_c, C_NULL) -semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver, boundary_conditions=boundary_conditions) - +semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver, + boundary_conditions = boundary_conditions) ############################################################################### # ODE solvers, callbacks etc. @@ -74,30 +77,29 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_restart = SaveRestartCallback(interval=100, - save_final_restart=true) +save_restart = SaveRestartCallback(interval = 100, + save_final_restart = true) -save_solution = SaveSolutionCallback(interval=100, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 100, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) -stepsize_callback = StepsizeCallback(cfl=1.2) +stepsize_callback = StepsizeCallback(cfl = 1.2) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, save_restart, save_solution, stepsize_callback) - ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), #maxiters=1, - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), #maxiters=1, + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/p4est_3d_dgsem/elixir_euler_sedov.jl b/examples/p4est_3d_dgsem/elixir_euler_sedov.jl index 6fa285b5565..8df95a3cc21 100644 --- a/examples/p4est_3d_dgsem/elixir_euler_sedov.jl +++ b/examples/p4est_3d_dgsem/elixir_euler_sedov.jl @@ -14,28 +14,29 @@ The Sedov blast wave setup based on Flash - https://flash.rochester.edu/site/flashcode/user_support/flash_ug_devel/node187.html#SECTION010114000000000000000 with smaller strength of the initial discontinuity. """ -function initial_condition_medium_sedov_blast_wave(x, t, equations::CompressibleEulerEquations3D) - # Set up polar coordinates - inicenter = SVector(0.0, 0.0, 0.0) - x_norm = x[1] - inicenter[1] - y_norm = x[2] - inicenter[2] - z_norm = x[3] - inicenter[3] - r = sqrt(x_norm^2 + y_norm^2 + z_norm^2) - - # Setup based on https://flash.rochester.edu/site/flashcode/user_support/flash_ug_devel/node187.html#SECTION010114000000000000000 - r0 = 0.21875 # = 3.5 * smallest dx (for domain length=4 and max-ref=6) - E = 1.0 - p0_inner = 3 * (equations.gamma - 1) * E / (4 * pi * r0^2) - p0_outer = 1.0e-3 - - # Calculate primitive variables - rho = 1.0 - v1 = 0.0 - v2 = 0.0 - v3 = 0.0 - p = r > r0 ? p0_outer : p0_inner - - return prim2cons(SVector(rho, v1, v2, v3, p), equations) +function initial_condition_medium_sedov_blast_wave(x, t, + equations::CompressibleEulerEquations3D) + # Set up polar coordinates + inicenter = SVector(0.0, 0.0, 0.0) + x_norm = x[1] - inicenter[1] + y_norm = x[2] - inicenter[2] + z_norm = x[3] - inicenter[3] + r = sqrt(x_norm^2 + y_norm^2 + z_norm^2) + + # Setup based on https://flash.rochester.edu/site/flashcode/user_support/flash_ug_devel/node187.html#SECTION010114000000000000000 + r0 = 0.21875 # = 3.5 * smallest dx (for domain length=4 and max-ref=6) + E = 1.0 + p0_inner = 3 * (equations.gamma - 1) * E / (4 * pi * r0^2) + p0_outer = 1.0e-3 + + # Calculate primitive variables + rho = 1.0 + v1 = 0.0 + v2 = 0.0 + v3 = 0.0 + p = r > r0 ? p0_outer : p0_inner + + return prim2cons(SVector(rho, v1, v2, v3, p), equations) end initial_condition = initial_condition_medium_sedov_blast_wave @@ -45,24 +46,25 @@ volume_flux = flux_ranocha polydeg = 5 basis = LobattoLegendreBasis(polydeg) indicator_sc = IndicatorHennemannGassner(equations, basis, - alpha_max=1.0, - alpha_min=0.001, - alpha_smooth=true, - variable=density_pressure) + alpha_max = 1.0, + alpha_min = 0.001, + alpha_smooth = true, + variable = density_pressure) volume_integral = VolumeIntegralShockCapturingHG(indicator_sc; - volume_flux_dg=volume_flux, - volume_flux_fv=surface_flux) + volume_flux_dg = volume_flux, + volume_flux_fv = surface_flux) -solver = DGSEM(polydeg=polydeg, surface_flux=surface_flux, volume_integral=volume_integral) +solver = DGSEM(polydeg = polydeg, surface_flux = surface_flux, + volume_integral = volume_integral) coordinates_min = (-1.0, -1.0, -1.0) -coordinates_max = ( 1.0, 1.0, 1.0) +coordinates_max = (1.0, 1.0, 1.0) trees_per_dimension = (4, 4, 4) mesh = P4estMesh(trees_per_dimension, - polydeg=4, initial_refinement_level=0, - coordinates_min=coordinates_min, coordinates_max=coordinates_max, - periodicity=true) + polydeg = 4, initial_refinement_level = 0, + coordinates_min = coordinates_min, coordinates_max = coordinates_max, + periodicity = true) # create the semi discretization object semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver) @@ -76,15 +78,15 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=100, - save_initial_solution=true, - save_final_solution=true) +save_solution = SaveSolutionCallback(interval = 100, + save_initial_solution = true, + save_final_solution = true) -stepsize_callback = StepsizeCallback(cfl=0.5) +stepsize_callback = StepsizeCallback(cfl = 0.5) callbacks = CallbackSet(summary_callback, analysis_callback, @@ -95,7 +97,7 @@ callbacks = CallbackSet(summary_callback, ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/p4est_3d_dgsem/elixir_euler_source_terms_nonconforming_earth.jl b/examples/p4est_3d_dgsem/elixir_euler_source_terms_nonconforming_earth.jl index c5e349934a2..28a300cd681 100644 --- a/examples/p4est_3d_dgsem/elixir_euler_source_terms_nonconforming_earth.jl +++ b/examples/p4est_3d_dgsem/elixir_euler_source_terms_nonconforming_earth.jl @@ -11,68 +11,68 @@ using LinearAlgebra gamma = 1.4 equations = CompressibleEulerEquations3D(gamma) +function initial_condition_convergence_test_sphere(x, t, + equations::CompressibleEulerEquations3D) + x_scaled = x / 6.371229e6 + t_scaled = t / 6.371229e6 -function initial_condition_convergence_test_sphere(x, t, equations::CompressibleEulerEquations3D) - x_scaled = x / 6.371229e6 - t_scaled = t / 6.371229e6 - - return initial_condition_convergence_test(x_scaled, t_scaled, equations) + return initial_condition_convergence_test(x_scaled, t_scaled, equations) end -@inline function source_terms_convergence_test_sphere(u, x, t, equations::CompressibleEulerEquations3D) - x_scaled = x / 6.371229e6 - t_scaled = t / 6.371229e6 +@inline function source_terms_convergence_test_sphere(u, x, t, + equations::CompressibleEulerEquations3D) + x_scaled = x / 6.371229e6 + t_scaled = t / 6.371229e6 - return source_terms_convergence_test(u, x_scaled, t_scaled, equations) / 6.371229e6 + return source_terms_convergence_test(u, x_scaled, t_scaled, equations) / 6.371229e6 end - -function indicator_test(u::AbstractArray{<:Any,5}, +function indicator_test(u::AbstractArray{<:Any, 5}, mesh, equations, dg::DGSEM, cache; kwargs...) - alpha = zeros(Int, nelements(dg, cache)) - - for element in eachelement(dg, cache) - for k in eachnode(dg), j in eachnode(dg), i in eachnode(dg) - x = Trixi.get_node_coords(cache.elements.node_coordinates, equations, dg, i, j, k, element) - lambda, phi, r = cart_to_sphere(x) - if 0.22 < lambda < 3.3 && 0.45 < phi < 1.3 - alpha[element] = 1 - end + alpha = zeros(Int, nelements(dg, cache)) + + for element in eachelement(dg, cache) + for k in eachnode(dg), j in eachnode(dg), i in eachnode(dg) + x = Trixi.get_node_coords(cache.elements.node_coordinates, equations, dg, i, j, + k, element) + lambda, phi, r = cart_to_sphere(x) + if 0.22 < lambda < 3.3 && 0.45 < phi < 1.3 + alpha[element] = 1 + end + end end - end - return alpha + return alpha end function cart_to_sphere(x) - r = norm(x) - lambda = atan(x[2], x[1]) - if lambda < 0 - lambda += 2 * pi - end - phi = asin(x[3] / r) - - return lambda, phi, r + r = norm(x) + lambda = atan(x[2], x[1]) + if lambda < 0 + lambda += 2 * pi + end + phi = asin(x[3] / r) + + return lambda, phi, r end -function Trixi.get_element_variables!(element_variables, indicator::typeof(indicator_test), ::AMRCallback) - return nothing +function Trixi.get_element_variables!(element_variables, indicator::typeof(indicator_test), + ::AMRCallback) + return nothing end initial_condition = initial_condition_convergence_test_sphere boundary_condition = BoundaryConditionDirichlet(initial_condition) -boundary_conditions = Dict( - :inside => boundary_condition, - :outside => boundary_condition -) +boundary_conditions = Dict(:inside => boundary_condition, + :outside => boundary_condition) surface_flux = flux_hll # Note that a free stream is not preserved if N < 2 * N_geo, where N is the # polydeg of the solver and N_geo is the polydeg of the mesh. # However, the FSP error is negligible in this example. -solver = DGSEM(polydeg=4, surface_flux=surface_flux) +solver = DGSEM(polydeg = 4, surface_flux = surface_flux) # For performance reasons, only one face of the cubed sphere can be used: @@ -87,12 +87,11 @@ solver = DGSEM(polydeg=4, surface_flux=surface_flux) trees_per_cube_face = (6, 2) mesh = Trixi.P4estMeshCubedSphere(trees_per_cube_face..., 6.371229e6, 30000.0, - polydeg=4, initial_refinement_level=0) + polydeg = 4, initial_refinement_level = 0) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver, - source_terms=source_terms_convergence_test_sphere, - boundary_conditions=boundary_conditions) - + source_terms = source_terms_convergence_test_sphere, + boundary_conditions = boundary_conditions) ############################################################################### # ODE solvers, callbacks etc. @@ -103,22 +102,22 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=100, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 100, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) amr_controller = ControllerThreeLevel(semi, indicator_test, - base_level=0, - max_level=1, max_threshold=0.6) + base_level = 0, + max_level = 1, max_threshold = 0.6) amr_callback = AMRCallback(semi, amr_controller, - interval=0, # Only initial refinement - adapt_initial_condition=true, - adapt_initial_condition_only_refine=true) + interval = 0, # Only initial refinement + adapt_initial_condition = true, + adapt_initial_condition_only_refine = true) callbacks = CallbackSet(summary_callback, analysis_callback, @@ -126,12 +125,11 @@ callbacks = CallbackSet(summary_callback, save_solution, amr_callback) - ############################################################################### # run the simulation # Use a Runge-Kutta method with automatic (error based) time step size control -sol = solve(ode, RDPK3SpFSAL49(); abstol=1.0e-6, reltol=1.0e-6, - ode_default_options()..., callback=callbacks); +sol = solve(ode, RDPK3SpFSAL49(); abstol = 1.0e-6, reltol = 1.0e-6, + ode_default_options()..., callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/p4est_3d_dgsem/elixir_euler_source_terms_nonconforming_unstructured_curved.jl b/examples/p4est_3d_dgsem/elixir_euler_source_terms_nonconforming_unstructured_curved.jl index dd394091758..0de22eaea40 100644 --- a/examples/p4est_3d_dgsem/elixir_euler_source_terms_nonconforming_unstructured_curved.jl +++ b/examples/p4est_3d_dgsem/elixir_euler_source_terms_nonconforming_unstructured_curved.jl @@ -11,73 +11,77 @@ equations = CompressibleEulerEquations3D(1.4) initial_condition = initial_condition_convergence_test boundary_condition = BoundaryConditionDirichlet(initial_condition) -boundary_conditions = Dict( - :all => boundary_condition -) +boundary_conditions = Dict(:all => boundary_condition) # Solver with polydeg=4 to ensure free stream preservation (FSP) on non-conforming meshes. # The polydeg of the solver must be at least twice as big as the polydeg of the mesh. # See https://doi.org/10.1007/s10915-018-00897-9, Section 6. -solver = DGSEM(polydeg=4, surface_flux=flux_lax_friedrichs, - volume_integral=VolumeIntegralWeakForm()) +solver = DGSEM(polydeg = 4, surface_flux = flux_lax_friedrichs, + volume_integral = VolumeIntegralWeakForm()) # Mapping as described in https://arxiv.org/abs/2012.12040 but with less warping. # The mapping will be interpolated at tree level, and then refined without changing # the geometry interpolant. The original mapping applied to this unstructured mesh # causes some Jacobians to be negative, which makes the mesh invalid. function mapping(xi, eta, zeta) - # Don't transform input variables between -1 and 1 onto [0,3] to obtain curved boundaries - # xi = 1.5 * xi_ + 1.5 - # eta = 1.5 * eta_ + 1.5 - # zeta = 1.5 * zeta_ + 1.5 - - y = eta + 1/6 * (cos(1.5 * pi * (2 * xi - 3)/3) * - cos(0.5 * pi * (2 * eta - 3)/3) * - cos(0.5 * pi * (2 * zeta - 3)/3)) - - x = xi + 1/6 * (cos(0.5 * pi * (2 * xi - 3)/3) * - cos(2 * pi * (2 * y - 3)/3) * - cos(0.5 * pi * (2 * zeta - 3)/3)) - - z = zeta + 1/6 * (cos(0.5 * pi * (2 * x - 3)/3) * - cos(pi * (2 * y - 3)/3) * - cos(0.5 * pi * (2 * zeta - 3)/3)) - - # Transform the weird deformed cube to be approximately the cube [0,2]^3 - return SVector(x + 1, y + 1, z + 1) + # Don't transform input variables between -1 and 1 onto [0,3] to obtain curved boundaries + # xi = 1.5 * xi_ + 1.5 + # eta = 1.5 * eta_ + 1.5 + # zeta = 1.5 * zeta_ + 1.5 + + y = eta + + 1 / 6 * (cos(1.5 * pi * (2 * xi - 3) / 3) * + cos(0.5 * pi * (2 * eta - 3) / 3) * + cos(0.5 * pi * (2 * zeta - 3) / 3)) + + x = xi + + 1 / 6 * (cos(0.5 * pi * (2 * xi - 3) / 3) * + cos(2 * pi * (2 * y - 3) / 3) * + cos(0.5 * pi * (2 * zeta - 3) / 3)) + + z = zeta + + 1 / 6 * (cos(0.5 * pi * (2 * x - 3) / 3) * + cos(pi * (2 * y - 3) / 3) * + cos(0.5 * pi * (2 * zeta - 3) / 3)) + + # Transform the weird deformed cube to be approximately the cube [0,2]^3 + return SVector(x + 1, y + 1, z + 1) end # Unstructured mesh with 68 cells of the cube domain [-1, 1]^3 mesh_file = joinpath(@__DIR__, "cube_unstructured_1.inp") -isfile(mesh_file) || download("https://gist.githubusercontent.com/efaulhaber/d45c8ac1e248618885fa7cc31a50ab40/raw/37fba24890ab37cfa49c39eae98b44faf4502882/cube_unstructured_1.inp", - mesh_file) +isfile(mesh_file) || + download("https://gist.githubusercontent.com/efaulhaber/d45c8ac1e248618885fa7cc31a50ab40/raw/37fba24890ab37cfa49c39eae98b44faf4502882/cube_unstructured_1.inp", + mesh_file) # Mesh polydeg of 2 (half the solver polydeg) to ensure FSP (see above). -mesh = P4estMesh{3}(mesh_file, polydeg=2, - mapping=mapping, - initial_refinement_level=0) +mesh = P4estMesh{3}(mesh_file, polydeg = 2, + mapping = mapping, + initial_refinement_level = 0) # Refine bottom left quadrant of each tree to level 2 function refine_fn(p8est, which_tree, quadrant) - quadrant_obj = unsafe_load(quadrant) - if quadrant_obj.x == 0 && quadrant_obj.y == 0 && quadrant_obj.z == 0 && quadrant_obj.level < 2 - # return true (refine) - return Cint(1) - else - # return false (don't refine) - return Cint(0) - end + quadrant_obj = unsafe_load(quadrant) + if quadrant_obj.x == 0 && quadrant_obj.y == 0 && quadrant_obj.z == 0 && + quadrant_obj.level < 2 + # return true (refine) + return Cint(1) + else + # return false (don't refine) + return Cint(0) + end end # Refine recursively until each bottom left quadrant of a tree has level 2 # The mesh will be rebalanced before the simulation starts -refine_fn_c = @cfunction(refine_fn, Cint, (Ptr{Trixi.p8est_t}, Ptr{Trixi.p4est_topidx_t}, Ptr{Trixi.p8est_quadrant_t})) +refine_fn_c = @cfunction(refine_fn, Cint, + (Ptr{Trixi.p8est_t}, Ptr{Trixi.p4est_topidx_t}, + Ptr{Trixi.p8est_quadrant_t})) Trixi.refine_p4est!(mesh.p4est, true, refine_fn_c, C_NULL) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver, - source_terms=source_terms_convergence_test, - boundary_conditions=boundary_conditions) - + source_terms = source_terms_convergence_test, + boundary_conditions = boundary_conditions) ############################################################################### # ODE solvers, callbacks etc. @@ -88,27 +92,26 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=100, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 100, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) -stepsize_callback = StepsizeCallback(cfl=0.6) +stepsize_callback = StepsizeCallback(cfl = 0.6) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, save_solution, stepsize_callback) - ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/p4est_3d_dgsem/elixir_euler_source_terms_nonperiodic.jl b/examples/p4est_3d_dgsem/elixir_euler_source_terms_nonperiodic.jl index cd796c33e47..fc5e4da3ceb 100644 --- a/examples/p4est_3d_dgsem/elixir_euler_source_terms_nonperiodic.jl +++ b/examples/p4est_3d_dgsem/elixir_euler_source_terms_nonperiodic.jl @@ -10,31 +10,28 @@ equations = CompressibleEulerEquations3D(1.4) initial_condition = initial_condition_convergence_test boundary_condition = BoundaryConditionDirichlet(initial_condition) -boundary_conditions = Dict( - :x_neg => boundary_condition, - :x_pos => boundary_condition, - :y_neg => boundary_condition, - :y_pos => boundary_condition, - :z_neg => boundary_condition, - :z_pos => boundary_condition -) - -solver = DGSEM(polydeg=3, surface_flux=flux_lax_friedrichs, - volume_integral=VolumeIntegralWeakForm()) +boundary_conditions = Dict(:x_neg => boundary_condition, + :x_pos => boundary_condition, + :y_neg => boundary_condition, + :y_pos => boundary_condition, + :z_neg => boundary_condition, + :z_pos => boundary_condition) + +solver = DGSEM(polydeg = 3, surface_flux = flux_lax_friedrichs, + volume_integral = VolumeIntegralWeakForm()) coordinates_min = (0.0, 0.0, 0.0) coordinates_max = (2.0, 2.0, 2.0) trees_per_dimension = (2, 2, 2) -mesh = P4estMesh(trees_per_dimension, polydeg=1, - coordinates_min=coordinates_min, coordinates_max=coordinates_max, - periodicity=false, initial_refinement_level=1) +mesh = P4estMesh(trees_per_dimension, polydeg = 1, + coordinates_min = coordinates_min, coordinates_max = coordinates_max, + periodicity = false, initial_refinement_level = 1) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver, - source_terms=source_terms_convergence_test, - boundary_conditions=boundary_conditions) - + source_terms = source_terms_convergence_test, + boundary_conditions = boundary_conditions) ############################################################################### # ODE solvers, callbacks etc. @@ -45,27 +42,26 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=100, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 100, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) -stepsize_callback = StepsizeCallback(cfl=0.6) +stepsize_callback = StepsizeCallback(cfl = 0.6) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, save_solution, stepsize_callback) - ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/p4est_3d_dgsem/elixir_euler_source_terms_nonperiodic_hohqmesh.jl b/examples/p4est_3d_dgsem/elixir_euler_source_terms_nonperiodic_hohqmesh.jl index ff101bea8aa..0fa3a28fe8b 100644 --- a/examples/p4est_3d_dgsem/elixir_euler_source_terms_nonperiodic_hohqmesh.jl +++ b/examples/p4est_3d_dgsem/elixir_euler_source_terms_nonperiodic_hohqmesh.jl @@ -11,25 +11,25 @@ equations = CompressibleEulerEquations3D(1.4) initial_condition = initial_condition_convergence_test boundary_condition = BoundaryConditionDirichlet(initial_condition) -boundary_conditions = Dict( :Bottom => boundary_condition, - :Top => boundary_condition, - :Circle => boundary_condition, - :Cut => boundary_condition ) +boundary_conditions = Dict(:Bottom => boundary_condition, + :Top => boundary_condition, + :Circle => boundary_condition, + :Cut => boundary_condition) -solver = DGSEM(polydeg=4, surface_flux=flux_lax_friedrichs) +solver = DGSEM(polydeg = 4, surface_flux = flux_lax_friedrichs) # Unstructured 3D half circle mesh from HOHQMesh default_mesh_file = joinpath(@__DIR__, "abaqus_half_circle_3d.inp") -isfile(default_mesh_file) || download("https://gist.githubusercontent.com/andrewwinters5000/11461efbfb02c42e06aca338b3d0b645/raw/81deeb1ebc4945952c30af5bb75fe222a18d975c/abaqus_half_circle_3d.inp", - default_mesh_file) +isfile(default_mesh_file) || + download("https://gist.githubusercontent.com/andrewwinters5000/11461efbfb02c42e06aca338b3d0b645/raw/81deeb1ebc4945952c30af5bb75fe222a18d975c/abaqus_half_circle_3d.inp", + default_mesh_file) mesh_file = default_mesh_file -mesh = P4estMesh{3}(mesh_file, initial_refinement_level=0) +mesh = P4estMesh{3}(mesh_file, initial_refinement_level = 0) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver, - source_terms=source_terms_convergence_test, - boundary_conditions=boundary_conditions) - + source_terms = source_terms_convergence_test, + boundary_conditions = boundary_conditions) ############################################################################### # ODE solvers, callbacks etc. @@ -40,17 +40,17 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval, - extra_analysis_integrals=(entropy,)) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval, + extra_analysis_integrals = (entropy,)) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=50, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 50, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) -stepsize_callback = StepsizeCallback(cfl=1.0) +stepsize_callback = StepsizeCallback(cfl = 1.0) callbacks = CallbackSet(summary_callback, analysis_callback, @@ -58,12 +58,11 @@ callbacks = CallbackSet(summary_callback, save_solution, stepsize_callback); - ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/p4est_3d_dgsem/elixir_mhd_alfven_wave_nonconforming.jl b/examples/p4est_3d_dgsem/elixir_mhd_alfven_wave_nonconforming.jl index 8fe96ae3dec..6a62368ef99 100644 --- a/examples/p4est_3d_dgsem/elixir_mhd_alfven_wave_nonconforming.jl +++ b/examples/p4est_3d_dgsem/elixir_mhd_alfven_wave_nonconforming.jl @@ -5,40 +5,43 @@ using Trixi ############################################################################### # semidiscretization of the compressible ideal GLM-MHD equations -equations = IdealGlmMhdEquations3D(5/3) +equations = IdealGlmMhdEquations3D(5 / 3) initial_condition = initial_condition_convergence_test volume_flux = (flux_hindenlang_gassner, flux_nonconservative_powell) -solver = DGSEM(polydeg=3, surface_flux=(flux_hll, flux_nonconservative_powell), - volume_integral=VolumeIntegralFluxDifferencing(volume_flux)) +solver = DGSEM(polydeg = 3, surface_flux = (flux_hll, flux_nonconservative_powell), + volume_integral = VolumeIntegralFluxDifferencing(volume_flux)) coordinates_min = (-1.0, -1.0, -1.0) -coordinates_max = ( 1.0, 1.0, 1.0) +coordinates_max = (1.0, 1.0, 1.0) # Create P4estMesh with 2 x 2 x 2 trees trees_per_dimension = (2, 2, 2) mesh = P4estMesh(trees_per_dimension, - polydeg=3, initial_refinement_level=2, - coordinates_min=coordinates_min, coordinates_max=coordinates_max, - periodicity=true) + polydeg = 3, initial_refinement_level = 2, + coordinates_min = coordinates_min, coordinates_max = coordinates_max, + periodicity = true) # OBS! Workaround to add a refinement patch after mesh is constructed # Refine bottom left quadrant of each tree to level 4 function refine_fn(p8est, which_tree, quadrant) - quadrant_obj = unsafe_load(quadrant) - if quadrant_obj.x == 0 && quadrant_obj.y == 0 && quadrant_obj.z == 0 && quadrant_obj.level < 4 - # return true (refine) - return Cint(1) - else - # return false (don't refine) - return Cint(0) - end + quadrant_obj = unsafe_load(quadrant) + if quadrant_obj.x == 0 && quadrant_obj.y == 0 && quadrant_obj.z == 0 && + quadrant_obj.level < 4 + # return true (refine) + return Cint(1) + else + # return false (don't refine) + return Cint(0) + end end # Refine recursively until each bottom left quadrant of a tree has level 4 # The mesh will be rebalanced before the simulation starts -refine_fn_c = @cfunction(refine_fn, Cint, (Ptr{Trixi.p8est_t}, Ptr{Trixi.p4est_topidx_t}, Ptr{Trixi.p8est_quadrant_t})) +refine_fn_c = @cfunction(refine_fn, Cint, + (Ptr{Trixi.p8est_t}, Ptr{Trixi.p4est_topidx_t}, + Ptr{Trixi.p8est_quadrant_t})) Trixi.refine_p4est!(mesh.p4est, true, refine_fn_c, C_NULL) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver) @@ -52,18 +55,18 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=100, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 100, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) cfl = 1.0 -stepsize_callback = StepsizeCallback(cfl=cfl) +stepsize_callback = StepsizeCallback(cfl = cfl) -glm_speed_callback = GlmSpeedCallback(glm_scale=0.5, cfl=cfl) +glm_speed_callback = GlmSpeedCallback(glm_scale = 0.5, cfl = cfl) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, @@ -71,11 +74,10 @@ callbacks = CallbackSet(summary_callback, stepsize_callback, glm_speed_callback) - ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/p4est_3d_dgsem/elixir_mhd_shockcapturing_amr.jl b/examples/p4est_3d_dgsem/elixir_mhd_shockcapturing_amr.jl index fc95d427abb..3941a40b2e4 100644 --- a/examples/p4est_3d_dgsem/elixir_mhd_shockcapturing_amr.jl +++ b/examples/p4est_3d_dgsem/elixir_mhd_shockcapturing_amr.jl @@ -17,71 +17,74 @@ Weak magnetic blast wave setup taken from Section 6.1 of the paper: [doi: 10.1016/j.jcp.2021.110580](https://doi.org/10.1016/j.jcp.2021.110580) """ function initial_condition_blast_wave(x, t, equations::IdealGlmMhdEquations3D) - # Center of the blast wave is selected for the domain [0, 3]^3 - inicenter = (1.5, 1.5, 1.5) - x_norm = x[1] - inicenter[1] - y_norm = x[2] - inicenter[2] - z_norm = x[3] - inicenter[3] - r = sqrt(x_norm^2 + y_norm^2 + z_norm^2) - - delta_0 = 0.1 - r_0 = 0.3 - lambda = exp(5.0 / delta_0 * (r - r_0)) - - prim_inner = SVector(1.2, 0.1, 0.0, 0.1, 0.9, 1.0, 1.0, 1.0, 0.0) - prim_outer = SVector(1.2, 0.2, -0.4, 0.2, 0.3, 1.0, 1.0, 1.0, 0.0) - prim_vars = (prim_inner + lambda * prim_outer) / (1.0 + lambda) - - return prim2cons(prim_vars, equations) + # Center of the blast wave is selected for the domain [0, 3]^3 + inicenter = (1.5, 1.5, 1.5) + x_norm = x[1] - inicenter[1] + y_norm = x[2] - inicenter[2] + z_norm = x[3] - inicenter[3] + r = sqrt(x_norm^2 + y_norm^2 + z_norm^2) + + delta_0 = 0.1 + r_0 = 0.3 + lambda = exp(5.0 / delta_0 * (r - r_0)) + + prim_inner = SVector(1.2, 0.1, 0.0, 0.1, 0.9, 1.0, 1.0, 1.0, 0.0) + prim_outer = SVector(1.2, 0.2, -0.4, 0.2, 0.3, 1.0, 1.0, 1.0, 0.0) + prim_vars = (prim_inner + lambda * prim_outer) / (1.0 + lambda) + + return prim2cons(prim_vars, equations) end initial_condition = initial_condition_blast_wave surface_flux = (flux_lax_friedrichs, flux_nonconservative_powell) -volume_flux = (flux_hindenlang_gassner, flux_nonconservative_powell) +volume_flux = (flux_hindenlang_gassner, flux_nonconservative_powell) polydeg = 3 basis = LobattoLegendreBasis(polydeg) indicator_sc = IndicatorHennemannGassner(equations, basis, - alpha_max=0.5, - alpha_min=0.001, - alpha_smooth=true, - variable=density_pressure) + alpha_max = 0.5, + alpha_min = 0.001, + alpha_smooth = true, + variable = density_pressure) volume_integral = VolumeIntegralShockCapturingHG(indicator_sc; - volume_flux_dg=volume_flux, - volume_flux_fv=surface_flux) - -solver = DGSEM(polydeg=polydeg, surface_flux=surface_flux, volume_integral=volume_integral) + volume_flux_dg = volume_flux, + volume_flux_fv = surface_flux) +solver = DGSEM(polydeg = polydeg, surface_flux = surface_flux, + volume_integral = volume_integral) # Mapping as described in https://arxiv.org/abs/2012.12040 but with slightly less warping. # The mapping will be interpolated at tree level, and then refined without changing # the geometry interpolant. function mapping(xi_, eta_, zeta_) - # Transform input variables between -1 and 1 onto [0,3] - xi = 1.5 * xi_ + 1.5 - eta = 1.5 * eta_ + 1.5 - zeta = 1.5 * zeta_ + 1.5 - - y = eta + 3/11 * (cos(1.5 * pi * (2 * xi - 3)/3) * - cos(0.5 * pi * (2 * eta - 3)/3) * - cos(0.5 * pi * (2 * zeta - 3)/3)) - - x = xi + 3/11 * (cos(0.5 * pi * (2 * xi - 3)/3) * - cos(2 * pi * (2 * y - 3)/3) * - cos(0.5 * pi * (2 * zeta - 3)/3)) - - z = zeta + 3/11 * (cos(0.5 * pi * (2 * x - 3)/3) * - cos(pi * (2 * y - 3)/3) * - cos(0.5 * pi * (2 * zeta - 3)/3)) - - return SVector(x, y, z) + # Transform input variables between -1 and 1 onto [0,3] + xi = 1.5 * xi_ + 1.5 + eta = 1.5 * eta_ + 1.5 + zeta = 1.5 * zeta_ + 1.5 + + y = eta + + 3 / 11 * (cos(1.5 * pi * (2 * xi - 3) / 3) * + cos(0.5 * pi * (2 * eta - 3) / 3) * + cos(0.5 * pi * (2 * zeta - 3) / 3)) + + x = xi + + 3 / 11 * (cos(0.5 * pi * (2 * xi - 3) / 3) * + cos(2 * pi * (2 * y - 3) / 3) * + cos(0.5 * pi * (2 * zeta - 3) / 3)) + + z = zeta + + 3 / 11 * (cos(0.5 * pi * (2 * x - 3) / 3) * + cos(pi * (2 * y - 3) / 3) * + cos(0.5 * pi * (2 * zeta - 3) / 3)) + + return SVector(x, y, z) end trees_per_dimension = (2, 2, 2) mesh = P4estMesh(trees_per_dimension, - polydeg=3, - mapping=mapping, - initial_refinement_level=2, - periodicity=true) + polydeg = 3, + mapping = mapping, + initial_refinement_level = 2, + periodicity = true) # create the semi discretization object semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver) @@ -95,24 +98,24 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) amr_indicator = IndicatorLöhner(semi, - variable=density_pressure) + variable = density_pressure) amr_controller = ControllerThreeLevel(semi, amr_indicator, - base_level=2, - max_level =4, max_threshold=0.15) + base_level = 2, + max_level = 4, max_threshold = 0.15) amr_callback = AMRCallback(semi, amr_controller, - interval=5, - adapt_initial_condition=true, - adapt_initial_condition_only_refine=true) + interval = 5, + adapt_initial_condition = true, + adapt_initial_condition_only_refine = true) cfl = 1.4 -stepsize_callback = StepsizeCallback(cfl=cfl) +stepsize_callback = StepsizeCallback(cfl = cfl) -glm_speed_callback = GlmSpeedCallback(glm_scale=0.5, cfl=cfl) +glm_speed_callback = GlmSpeedCallback(glm_scale = 0.5, cfl = cfl) callbacks = CallbackSet(summary_callback, analysis_callback, @@ -121,11 +124,10 @@ callbacks = CallbackSet(summary_callback, stepsize_callback, glm_speed_callback) - ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/p4est_3d_dgsem/elixir_navierstokes_convergence.jl b/examples/p4est_3d_dgsem/elixir_navierstokes_convergence.jl index 0109e58dfb3..c640b255b05 100644 --- a/examples/p4est_3d_dgsem/elixir_navierstokes_convergence.jl +++ b/examples/p4est_3d_dgsem/elixir_navierstokes_convergence.jl @@ -8,240 +8,241 @@ prandtl_number() = 0.72 mu() = 0.01 equations = CompressibleEulerEquations3D(1.4) -equations_parabolic = CompressibleNavierStokesDiffusion3D(equations, mu=mu(), Prandtl=prandtl_number(), - gradient_variables=GradientVariablesPrimitive()) +equations_parabolic = CompressibleNavierStokesDiffusion3D(equations, mu = mu(), + Prandtl = prandtl_number(), + gradient_variables = GradientVariablesPrimitive()) # Create DG solver with polynomial degree = 3 and (local) Lax-Friedrichs/Rusanov flux as surface flux -solver = DGSEM(polydeg=3, surface_flux=flux_lax_friedrichs, - volume_integral=VolumeIntegralWeakForm()) +solver = DGSEM(polydeg = 3, surface_flux = flux_lax_friedrichs, + volume_integral = VolumeIntegralWeakForm()) coordinates_min = (-1.0, -1.0, -1.0) # minimum coordinates (min(x), min(y), min(z)) -coordinates_max = ( 1.0, 1.0, 1.0) # maximum coordinates (max(x), max(y), max(z)) +coordinates_max = (1.0, 1.0, 1.0) # maximum coordinates (max(x), max(y), max(z)) trees_per_dimension = (2, 2, 2) -mesh = P4estMesh(trees_per_dimension, polydeg=3, - coordinates_min=coordinates_min, coordinates_max=coordinates_max, - periodicity=(true, false, true), initial_refinement_level=2) +mesh = P4estMesh(trees_per_dimension, polydeg = 3, + coordinates_min = coordinates_min, coordinates_max = coordinates_max, + periodicity = (true, false, true), initial_refinement_level = 2) # Note: the initial condition cannot be specialized to `CompressibleNavierStokesDiffusion3D` # since it is called by both the parabolic solver (which passes in `CompressibleNavierStokesDiffusion3D`) # and by the initial condition (which passes in `CompressibleEulerEquations3D`). # This convergence test setup was originally derived by Andrew Winters (@andrewwinters5000) function initial_condition_navier_stokes_convergence_test(x, t, equations) - # Constants. OBS! Must match those in `source_terms_navier_stokes_convergence_test` - c = 2.0 - A1 = 0.5 - A2 = 1.0 - A3 = 0.5 - - # Convenience values for trig. functions - pi_x = pi * x[1] - pi_y = pi * x[2] - pi_z = pi * x[3] - pi_t = pi * t - - rho = c + A1 * sin(pi_x) * cos(pi_y) * sin(pi_z) * cos(pi_t) - v1 = A2 * sin(pi_x) * log(x[2] + 2.0) * (1.0 - exp(-A3 * (x[2] - 1.0))) * sin(pi_z) * cos(pi_t) - v2 = v1 - v3 = v1 - p = rho^2 - - return prim2cons(SVector(rho, v1, v2, v3, p), equations) + # Constants. OBS! Must match those in `source_terms_navier_stokes_convergence_test` + c = 2.0 + A1 = 0.5 + A2 = 1.0 + A3 = 0.5 + + # Convenience values for trig. functions + pi_x = pi * x[1] + pi_y = pi * x[2] + pi_z = pi * x[3] + pi_t = pi * t + + rho = c + A1 * sin(pi_x) * cos(pi_y) * sin(pi_z) * cos(pi_t) + v1 = A2 * sin(pi_x) * log(x[2] + 2.0) * (1.0 - exp(-A3 * (x[2] - 1.0))) * sin(pi_z) * + cos(pi_t) + v2 = v1 + v3 = v1 + p = rho^2 + + return prim2cons(SVector(rho, v1, v2, v3, p), equations) end @inline function source_terms_navier_stokes_convergence_test(u, x, t, equations) - # TODO: parabolic - # we currently need to hardcode these parameters until we fix the "combined equation" issue - # see also https://github.com/trixi-framework/Trixi.jl/pull/1160 - inv_gamma_minus_one = inv(equations.gamma - 1) - Pr = prandtl_number() - mu_ = mu() - - # Constants. OBS! Must match those in `initial_condition_navier_stokes_convergence_test` - c = 2.0 - A1 = 0.5 - A2 = 1.0 - A3 = 0.5 - - # Convenience values for trig. functions - pi_x = pi * x[1] - pi_y = pi * x[2] - pi_z = pi * x[3] - pi_t = pi * t - - # Define auxiliary functions for the strange function of the y variable - # to make expressions easier to read - g = log(x[2] + 2.0) * (1.0 - exp(-A3 * (x[2] - 1.0))) - g_y = ( A3 * log(x[2] + 2.0) * exp(-A3 * (x[2] - 1.0)) - + (1.0 - exp(-A3 * (x[2] - 1.0))) / (x[2] + 2.0) ) - g_yy = ( 2.0 * A3 * exp(-A3 * (x[2] - 1.0)) / (x[2] + 2.0) - - (1.0 - exp(-A3 * (x[2] - 1.0))) / ((x[2] + 2.0)^2) - - A3^2 * log(x[2] + 2.0) * exp(-A3 * (x[2] - 1.0)) ) - - # Density and its derivatives - rho = c + A1 * sin(pi_x) * cos(pi_y) * sin(pi_z) * cos(pi_t) - rho_t = -pi * A1 * sin(pi_x) * cos(pi_y) * sin(pi_z) * sin(pi_t) - rho_x = pi * A1 * cos(pi_x) * cos(pi_y) * sin(pi_z) * cos(pi_t) - rho_y = -pi * A1 * sin(pi_x) * sin(pi_y) * sin(pi_z) * cos(pi_t) - rho_z = pi * A1 * sin(pi_x) * cos(pi_y) * cos(pi_z) * cos(pi_t) - rho_xx = -pi^2 * (rho - c) - rho_yy = -pi^2 * (rho - c) - rho_zz = -pi^2 * (rho - c) - - # Velocities and their derivatives - # v1 terms - v1 = A2 * sin(pi_x) * g * sin(pi_z) * cos(pi_t) - v1_t = -pi * A2 * sin(pi_x) * g * sin(pi_z) * sin(pi_t) - v1_x = pi * A2 * cos(pi_x) * g * sin(pi_z) * cos(pi_t) - v1_y = A2 * sin(pi_x) * g_y * sin(pi_z) * cos(pi_t) - v1_z = pi * A2 * sin(pi_x) * g * cos(pi_z) * cos(pi_t) - v1_xx = -pi^2 * v1 - v1_yy = A2 * sin(pi_x) * g_yy * sin(pi_z) * cos(pi_t) - v1_zz = -pi^2 * v1 - v1_xy = pi * A2 * cos(pi_x) * g_y * sin(pi_z) * cos(pi_t) - v1_xz = pi^2 * A2 * cos(pi_x) * g * cos(pi_z) * cos(pi_t) - v1_yz = pi * A2 * sin(pi_x) * g_y * cos(pi_z) * cos(pi_t) - # v2 terms (simplifies from ansatz) - v2 = v1 - v2_t = v1_t - v2_x = v1_x - v2_y = v1_y - v2_z = v1_z - v2_xx = v1_xx - v2_yy = v1_yy - v2_zz = v1_zz - v2_xy = v1_xy - v2_yz = v1_yz - # v3 terms (simplifies from ansatz) - v3 = v1 - v3_t = v1_t - v3_x = v1_x - v3_y = v1_y - v3_z = v1_z - v3_xx = v1_xx - v3_yy = v1_yy - v3_zz = v1_zz - v3_xz = v1_xz - v3_yz = v1_yz - - # Pressure and its derivatives - p = rho^2 - p_t = 2.0 * rho * rho_t - p_x = 2.0 * rho * rho_x - p_y = 2.0 * rho * rho_y - p_z = 2.0 * rho * rho_z - - # Total energy and its derivatives; simiplifies from ansatz that v2 = v1 and v3 = v1 - E = p * inv_gamma_minus_one + 1.5 * rho * v1^2 - E_t = p_t * inv_gamma_minus_one + 1.5 * rho_t * v1^2 + 3.0 * rho * v1 * v1_t - E_x = p_x * inv_gamma_minus_one + 1.5 * rho_x * v1^2 + 3.0 * rho * v1 * v1_x - E_y = p_y * inv_gamma_minus_one + 1.5 * rho_y * v1^2 + 3.0 * rho * v1 * v1_y - E_z = p_z * inv_gamma_minus_one + 1.5 * rho_z * v1^2 + 3.0 * rho * v1 * v1_z - - # Divergence of Fick's law ∇⋅∇q = kappa ∇⋅∇T; simplifies because p = rho², so T = p/rho = rho - kappa = equations.gamma * inv_gamma_minus_one / Pr - q_xx = kappa * rho_xx # kappa T_xx - q_yy = kappa * rho_yy # kappa T_yy - q_zz = kappa * rho_zz # kappa T_zz - - # Stress tensor and its derivatives (exploit symmetry) - tau11 = 4.0 / 3.0 * v1_x - 2.0 / 3.0 * (v2_y + v3_z) - tau12 = v1_y + v2_x - tau13 = v1_z + v3_x - tau22 = 4.0 / 3.0 * v2_y - 2.0 / 3.0 * (v1_x + v3_z) - tau23 = v2_z + v3_y - tau33 = 4.0 / 3.0 * v3_z - 2.0 / 3.0 * (v1_x + v2_y) - - tau11_x = 4.0 / 3.0 * v1_xx - 2.0 / 3.0 * (v2_xy + v3_xz) - tau12_x = v1_xy + v2_xx - tau13_x = v1_xz + v3_xx - - tau12_y = v1_yy + v2_xy - tau22_y = 4.0 / 3.0 * v2_yy - 2.0 / 3.0 * (v1_xy + v3_yz) - tau23_y = v2_yz + v3_yy - - tau13_z = v1_zz + v3_xz - tau23_z = v2_zz + v3_yz - tau33_z = 4.0 / 3.0 * v3_zz - 2.0 / 3.0 * (v1_xz + v2_yz) - - # Compute the source terms - # Density equation - du1 = ( rho_t + rho_x * v1 + rho * v1_x - + rho_y * v2 + rho * v2_y - + rho_z * v3 + rho * v3_z ) - # x-momentum equation - du2 = ( rho_t * v1 + rho * v1_t + p_x + rho_x * v1^2 - + 2.0 * rho * v1 * v1_x - + rho_y * v1 * v2 - + rho * v1_y * v2 - + rho * v1 * v2_y - + rho_z * v1 * v3 - + rho * v1_z * v3 - + rho * v1 * v3_z - - mu_ * (tau11_x + tau12_y + tau13_z) ) - # y-momentum equation - du3 = ( rho_t * v2 + rho * v2_t + p_y + rho_x * v1 * v2 - + rho * v1_x * v2 - + rho * v1 * v2_x - + rho_y * v2^2 - + 2.0 * rho * v2 * v2_y - + rho_z * v2 * v3 - + rho * v2_z * v3 - + rho * v2 * v3_z - - mu_ * (tau12_x + tau22_y + tau23_z) ) - # z-momentum equation - du4 = ( rho_t * v3 + rho * v3_t + p_z + rho_x * v1 * v3 - + rho * v1_x * v3 - + rho * v1 * v3_x - + rho_y * v2 * v3 - + rho * v2_y * v3 - + rho * v2 * v3_y - + rho_z * v3^2 - + 2.0 * rho * v3 * v3_z - - mu_ * (tau13_x + tau23_y + tau33_z) ) - # Total energy equation - du5 = ( E_t + v1_x * (E + p) + v1 * (E_x + p_x) - + v2_y * (E + p) + v2 * (E_y + p_y) - + v3_z * (E + p) + v3 * (E_z + p_z) - # stress tensor and temperature gradient from x-direction - - mu_ * ( q_xx + v1_x * tau11 + v2_x * tau12 + v3_x * tau13 - + v1 * tau11_x + v2 * tau12_x + v3 * tau13_x) - # stress tensor and temperature gradient terms from y-direction - - mu_ * ( q_yy + v1_y * tau12 + v2_y * tau22 + v3_y * tau23 - + v1 * tau12_y + v2 * tau22_y + v3 * tau23_y) - # stress tensor and temperature gradient terms from z-direction - - mu_ * ( q_zz + v1_z * tau13 + v2_z * tau23 + v3_z * tau33 - + v1 * tau13_z + v2 * tau23_z + v3 * tau33_z) ) - - return SVector(du1, du2, du3, du4, du5) + # TODO: parabolic + # we currently need to hardcode these parameters until we fix the "combined equation" issue + # see also https://github.com/trixi-framework/Trixi.jl/pull/1160 + inv_gamma_minus_one = inv(equations.gamma - 1) + Pr = prandtl_number() + mu_ = mu() + + # Constants. OBS! Must match those in `initial_condition_navier_stokes_convergence_test` + c = 2.0 + A1 = 0.5 + A2 = 1.0 + A3 = 0.5 + + # Convenience values for trig. functions + pi_x = pi * x[1] + pi_y = pi * x[2] + pi_z = pi * x[3] + pi_t = pi * t + + # Define auxiliary functions for the strange function of the y variable + # to make expressions easier to read + g = log(x[2] + 2.0) * (1.0 - exp(-A3 * (x[2] - 1.0))) + g_y = (A3 * log(x[2] + 2.0) * exp(-A3 * (x[2] - 1.0)) + + (1.0 - exp(-A3 * (x[2] - 1.0))) / (x[2] + 2.0)) + g_yy = (2.0 * A3 * exp(-A3 * (x[2] - 1.0)) / (x[2] + 2.0) - + (1.0 - exp(-A3 * (x[2] - 1.0))) / ((x[2] + 2.0)^2) - + A3^2 * log(x[2] + 2.0) * exp(-A3 * (x[2] - 1.0))) + + # Density and its derivatives + rho = c + A1 * sin(pi_x) * cos(pi_y) * sin(pi_z) * cos(pi_t) + rho_t = -pi * A1 * sin(pi_x) * cos(pi_y) * sin(pi_z) * sin(pi_t) + rho_x = pi * A1 * cos(pi_x) * cos(pi_y) * sin(pi_z) * cos(pi_t) + rho_y = -pi * A1 * sin(pi_x) * sin(pi_y) * sin(pi_z) * cos(pi_t) + rho_z = pi * A1 * sin(pi_x) * cos(pi_y) * cos(pi_z) * cos(pi_t) + rho_xx = -pi^2 * (rho - c) + rho_yy = -pi^2 * (rho - c) + rho_zz = -pi^2 * (rho - c) + + # Velocities and their derivatives + # v1 terms + v1 = A2 * sin(pi_x) * g * sin(pi_z) * cos(pi_t) + v1_t = -pi * A2 * sin(pi_x) * g * sin(pi_z) * sin(pi_t) + v1_x = pi * A2 * cos(pi_x) * g * sin(pi_z) * cos(pi_t) + v1_y = A2 * sin(pi_x) * g_y * sin(pi_z) * cos(pi_t) + v1_z = pi * A2 * sin(pi_x) * g * cos(pi_z) * cos(pi_t) + v1_xx = -pi^2 * v1 + v1_yy = A2 * sin(pi_x) * g_yy * sin(pi_z) * cos(pi_t) + v1_zz = -pi^2 * v1 + v1_xy = pi * A2 * cos(pi_x) * g_y * sin(pi_z) * cos(pi_t) + v1_xz = pi^2 * A2 * cos(pi_x) * g * cos(pi_z) * cos(pi_t) + v1_yz = pi * A2 * sin(pi_x) * g_y * cos(pi_z) * cos(pi_t) + # v2 terms (simplifies from ansatz) + v2 = v1 + v2_t = v1_t + v2_x = v1_x + v2_y = v1_y + v2_z = v1_z + v2_xx = v1_xx + v2_yy = v1_yy + v2_zz = v1_zz + v2_xy = v1_xy + v2_yz = v1_yz + # v3 terms (simplifies from ansatz) + v3 = v1 + v3_t = v1_t + v3_x = v1_x + v3_y = v1_y + v3_z = v1_z + v3_xx = v1_xx + v3_yy = v1_yy + v3_zz = v1_zz + v3_xz = v1_xz + v3_yz = v1_yz + + # Pressure and its derivatives + p = rho^2 + p_t = 2.0 * rho * rho_t + p_x = 2.0 * rho * rho_x + p_y = 2.0 * rho * rho_y + p_z = 2.0 * rho * rho_z + + # Total energy and its derivatives; simiplifies from ansatz that v2 = v1 and v3 = v1 + E = p * inv_gamma_minus_one + 1.5 * rho * v1^2 + E_t = p_t * inv_gamma_minus_one + 1.5 * rho_t * v1^2 + 3.0 * rho * v1 * v1_t + E_x = p_x * inv_gamma_minus_one + 1.5 * rho_x * v1^2 + 3.0 * rho * v1 * v1_x + E_y = p_y * inv_gamma_minus_one + 1.5 * rho_y * v1^2 + 3.0 * rho * v1 * v1_y + E_z = p_z * inv_gamma_minus_one + 1.5 * rho_z * v1^2 + 3.0 * rho * v1 * v1_z + + # Divergence of Fick's law ∇⋅∇q = kappa ∇⋅∇T; simplifies because p = rho², so T = p/rho = rho + kappa = equations.gamma * inv_gamma_minus_one / Pr + q_xx = kappa * rho_xx # kappa T_xx + q_yy = kappa * rho_yy # kappa T_yy + q_zz = kappa * rho_zz # kappa T_zz + + # Stress tensor and its derivatives (exploit symmetry) + tau11 = 4.0 / 3.0 * v1_x - 2.0 / 3.0 * (v2_y + v3_z) + tau12 = v1_y + v2_x + tau13 = v1_z + v3_x + tau22 = 4.0 / 3.0 * v2_y - 2.0 / 3.0 * (v1_x + v3_z) + tau23 = v2_z + v3_y + tau33 = 4.0 / 3.0 * v3_z - 2.0 / 3.0 * (v1_x + v2_y) + + tau11_x = 4.0 / 3.0 * v1_xx - 2.0 / 3.0 * (v2_xy + v3_xz) + tau12_x = v1_xy + v2_xx + tau13_x = v1_xz + v3_xx + + tau12_y = v1_yy + v2_xy + tau22_y = 4.0 / 3.0 * v2_yy - 2.0 / 3.0 * (v1_xy + v3_yz) + tau23_y = v2_yz + v3_yy + + tau13_z = v1_zz + v3_xz + tau23_z = v2_zz + v3_yz + tau33_z = 4.0 / 3.0 * v3_zz - 2.0 / 3.0 * (v1_xz + v2_yz) + + # Compute the source terms + # Density equation + du1 = (rho_t + rho_x * v1 + rho * v1_x + + rho_y * v2 + rho * v2_y + + rho_z * v3 + rho * v3_z) + # x-momentum equation + du2 = (rho_t * v1 + rho * v1_t + p_x + rho_x * v1^2 + + 2.0 * rho * v1 * v1_x + + rho_y * v1 * v2 + + rho * v1_y * v2 + + rho * v1 * v2_y + + rho_z * v1 * v3 + + rho * v1_z * v3 + + rho * v1 * v3_z - + mu_ * (tau11_x + tau12_y + tau13_z)) + # y-momentum equation + du3 = (rho_t * v2 + rho * v2_t + p_y + rho_x * v1 * v2 + + rho * v1_x * v2 + + rho * v1 * v2_x + + rho_y * v2^2 + + 2.0 * rho * v2 * v2_y + + rho_z * v2 * v3 + + rho * v2_z * v3 + + rho * v2 * v3_z - + mu_ * (tau12_x + tau22_y + tau23_z)) + # z-momentum equation + du4 = (rho_t * v3 + rho * v3_t + p_z + rho_x * v1 * v3 + + rho * v1_x * v3 + + rho * v1 * v3_x + + rho_y * v2 * v3 + + rho * v2_y * v3 + + rho * v2 * v3_y + + rho_z * v3^2 + + 2.0 * rho * v3 * v3_z - + mu_ * (tau13_x + tau23_y + tau33_z)) + # Total energy equation + du5 = (E_t + v1_x * (E + p) + v1 * (E_x + p_x) + + v2_y * (E + p) + v2 * (E_y + p_y) + + v3_z * (E + p) + v3 * (E_z + p_z) - + # stress tensor and temperature gradient from x-direction + mu_ * (q_xx + v1_x * tau11 + v2_x * tau12 + v3_x * tau13 + + v1 * tau11_x + v2 * tau12_x + v3 * tau13_x) - + # stress tensor and temperature gradient terms from y-direction + mu_ * (q_yy + v1_y * tau12 + v2_y * tau22 + v3_y * tau23 + + v1 * tau12_y + v2 * tau22_y + v3 * tau23_y) - + # stress tensor and temperature gradient terms from z-direction + mu_ * (q_zz + v1_z * tau13 + v2_z * tau23 + v3_z * tau33 + + v1 * tau13_z + v2 * tau23_z + v3 * tau33_z)) + + return SVector(du1, du2, du3, du4, du5) end initial_condition = initial_condition_navier_stokes_convergence_test # BC types velocity_bc_top_bottom = NoSlip() do x, t, equations - u = initial_condition_navier_stokes_convergence_test(x, t, equations) - return SVector(u[2], u[3], u[4]) + u = initial_condition_navier_stokes_convergence_test(x, t, equations) + return SVector(u[2], u[3], u[4]) end heat_bc_top_bottom = Adiabatic((x, t, equations) -> 0.0) -boundary_condition_top_bottom = BoundaryConditionNavierStokesWall(velocity_bc_top_bottom, heat_bc_top_bottom) +boundary_condition_top_bottom = BoundaryConditionNavierStokesWall(velocity_bc_top_bottom, + heat_bc_top_bottom) # define inviscid boundary conditions -boundary_conditions = Dict( - :y_neg => boundary_condition_slip_wall, - :y_pos => boundary_condition_slip_wall - ) +boundary_conditions = Dict(:y_neg => boundary_condition_slip_wall, + :y_pos => boundary_condition_slip_wall) # define viscous boundary conditions -boundary_conditions_parabolic = Dict( - :y_neg => boundary_condition_top_bottom, - :y_pos => boundary_condition_top_bottom - ) +boundary_conditions_parabolic = Dict(:y_neg => boundary_condition_top_bottom, + :y_pos => boundary_condition_top_bottom) -semi = SemidiscretizationHyperbolicParabolic(mesh, (equations, equations_parabolic), initial_condition, solver; - boundary_conditions=(boundary_conditions, boundary_conditions_parabolic), - source_terms=source_terms_navier_stokes_convergence_test) +semi = SemidiscretizationHyperbolicParabolic(mesh, (equations, equations_parabolic), + initial_condition, solver; + boundary_conditions = (boundary_conditions, + boundary_conditions_parabolic), + source_terms = source_terms_navier_stokes_convergence_test) ############################################################################### # ODE solvers, callbacks etc. @@ -251,16 +252,15 @@ tspan = (0.0, 0.2) ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() -alive_callback = AliveCallback(alive_interval=10) +alive_callback = AliveCallback(alive_interval = 10) analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) callbacks = CallbackSet(summary_callback, alive_callback, analysis_callback) ############################################################################### # run the simulation time_int_tol = 1e-8 -sol = solve(ode, RDPK3SpFSAL49(); abstol=time_int_tol, reltol=time_int_tol, dt = 1e-5, - ode_default_options()..., callback=callbacks) +sol = solve(ode, RDPK3SpFSAL49(); abstol = time_int_tol, reltol = time_int_tol, dt = 1e-5, + ode_default_options()..., callback = callbacks) summary_callback() # print the timer summary - diff --git a/examples/p4est_3d_dgsem/elixir_navierstokes_taylor_green_vortex.jl b/examples/p4est_3d_dgsem/elixir_navierstokes_taylor_green_vortex.jl index c5b9ccf2e38..d785013f5a9 100644 --- a/examples/p4est_3d_dgsem/elixir_navierstokes_taylor_green_vortex.jl +++ b/examples/p4est_3d_dgsem/elixir_navierstokes_taylor_green_vortex.jl @@ -10,42 +10,45 @@ prandtl_number() = 0.72 mu() = 6.25e-4 # equivalent to Re = 1600 equations = CompressibleEulerEquations3D(1.4) -equations_parabolic = CompressibleNavierStokesDiffusion3D(equations, mu=mu(), - Prandtl=prandtl_number()) +equations_parabolic = CompressibleNavierStokesDiffusion3D(equations, mu = mu(), + Prandtl = prandtl_number()) """ initial_condition_taylor_green_vortex(x, t, equations::CompressibleEulerEquations3D) The classical inviscid Taylor-Green vortex. """ -function initial_condition_taylor_green_vortex(x, t, equations::CompressibleEulerEquations3D) - A = 1.0 # magnitude of speed - Ms = 0.1 # maximum Mach number - - rho = 1.0 - v1 = A * sin(x[1]) * cos(x[2]) * cos(x[3]) - v2 = -A * cos(x[1]) * sin(x[2]) * cos(x[3]) - v3 = 0.0 - p = (A / Ms)^2 * rho / equations.gamma # scaling to get Ms - p = p + 1.0/16.0 * A^2 * rho * (cos(2*x[1])*cos(2*x[3]) + 2*cos(2*x[2]) + 2*cos(2*x[1]) + cos(2*x[2])*cos(2*x[3])) - - return prim2cons(SVector(rho, v1, v2, v3, p), equations) +function initial_condition_taylor_green_vortex(x, t, + equations::CompressibleEulerEquations3D) + A = 1.0 # magnitude of speed + Ms = 0.1 # maximum Mach number + + rho = 1.0 + v1 = A * sin(x[1]) * cos(x[2]) * cos(x[3]) + v2 = -A * cos(x[1]) * sin(x[2]) * cos(x[3]) + v3 = 0.0 + p = (A / Ms)^2 * rho / equations.gamma # scaling to get Ms + p = p + + 1.0 / 16.0 * A^2 * rho * + (cos(2 * x[1]) * cos(2 * x[3]) + 2 * cos(2 * x[2]) + 2 * cos(2 * x[1]) + + cos(2 * x[2]) * cos(2 * x[3])) + + return prim2cons(SVector(rho, v1, v2, v3, p), equations) end initial_condition = initial_condition_taylor_green_vortex volume_flux = flux_ranocha -solver = DGSEM(polydeg=3, surface_flux=flux_hll, - volume_integral=VolumeIntegralFluxDifferencing(volume_flux)) +solver = DGSEM(polydeg = 3, surface_flux = flux_hll, + volume_integral = VolumeIntegralFluxDifferencing(volume_flux)) coordinates_min = (-1.0, -1.0, -1.0) .* pi -coordinates_max = ( 1.0, 1.0, 1.0) .* pi +coordinates_max = (1.0, 1.0, 1.0) .* pi trees_per_dimension = (2, 2, 2) -mesh = P4estMesh(trees_per_dimension, polydeg=3, - coordinates_min=coordinates_min, coordinates_max=coordinates_max, - periodicity=(true, true, true), initial_refinement_level=2) - +mesh = P4estMesh(trees_per_dimension, polydeg = 3, + coordinates_min = coordinates_min, coordinates_max = coordinates_max, + periodicity = (true, true, true), initial_refinement_level = 2) semi = SemidiscretizationHyperbolicParabolic(mesh, (equations, equations_parabolic), initial_condition, solver) @@ -59,24 +62,25 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 50 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval, save_analysis=true, - extra_analysis_integrals=(energy_kinetic, - energy_internal, - enstrophy)) -save_solution = SaveSolutionCallback(interval=100, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) -alive_callback = AliveCallback(analysis_interval=analysis_interval,) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval, + save_analysis = true, + extra_analysis_integrals = (energy_kinetic, + energy_internal, + enstrophy)) +save_solution = SaveSolutionCallback(interval = 100, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) +alive_callback = AliveCallback(analysis_interval = analysis_interval) callbacks = CallbackSet(summary_callback, analysis_callback, - alive_callback,save_solution) + alive_callback, save_solution) ############################################################################### # run the simulation time_int_tol = 1e-8 -sol = solve(ode, RDPK3SpFSAL49(); abstol=time_int_tol, reltol=time_int_tol, - ode_default_options()..., callback=callbacks) +sol = solve(ode, RDPK3SpFSAL49(); abstol = time_int_tol, reltol = time_int_tol, + ode_default_options()..., callback = callbacks) summary_callback() # print the timer summary diff --git a/examples/paper_self_gravitating_gas_dynamics/elixir_euler_convergence.jl b/examples/paper_self_gravitating_gas_dynamics/elixir_euler_convergence.jl index 316f36adc9b..aabfce0f66b 100644 --- a/examples/paper_self_gravitating_gas_dynamics/elixir_euler_convergence.jl +++ b/examples/paper_self_gravitating_gas_dynamics/elixir_euler_convergence.jl @@ -8,18 +8,16 @@ equations = CompressibleEulerEquations2D(2.0) initial_condition = initial_condition_eoc_test_coupled_euler_gravity -solver = DGSEM(polydeg=3, surface_flux=flux_hll) +solver = DGSEM(polydeg = 3, surface_flux = flux_hll) coordinates_min = (0.0, 0.0) coordinates_max = (2.0, 2.0) mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=2, - n_cells_max=10_000) - + initial_refinement_level = 2, + n_cells_max = 10_000) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver, - source_terms=source_terms_eoc_test_euler) - + source_terms = source_terms_eoc_test_euler) ############################################################################### # ODE solvers, callbacks etc. @@ -29,26 +27,25 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() -stepsize_callback = StepsizeCallback(cfl=0.8) +stepsize_callback = StepsizeCallback(cfl = 0.8) -save_solution = SaveSolutionCallback(interval=100, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 100, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) analysis_interval = 100 -alive_callback = AliveCallback(analysis_interval=analysis_interval) -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) callbacks = CallbackSet(summary_callback, stepsize_callback, save_solution, analysis_callback, alive_callback) - ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/paper_self_gravitating_gas_dynamics/elixir_eulergravity_convergence.jl b/examples/paper_self_gravitating_gas_dynamics/elixir_eulergravity_convergence.jl index f2693c89583..ce1d2cd05bd 100644 --- a/examples/paper_self_gravitating_gas_dynamics/elixir_eulergravity_convergence.jl +++ b/examples/paper_self_gravitating_gas_dynamics/elixir_eulergravity_convergence.jl @@ -2,10 +2,8 @@ using OrdinaryDiffEq using Trixi - initial_condition = initial_condition_eoc_test_coupled_euler_gravity - ############################################################################### # semidiscretization of the compressible Euler equations gamma = 2.0 @@ -17,12 +15,12 @@ solver_euler = DGSEM(polydeg, flux_hll) coordinates_min = (0.0, 0.0) coordinates_max = (2.0, 2.0) mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=2, - n_cells_max=10_000) - -semi_euler = SemidiscretizationHyperbolic(mesh, equations_euler, initial_condition, solver_euler, - source_terms=source_terms_eoc_test_coupled_euler_gravity) + initial_refinement_level = 2, + n_cells_max = 10_000) +semi_euler = SemidiscretizationHyperbolic(mesh, equations_euler, initial_condition, + solver_euler, + source_terms = source_terms_eoc_test_coupled_euler_gravity) ############################################################################### # semidiscretization of the hyperbolic diffusion equations @@ -30,24 +28,23 @@ equations_gravity = HyperbolicDiffusionEquations2D() solver_gravity = DGSEM(polydeg, flux_lax_friedrichs) -semi_gravity = SemidiscretizationHyperbolic(mesh, equations_gravity, initial_condition, solver_gravity, - source_terms=source_terms_harmonic) - +semi_gravity = SemidiscretizationHyperbolic(mesh, equations_gravity, initial_condition, + solver_gravity, + source_terms = source_terms_harmonic) ############################################################################### # combining both semidiscretizations for Euler + self-gravity -parameters = ParametersEulerGravity(background_density=2.0, # aka rho0 +parameters = ParametersEulerGravity(background_density = 2.0, # aka rho0 # rho0 is (ab)used to add a "+8π" term to the source terms # for the manufactured solution - gravitational_constant=1.0, # aka G - cfl=1.1, - resid_tol=1.0e-10, - n_iterations_max=1000, - timestep_gravity=timestep_gravity_erk52_3Sstar!) + gravitational_constant = 1.0, # aka G + cfl = 1.1, + resid_tol = 1.0e-10, + n_iterations_max = 1000, + timestep_gravity = timestep_gravity_erk52_3Sstar!) semi = SemidiscretizationEulerGravity(semi_euler, semi_gravity, parameters) - ############################################################################### # ODE solvers, callbacks etc. tspan = (0.0, 0.5) @@ -55,28 +52,27 @@ ode = semidiscretize(semi, tspan); summary_callback = SummaryCallback() -stepsize_callback = StepsizeCallback(cfl=0.8) +stepsize_callback = StepsizeCallback(cfl = 0.8) -save_solution = SaveSolutionCallback(interval=10, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 10, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) analysis_interval = 100 -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -analysis_callback = AnalysisCallback(semi_euler, interval=analysis_interval, - save_analysis=true) +analysis_callback = AnalysisCallback(semi_euler, interval = analysis_interval, + save_analysis = true) callbacks = CallbackSet(summary_callback, stepsize_callback, save_solution, analysis_callback, alive_callback) - ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary println("Number of gravity subcycles: ", semi.gravity_counter.ncalls_since_readout) diff --git a/examples/paper_self_gravitating_gas_dynamics/elixir_eulergravity_jeans_instability.jl b/examples/paper_self_gravitating_gas_dynamics/elixir_eulergravity_jeans_instability.jl index fb445616cd4..f081f6bb91a 100644 --- a/examples/paper_self_gravitating_gas_dynamics/elixir_eulergravity_jeans_instability.jl +++ b/examples/paper_self_gravitating_gas_dynamics/elixir_eulergravity_jeans_instability.jl @@ -2,7 +2,6 @@ using OrdinaryDiffEq using Trixi - """ initial_condition_jeans_instability(x, t, equations::Union{CompressibleEulerEquations2D, @@ -19,52 +18,51 @@ The classical Jeans instability taken from in CGS (centimeter, gram, second) units. """ function initial_condition_jeans_instability(x, t, - equations::CompressibleEulerEquations2D) - # Jeans gravitational instability test case - # see Derigs et al. https://arxiv.org/abs/1605.03572; Sec. 4.6 - # OBS! this uses cgs (centimeter, gram, second) units - # periodic boundaries - # domain size [0,L]^2 depends on the wave number chosen for the perturbation - # OBS! Be very careful here L must be chosen such that problem is periodic - # typical final time is T = 5 - # gamma = 5/3 - dens0 = 1.5e7 # g/cm^3 - pres0 = 1.5e7 # dyn/cm^2 - delta0 = 1e-3 - # set wave vector values for perturbation (units 1/cm) - # see FLASH manual: https://flash.rochester.edu/site/flashcode/user_support/flash_ug_devel/node189.html#SECTION010131000000000000000 - kx = 2.0*pi/0.5 # 2π/λ_x, λ_x = 0.5 - ky = 0.0 # 2π/λ_y, λ_y = 1e10 - k_dot_x = kx*x[1] + ky*x[2] - # perturb density and pressure away from reference states ρ_0 and p_0 - dens = dens0*(1.0 + delta0*cos(k_dot_x)) # g/cm^3 - pres = pres0*(1.0 + equations.gamma*delta0*cos(k_dot_x)) # dyn/cm^2 - # flow starts as stationary - velx = 0.0 # cm/s - vely = 0.0 # cm/s - return prim2cons((dens, velx, vely, pres), equations) + equations::CompressibleEulerEquations2D) + # Jeans gravitational instability test case + # see Derigs et al. https://arxiv.org/abs/1605.03572; Sec. 4.6 + # OBS! this uses cgs (centimeter, gram, second) units + # periodic boundaries + # domain size [0,L]^2 depends on the wave number chosen for the perturbation + # OBS! Be very careful here L must be chosen such that problem is periodic + # typical final time is T = 5 + # gamma = 5/3 + dens0 = 1.5e7 # g/cm^3 + pres0 = 1.5e7 # dyn/cm^2 + delta0 = 1e-3 + # set wave vector values for perturbation (units 1/cm) + # see FLASH manual: https://flash.rochester.edu/site/flashcode/user_support/flash_ug_devel/node189.html#SECTION010131000000000000000 + kx = 2.0 * pi / 0.5 # 2π/λ_x, λ_x = 0.5 + ky = 0.0 # 2π/λ_y, λ_y = 1e10 + k_dot_x = kx * x[1] + ky * x[2] + # perturb density and pressure away from reference states ρ_0 and p_0 + dens = dens0 * (1.0 + delta0 * cos(k_dot_x)) # g/cm^3 + pres = pres0 * (1.0 + equations.gamma * delta0 * cos(k_dot_x)) # dyn/cm^2 + # flow starts as stationary + velx = 0.0 # cm/s + vely = 0.0 # cm/s + return prim2cons((dens, velx, vely, pres), equations) end function initial_condition_jeans_instability(x, t, equations::HyperbolicDiffusionEquations2D) - # gravity equation: -Δϕ = -4πGρ - # Constants taken from the FLASH manual - # https://flash.rochester.edu/site/flashcode/user_support/flash_ug_devel/node189.html#SECTION010131000000000000000 - rho0 = 1.5e7 - delta0 = 1e-3 - - phi = rho0*delta0 # constant background perturbation magnitude - q1 = 0.0 - q2 = 0.0 - return (phi, q1, q2) + # gravity equation: -Δϕ = -4πGρ + # Constants taken from the FLASH manual + # https://flash.rochester.edu/site/flashcode/user_support/flash_ug_devel/node189.html#SECTION010131000000000000000 + rho0 = 1.5e7 + delta0 = 1e-3 + + phi = rho0 * delta0 # constant background perturbation magnitude + q1 = 0.0 + q2 = 0.0 + return (phi, q1, q2) end initial_condition = initial_condition_jeans_instability - ############################################################################### # semidiscretization of the compressible Euler equations -gamma = 5/3 +gamma = 5 / 3 equations_euler = CompressibleEulerEquations2D(gamma) polydeg = 3 @@ -73,11 +71,11 @@ solver_euler = DGSEM(polydeg, flux_hll) coordinates_min = (0.0, 0.0) coordinates_max = (1.0, 1.0) mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=4, - n_cells_max=10_000) - -semi_euler = SemidiscretizationHyperbolic(mesh, equations_euler, initial_condition, solver_euler) + initial_refinement_level = 4, + n_cells_max = 10_000) +semi_euler = SemidiscretizationHyperbolic(mesh, equations_euler, initial_condition, + solver_euler) ############################################################################### # semidiscretization of the hyperbolic diffusion equations @@ -85,22 +83,21 @@ equations_gravity = HyperbolicDiffusionEquations2D() solver_gravity = DGSEM(polydeg, flux_lax_friedrichs) -semi_gravity = SemidiscretizationHyperbolic(mesh, equations_gravity, initial_condition, solver_gravity, - source_terms=source_terms_harmonic) - +semi_gravity = SemidiscretizationHyperbolic(mesh, equations_gravity, initial_condition, + solver_gravity, + source_terms = source_terms_harmonic) ############################################################################### # combining both semidiscretizations for Euler + self-gravity -parameters = ParametersEulerGravity(background_density=1.5e7, # aka rho0 - gravitational_constant=6.674e-8, # aka G - cfl=1.6, - resid_tol=1.0e-4, - n_iterations_max=1000, - timestep_gravity=timestep_gravity_carpenter_kennedy_erk54_2N!) +parameters = ParametersEulerGravity(background_density = 1.5e7, # aka rho0 + gravitational_constant = 6.674e-8, # aka G + cfl = 1.6, + resid_tol = 1.0e-4, + n_iterations_max = 1000, + timestep_gravity = timestep_gravity_carpenter_kennedy_erk54_2N!) semi = SemidiscretizationEulerGravity(semi_euler, semi_gravity, parameters) - ############################################################################### # ODE solvers, callbacks etc. tspan = (0.0, 5.0) @@ -108,51 +105,58 @@ ode = semidiscretize(semi, tspan); summary_callback = SummaryCallback() -stepsize_callback = StepsizeCallback(cfl=1.0) +stepsize_callback = StepsizeCallback(cfl = 1.0) -save_solution = SaveSolutionCallback(interval=10, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 10, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) -save_restart = SaveRestartCallback(interval=100, - save_final_restart=true) +save_restart = SaveRestartCallback(interval = 100, + save_final_restart = true) analysis_interval = 100 -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) Trixi.pretty_form_utf(::Val{:energy_potential}) = "∑e_potential" Trixi.pretty_form_ascii(::Val{:energy_potential}) = "e_potential" -function Trixi.analyze(::Val{:energy_potential}, du, u_euler, t, semi::SemidiscretizationEulerGravity) - - u_gravity = Trixi.wrap_array(semi.cache.u_ode, semi.semi_gravity) - - mesh, equations_euler, dg, cache = Trixi.mesh_equations_solver_cache(semi.semi_euler) - _, equations_gravity, _, _ = Trixi.mesh_equations_solver_cache(semi.semi_gravity) - - e_potential = Trixi.integrate_via_indices(u_euler, mesh, equations_euler, dg, cache, equations_gravity, u_gravity) do u, i, j, element, equations_euler, dg, equations_gravity, u_gravity - u_euler_local = Trixi.get_node_vars(u_euler, equations_euler, dg, i, j, element) - u_gravity_local = Trixi.get_node_vars(u_gravity, equations_gravity, dg, i, j, element) - # OBS! subtraction is specific to Jeans instability test where rho0 = 1.5e7 - return (u_euler_local[1] - 1.5e7) * u_gravity_local[1] - end - return e_potential +function Trixi.analyze(::Val{:energy_potential}, du, u_euler, t, + semi::SemidiscretizationEulerGravity) + u_gravity = Trixi.wrap_array(semi.cache.u_ode, semi.semi_gravity) + + mesh, equations_euler, dg, cache = Trixi.mesh_equations_solver_cache(semi.semi_euler) + _, equations_gravity, _, _ = Trixi.mesh_equations_solver_cache(semi.semi_gravity) + + e_potential = Trixi.integrate_via_indices(u_euler, mesh, equations_euler, dg, cache, + equations_gravity, + u_gravity) do u, i, j, element, + equations_euler, dg, + equations_gravity, u_gravity + u_euler_local = Trixi.get_node_vars(u_euler, equations_euler, dg, i, j, element) + u_gravity_local = Trixi.get_node_vars(u_gravity, equations_gravity, dg, i, j, + element) + # OBS! subtraction is specific to Jeans instability test where rho0 = 1.5e7 + return (u_euler_local[1] - 1.5e7) * u_gravity_local[1] + end + return e_potential end -analysis_callback = AnalysisCallback(semi_euler, interval=analysis_interval, - save_analysis=true, - extra_analysis_integrals=(energy_total, energy_kinetic, energy_internal, Val(:energy_potential))) +analysis_callback = AnalysisCallback(semi_euler, interval = analysis_interval, + save_analysis = true, + extra_analysis_integrals = (energy_total, + energy_kinetic, + energy_internal, + Val(:energy_potential))) callbacks = CallbackSet(summary_callback, stepsize_callback, save_restart, save_solution, analysis_callback, alive_callback) - ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary println("Number of gravity subcycles: ", semi.gravity_counter.ncalls_since_readout) diff --git a/examples/paper_self_gravitating_gas_dynamics/elixir_eulergravity_sedov_blast_wave.jl b/examples/paper_self_gravitating_gas_dynamics/elixir_eulergravity_sedov_blast_wave.jl index 8933224a2c7..b7be2320228 100644 --- a/examples/paper_self_gravitating_gas_dynamics/elixir_eulergravity_sedov_blast_wave.jl +++ b/examples/paper_self_gravitating_gas_dynamics/elixir_eulergravity_sedov_blast_wave.jl @@ -19,33 +19,33 @@ based on Should be used together with [`boundary_condition_sedov_self_gravity`](@ref). """ function initial_condition_sedov_self_gravity(x, t, equations::CompressibleEulerEquations2D) - # Set up polar coordinates - r = sqrt(x[1]^2 + x[2]^2) - - # Setup based on https://flash.rochester.edu/site/flashcode/user_support/flash_ug_devel/node187.html#SECTION010114100000000000000 - r0 = 0.125 # = 4.0 * smallest dx (for domain length=8 and max-ref=8) - E = 1.0 - p_inner = (equations.gamma - 1) * E / (pi * r0^2) - p_ambient = 1e-5 # = true Sedov setup - - # Calculate primitive variables - # use a logistic function to transfer density value smoothly - L = 1.0 # maximum of function - x0 = 1.0 # center point of function - k = -150.0 # sharpness of transfer - logistic_function_rho = L/(1.0 + exp(-k*(r - x0))) - rho_ambient = 1e-5 - rho = max(logistic_function_rho, rho_ambient) # clip background density to not be so tiny - - # velocities are zero - v1 = 0.0 - v2 = 0.0 - - # use a logistic function to transfer pressure value smoothly - logistic_function_p = p_inner/(1.0 + exp(-k*(r - r0))) - p = max(logistic_function_p, p_ambient) - - return prim2cons(SVector(rho, v1, v2, p), equations) + # Set up polar coordinates + r = sqrt(x[1]^2 + x[2]^2) + + # Setup based on https://flash.rochester.edu/site/flashcode/user_support/flash_ug_devel/node187.html#SECTION010114100000000000000 + r0 = 0.125 # = 4.0 * smallest dx (for domain length=8 and max-ref=8) + E = 1.0 + p_inner = (equations.gamma - 1) * E / (pi * r0^2) + p_ambient = 1e-5 # = true Sedov setup + + # Calculate primitive variables + # use a logistic function to transfer density value smoothly + L = 1.0 # maximum of function + x0 = 1.0 # center point of function + k = -150.0 # sharpness of transfer + logistic_function_rho = L / (1.0 + exp(-k * (r - x0))) + rho_ambient = 1e-5 + rho = max(logistic_function_rho, rho_ambient) # clip background density to not be so tiny + + # velocities are zero + v1 = 0.0 + v2 = 0.0 + + # use a logistic function to transfer pressure value smoothly + logistic_function_p = p_inner / (1.0 + exp(-k * (r - r0))) + p = max(logistic_function_p, p_ambient) + + return prim2cons(SVector(rho, v1, v2, p), equations) end initial_condition = initial_condition_sedov_self_gravity @@ -65,50 +65,50 @@ Should be used together with [`initial_condition_sedov_self_gravity`](@ref). function boundary_condition_sedov_self_gravity(u_inner, orientation, direction, x, t, surface_flux_function, equations::CompressibleEulerEquations2D) - # velocities are zero, density/pressure are ambient values according to - # initial_condition_sedov_self_gravity - rho = 1e-5 - v1 = 0.0 - v2 = 0.0 - p = 1e-5 - - u_boundary = prim2cons(SVector(rho, v1, v2, p), equations) - - # Calculate boundary flux - if iseven(direction) # u_inner is "left" of boundary, u_boundary is "right" of boundary - flux = surface_flux_function(u_inner, u_boundary, orientation, equations) - else # u_boundary is "left" of boundary, u_inner is "right" of boundary - flux = surface_flux_function(u_boundary, u_inner, orientation, equations) - end - - return flux + # velocities are zero, density/pressure are ambient values according to + # initial_condition_sedov_self_gravity + rho = 1e-5 + v1 = 0.0 + v2 = 0.0 + p = 1e-5 + + u_boundary = prim2cons(SVector(rho, v1, v2, p), equations) + + # Calculate boundary flux + if iseven(direction) # u_inner is "left" of boundary, u_boundary is "right" of boundary + flux = surface_flux_function(u_inner, u_boundary, orientation, equations) + else # u_boundary is "left" of boundary, u_inner is "right" of boundary + flux = surface_flux_function(u_boundary, u_inner, orientation, equations) + end + + return flux end boundary_conditions = boundary_condition_sedov_self_gravity surface_flux = flux_hll -volume_flux = flux_chandrashekar +volume_flux = flux_chandrashekar polydeg = 3 basis = LobattoLegendreBasis(polydeg) indicator_sc = IndicatorHennemannGassner(equations_euler, basis, - alpha_max=0.5, - alpha_min=0.001, - alpha_smooth=true, - variable=density_pressure) + alpha_max = 0.5, + alpha_min = 0.001, + alpha_smooth = true, + variable = density_pressure) volume_integral = VolumeIntegralShockCapturingHG(indicator_sc; - volume_flux_dg=volume_flux, - volume_flux_fv=surface_flux) + volume_flux_dg = volume_flux, + volume_flux_fv = surface_flux) solver_euler = DGSEM(basis, surface_flux, volume_integral) coordinates_min = (-4, -4) -coordinates_max = ( 4, 4) +coordinates_max = (4, 4) mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=2, - n_cells_max=100_000, - periodicity=false) - -semi_euler = SemidiscretizationHyperbolic(mesh, equations_euler, initial_condition, solver_euler, - boundary_conditions=boundary_conditions) + initial_refinement_level = 2, + n_cells_max = 100_000, + periodicity = false) +semi_euler = SemidiscretizationHyperbolic(mesh, equations_euler, initial_condition, + solver_euler, + boundary_conditions = boundary_conditions) ############################################################################### # semidiscretization of the hyperbolic diffusion equations @@ -125,12 +125,13 @@ based on - https://flash.rochester.edu/site/flashcode/user_support/flash_ug_devel/node187.html#SECTION010114100000000000000 Should be used together with [`boundary_condition_sedov_self_gravity`](@ref). """ -function initial_condition_sedov_self_gravity(x, t, equations::HyperbolicDiffusionEquations2D) - # for now just use constant initial condition for sedov blast wave (can likely be improved) - phi = 0.0 - q1 = 0.0 - q2 = 0.0 - return SVector(phi, q1, q2) +function initial_condition_sedov_self_gravity(x, t, + equations::HyperbolicDiffusionEquations2D) + # for now just use constant initial condition for sedov blast wave (can likely be improved) + phi = 0.0 + q1 = 0.0 + q2 = 0.0 + return SVector(phi, q1, q2) end """ @@ -147,39 +148,38 @@ based on Should be used together with [`initial_condition_sedov_self_gravity`](@ref). """ function boundary_condition_sedov_self_gravity(u_inner, orientation, direction, x, t, - surface_flux_function, - equations::HyperbolicDiffusionEquations2D) - u_boundary = initial_condition_sedov_self_gravity(x, t, equations) - - # Calculate boundary flux - if iseven(direction) # u_inner is "left" of boundary, u_boundary is "right" of boundary - flux = surface_flux_function(u_inner, u_boundary, orientation, equations) - else # u_boundary is "left" of boundary, u_inner is "right" of boundary - flux = surface_flux_function(u_boundary, u_inner, orientation, equations) - end - - return flux + surface_flux_function, + equations::HyperbolicDiffusionEquations2D) + u_boundary = initial_condition_sedov_self_gravity(x, t, equations) + + # Calculate boundary flux + if iseven(direction) # u_inner is "left" of boundary, u_boundary is "right" of boundary + flux = surface_flux_function(u_inner, u_boundary, orientation, equations) + else # u_boundary is "left" of boundary, u_inner is "right" of boundary + flux = surface_flux_function(u_boundary, u_inner, orientation, equations) + end + + return flux end solver_gravity = DGSEM(polydeg, flux_lax_friedrichs) -semi_gravity = SemidiscretizationHyperbolic(mesh, equations_gravity, initial_condition, solver_gravity, - boundary_conditions=boundary_conditions, - source_terms=source_terms_harmonic) - +semi_gravity = SemidiscretizationHyperbolic(mesh, equations_gravity, initial_condition, + solver_gravity, + boundary_conditions = boundary_conditions, + source_terms = source_terms_harmonic) ############################################################################### # combining both semidiscretizations for Euler + self-gravity -parameters = ParametersEulerGravity(background_density=0.0, # aka rho0 - gravitational_constant=6.674e-8, # aka G - cfl=2.4, - resid_tol=1.0e-4, - n_iterations_max=100, - timestep_gravity=timestep_gravity_erk52_3Sstar!) +parameters = ParametersEulerGravity(background_density = 0.0, # aka rho0 + gravitational_constant = 6.674e-8, # aka G + cfl = 2.4, + resid_tol = 1.0e-4, + n_iterations_max = 100, + timestep_gravity = timestep_gravity_erk52_3Sstar!) semi = SemidiscretizationEulerGravity(semi_euler, semi_gravity, parameters) - ############################################################################### # ODE solvers, callbacks etc. tspan = (0.0, 1.0) @@ -188,41 +188,42 @@ ode = semidiscretize(semi, tspan); summary_callback = SummaryCallback() amr_indicator = IndicatorHennemannGassner(semi, - alpha_max=1.0, - alpha_min=0.0, - alpha_smooth=false, - variable=density_pressure) + alpha_max = 1.0, + alpha_min = 0.0, + alpha_smooth = false, + variable = density_pressure) amr_controller = ControllerThreeLevel(semi, amr_indicator, - base_level=2, - max_level =8, max_threshold=0.0003) + base_level = 2, + max_level = 8, max_threshold = 0.0003) amr_callback = AMRCallback(semi, amr_controller, - interval=1, - adapt_initial_condition=true, - adapt_initial_condition_only_refine=true) + interval = 1, + adapt_initial_condition = true, + adapt_initial_condition_only_refine = true) -stepsize_callback = StepsizeCallback(cfl=1.0) +stepsize_callback = StepsizeCallback(cfl = 1.0) -save_solution = SaveSolutionCallback(interval=100, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 100, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) analysis_interval = 100 -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -analysis_callback = AnalysisCallback(semi_euler, interval=analysis_interval, - save_analysis=true, - extra_analysis_integrals=(energy_total, energy_kinetic, energy_internal)) +analysis_callback = AnalysisCallback(semi_euler, interval = analysis_interval, + save_analysis = true, + extra_analysis_integrals = (energy_total, + energy_kinetic, + energy_internal)) callbacks = CallbackSet(summary_callback, amr_callback, stepsize_callback, save_solution, analysis_callback, alive_callback) - ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary println("Number of gravity subcycles: ", semi.gravity_counter.ncalls_since_readout) diff --git a/examples/paper_self_gravitating_gas_dynamics/elixir_hypdiff_convergence.jl b/examples/paper_self_gravitating_gas_dynamics/elixir_hypdiff_convergence.jl index 029c19380cf..df6e4e6349f 100644 --- a/examples/paper_self_gravitating_gas_dynamics/elixir_hypdiff_convergence.jl +++ b/examples/paper_self_gravitating_gas_dynamics/elixir_hypdiff_convergence.jl @@ -9,10 +9,10 @@ equations = HyperbolicDiffusionEquations2D() initial_condition = initial_condition_poisson_nonperiodic # 1 => -x, 2 => +x, 3 => -y, 4 => +y as usual for orientations -boundary_conditions = (x_neg=boundary_condition_poisson_nonperiodic, - x_pos=boundary_condition_poisson_nonperiodic, - y_neg=boundary_condition_periodic, - y_pos=boundary_condition_periodic) +boundary_conditions = (x_neg = boundary_condition_poisson_nonperiodic, + x_pos = boundary_condition_poisson_nonperiodic, + y_neg = boundary_condition_periodic, + y_pos = boundary_condition_periodic) polydeg = 3 surface_flux = flux_lax_friedrichs @@ -21,15 +21,13 @@ solver = DGSEM(polydeg, surface_flux) coordinates_min = (0.0, 0.0) coordinates_max = (1.0, 1.0) mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=2, - n_cells_max=30_000, - periodicity=(false, true)) - + initial_refinement_level = 2, + n_cells_max = 30_000, + periodicity = (false, true)) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver, - source_terms=source_terms_poisson_nonperiodic, - boundary_conditions=boundary_conditions) - + source_terms = source_terms_poisson_nonperiodic, + boundary_conditions = boundary_conditions) ############################################################################### # ODE solvers, callbacks etc. @@ -40,29 +38,28 @@ ode = semidiscretize(semi, tspan); summary_callback = SummaryCallback() resid_tol = 1.0e-10 -steady_state_callback = SteadyStateCallback(abstol=resid_tol, reltol=0.0) +steady_state_callback = SteadyStateCallback(abstol = resid_tol, reltol = 0.0) -stepsize_callback = StepsizeCallback(cfl=1.0) +stepsize_callback = StepsizeCallback(cfl = 1.0) -save_solution = SaveSolutionCallback(interval=100, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 100, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) analysis_interval = 500 -alive_callback = AliveCallback(analysis_interval=analysis_interval) -analysis_callback = AnalysisCallback(semi, interval=analysis_interval, - extra_analysis_integrals=(entropy, energy_total)) +alive_callback = AliveCallback(analysis_interval = analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval, + extra_analysis_integrals = (entropy, energy_total)) callbacks = CallbackSet(summary_callback, steady_state_callback, stepsize_callback, save_solution, analysis_callback, alive_callback) - ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/special_elixirs/elixir_euler_ad.jl b/examples/special_elixirs/elixir_euler_ad.jl index 48fd37cc9d4..3aa44f9a773 100644 --- a/examples/special_elixirs/elixir_euler_ad.jl +++ b/examples/special_elixirs/elixir_euler_ad.jl @@ -6,10 +6,10 @@ using Trixi, LinearAlgebra, ForwardDiff equations = CompressibleEulerEquations2D(1.4) mesh = TreeMesh((-1.0, -1.0), (1.0, 1.0), - initial_refinement_level=2, n_cells_max=10^5) + initial_refinement_level = 2, n_cells_max = 10^5) -solver = DGSEM(polydeg=3, surface_flux=flux_lax_friedrichs, - volume_integral=VolumeIntegralFluxDifferencing(flux_ranocha)) +solver = DGSEM(polydeg = 3, surface_flux = flux_lax_friedrichs, + volume_integral = VolumeIntegralFluxDifferencing(flux_ranocha)) """ initial_condition_isentropic_vortex(x, t, equations::CompressibleEulerEquations2D) @@ -21,43 +21,45 @@ The classical isentropic vortex test case of [NASA/CR-97-206253](https://ntrs.nasa.gov/citations/19980007543) """ function initial_condition_isentropic_vortex(x, t, equations::CompressibleEulerEquations2D) - # needs appropriate mesh size, e.g. [-10,-10]x[10,10] - # for error convergence: make sure that the end time is such that the vortex is back at the initial state!! - # for the current velocity and domain size: t_end should be a multiple of 20s - # initial center of the vortex - inicenter = SVector(0.0, 0.0) - # size and strength of the vortex - iniamplitude = 5.0 - # base flow - rho = 1.0 - v1 = 1.0 - v2 = 1.0 - vel = SVector(v1, v2) - p = 25.0 - rt = p / rho # ideal gas equation - t_loc = 0.0 - cent = inicenter + vel*t_loc # advection of center - # ATTENTION: handle periodic BC, but only for v1 = v2 = 1.0 (!!!!) - cent = x - cent # distance to center point - # cent = cross(iniaxis, cent) # distance to axis, tangent vector, length r - # cross product with iniaxis = [0, 0, 1] - cent = SVector(-cent[2], cent[1]) - r2 = cent[1]^2 + cent[2]^2 - du = iniamplitude / (2*π) * exp(0.5 * (1 - r2)) # vel. perturbation - dtemp = -(equations.gamma - 1) / (2 * equations.gamma * rt) * du^2 # isentropic - rho = rho * (1 + dtemp)^(1 / (equations.gamma - 1)) - vel = vel + du * cent - v1, v2 = vel - p = p * (1 + dtemp)^(equations.gamma / (equations.gamma - 1)) - prim = SVector(rho, v1, v2, p) - return prim2cons(prim, equations) + # needs appropriate mesh size, e.g. [-10,-10]x[10,10] + # for error convergence: make sure that the end time is such that the vortex is back at the initial state!! + # for the current velocity and domain size: t_end should be a multiple of 20s + # initial center of the vortex + inicenter = SVector(0.0, 0.0) + # size and strength of the vortex + iniamplitude = 5.0 + # base flow + rho = 1.0 + v1 = 1.0 + v2 = 1.0 + vel = SVector(v1, v2) + p = 25.0 + rt = p / rho # ideal gas equation + t_loc = 0.0 + cent = inicenter + vel * t_loc # advection of center + # ATTENTION: handle periodic BC, but only for v1 = v2 = 1.0 (!!!!) + cent = x - cent # distance to center point + # cent = cross(iniaxis, cent) # distance to axis, tangent vector, length r + # cross product with iniaxis = [0, 0, 1] + cent = SVector(-cent[2], cent[1]) + r2 = cent[1]^2 + cent[2]^2 + du = iniamplitude / (2 * π) * exp(0.5 * (1 - r2)) # vel. perturbation + dtemp = -(equations.gamma - 1) / (2 * equations.gamma * rt) * du^2 # isentropic + rho = rho * (1 + dtemp)^(1 / (equations.gamma - 1)) + vel = vel + du * cent + v1, v2 = vel + p = p * (1 + dtemp)^(equations.gamma / (equations.gamma - 1)) + prim = SVector(rho, v1, v2, p) + return prim2cons(prim, equations) end -semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition_isentropic_vortex, solver) +semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition_isentropic_vortex, + solver) u0_ode = compute_coefficients(0.0, semi) J = ForwardDiff.jacobian((du_ode, γ) -> begin - equations_inner = CompressibleEulerEquations2D(first(γ)) - semi_inner = Trixi.remake(semi, equations=equations_inner, uEltype=eltype(γ)) - Trixi.rhs!(du_ode, u0_ode, semi_inner, 0.0) - end, similar(u0_ode), [1.4]); # γ needs to be an `AbstractArray` + equations_inner = CompressibleEulerEquations2D(first(γ)) + semi_inner = Trixi.remake(semi, equations = equations_inner, + uEltype = eltype(γ)) + Trixi.rhs!(du_ode, u0_ode, semi_inner, 0.0) + end, similar(u0_ode), [1.4]); # γ needs to be an `AbstractArray` diff --git a/examples/structured_1d_dgsem/elixir_advection_basic.jl b/examples/structured_1d_dgsem/elixir_advection_basic.jl index 82464f23964..cdabeb4c61a 100644 --- a/examples/structured_1d_dgsem/elixir_advection_basic.jl +++ b/examples/structured_1d_dgsem/elixir_advection_basic.jl @@ -11,7 +11,7 @@ advection_velocity = 1.0 equations = LinearScalarAdvectionEquation1D(advection_velocity) # Create DG solver with polynomial degree = 3 and (local) Lax-Friedrichs/Rusanov flux as surface flux -solver = DGSEM(polydeg=3, surface_flux=flux_lax_friedrichs) +solver = DGSEM(polydeg = 3, surface_flux = flux_lax_friedrichs) coordinates_min = (-1.0,) # minimum coordinate coordinates_max = (1.0,) # maximum coordinate @@ -21,8 +21,8 @@ cells_per_dimension = (16,) mesh = StructuredMesh(cells_per_dimension, coordinates_min, coordinates_max) # A semidiscretization collects data structures and functions for the spatial discretization -semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition_convergence_test, solver) - +semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition_convergence_test, + solver) ############################################################################### # ODE solvers, callbacks etc. @@ -35,26 +35,26 @@ ode = semidiscretize(semi, (0.0, 1.0)); summary_callback = SummaryCallback() # The AnalysisCallback allows to analyse the solution in regular intervals and prints the results -analysis_callback = AnalysisCallback(semi, interval=100) +analysis_callback = AnalysisCallback(semi, interval = 100) # The SaveSolutionCallback allows to save the solution to a file in regular intervals -save_solution = SaveSolutionCallback(interval=100, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 100, + solution_variables = cons2prim) # The StepsizeCallback handles the re-calculation of the maximum Δt after each time step -stepsize_callback = StepsizeCallback(cfl=1.6) +stepsize_callback = StepsizeCallback(cfl = 1.6) # Create a CallbackSet to collect all callbacks such that they can be passed to the ODE solver -callbacks = CallbackSet(summary_callback, analysis_callback, save_solution, stepsize_callback) - +callbacks = CallbackSet(summary_callback, analysis_callback, save_solution, + stepsize_callback) ############################################################################### # run the simulation # OrdinaryDiffEq's `solve` method evolves the solution in time and executes the passed callbacks -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); # Print the timer summary summary_callback() diff --git a/examples/structured_1d_dgsem/elixir_advection_nonperiodic.jl b/examples/structured_1d_dgsem/elixir_advection_nonperiodic.jl index e87e0b36b0a..1e0c579ffcf 100644 --- a/examples/structured_1d_dgsem/elixir_advection_nonperiodic.jl +++ b/examples/structured_1d_dgsem/elixir_advection_nonperiodic.jl @@ -11,18 +11,16 @@ equations = LinearScalarAdvectionEquation1D(advection_velocity) initial_condition = initial_condition_gauss boundary_conditions = BoundaryConditionDirichlet(initial_condition) -solver = DGSEM(polydeg=3, surface_flux=flux_lax_friedrichs) +solver = DGSEM(polydeg = 3, surface_flux = flux_lax_friedrichs) coordinates_min = (0.0,) coordinates_max = (5.0,) -mesh = StructuredMesh((16,), coordinates_min, coordinates_max, periodicity=false) - +mesh = StructuredMesh((16,), coordinates_min, coordinates_max, periodicity = false) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver, - boundary_conditions=boundary_conditions) - + boundary_conditions = boundary_conditions) ############################################################################### # ODE solvers, callbacks etc. @@ -33,31 +31,30 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval, - extra_analysis_integrals=(entropy,)) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval, + extra_analysis_integrals = (entropy,)) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_restart = SaveRestartCallback(interval=100, - save_final_restart=true) +save_restart = SaveRestartCallback(interval = 100, + save_final_restart = true) -save_solution = SaveSolutionCallback(interval=100, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 100, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) -stepsize_callback = StepsizeCallback(cfl=1.6) +stepsize_callback = StepsizeCallback(cfl = 1.6) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, save_restart, save_solution, stepsize_callback); - ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=stepsize_callback(ode), # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = stepsize_callback(ode), # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/structured_1d_dgsem/elixir_advection_shockcapturing.jl b/examples/structured_1d_dgsem/elixir_advection_shockcapturing.jl index 313812fe08d..96566bc2373 100644 --- a/examples/structured_1d_dgsem/elixir_advection_shockcapturing.jl +++ b/examples/structured_1d_dgsem/elixir_advection_shockcapturing.jl @@ -17,30 +17,30 @@ Slight simplification from [DOI: 10.1006/jcph.1996.0130](https://doi.org/10.1006/jcph.1996.0130) """ function initial_condition_composite(x, t, equations::LinearScalarAdvectionEquation1D) - xmin, xmax = -1.0, 1.0 # Only works if the domain is [-1.0,1.0] - x_trans = x[1] - t - L = xmax - xmin - if x_trans > xmax - x_ = x_trans - L * floor((x_trans + xmin) / L) - elseif x_trans < xmin - x_ = x_trans + L * floor((xmax - x_trans) / L) - else - x_ = x_trans - end - - if x_ > -0.8 && x_ < -0.6 - value = exp(-log(2.0) * (x_ + 0.7)^2 / 0.0009) - elseif x_ > -0.4 && x_ < -0.2 - value = 1.0 - elseif x_ > 0.0 && x_ < 0.2 - value = 1.0 - abs(10.0 * (x_ - 0.1)) - elseif x_ > 0.4 && x_ < 0.6 - value = sqrt(1.0 - 100.0 * (x_ - 0.5)^2) - else - value = 0.0 - end - - return SVector(value) + xmin, xmax = -1.0, 1.0 # Only works if the domain is [-1.0,1.0] + x_trans = x[1] - t + L = xmax - xmin + if x_trans > xmax + x_ = x_trans - L * floor((x_trans + xmin) / L) + elseif x_trans < xmin + x_ = x_trans + L * floor((xmax - x_trans) / L) + else + x_ = x_trans + end + + if x_ > -0.8 && x_ < -0.6 + value = exp(-log(2.0) * (x_ + 0.7)^2 / 0.0009) + elseif x_ > -0.4 && x_ < -0.2 + value = 1.0 + elseif x_ > 0.0 && x_ < 0.2 + value = 1.0 - abs(10.0 * (x_ - 0.1)) + elseif x_ > 0.4 && x_ < 0.6 + value = sqrt(1.0 - 100.0 * (x_ - 0.5)^2) + else + value = 0.0 + end + + return SVector(value) end initial_condition = initial_condition_composite @@ -52,13 +52,13 @@ volume_flux = flux_central polydeg = 3 basis = LobattoLegendreBasis(polydeg) indicator_sc = IndicatorHennemannGassner(equations, basis, - alpha_max=0.5, - alpha_min=0.001, - alpha_smooth=true, - variable=Trixi.first) + alpha_max = 0.5, + alpha_min = 0.001, + alpha_smooth = true, + variable = Trixi.first) volume_integral = VolumeIntegralShockCapturingHG(indicator_sc; - volume_flux_dg=volume_flux, - volume_flux_fv=surface_flux) + volume_flux_dg = volume_flux, + volume_flux_fv = surface_flux) solver = DGSEM(basis, surface_flux, volume_integral) # Create curved mesh @@ -66,12 +66,11 @@ cells_per_dimension = (120,) coordinates_min = (-1.0,) # minimum coordinate coordinates_max = (1.0,) # maximum coordinate mesh = StructuredMesh(cells_per_dimension, coordinates_min, coordinates_max, - periodicity=true) + periodicity = true) # A semidiscretization collects data structures and functions for the spatial discretization semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver) - ############################################################################### # ODE solvers, callbacks etc. @@ -84,23 +83,23 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() # The AnalysisCallback allows to analyse the solution in regular intervals and prints the results -analysis_callback = AnalysisCallback(semi, interval=100) +analysis_callback = AnalysisCallback(semi, interval = 100) # The SaveSolutionCallback allows to save the solution to a file in regular intervals -save_solution = SaveSolutionCallback(interval=100, solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 100, solution_variables = cons2prim) # The StepsizeCallback handles the re-calculation of the maximum Δt after each time step -stepsize_callback = StepsizeCallback(cfl=0.5) +stepsize_callback = StepsizeCallback(cfl = 0.5) # Create a CallbackSet to collect all callbacks such that they can be passed to the ODE solver -callbacks = CallbackSet(summary_callback, analysis_callback, save_solution, stepsize_callback) - +callbacks = CallbackSet(summary_callback, analysis_callback, save_solution, + stepsize_callback) ############################################################################### # run the simulation # OrdinaryDiffEq's `solve` method evolves the solution in time and executes the passed callbacks -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); -summary_callback() # print the timer summary \ No newline at end of file +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); +summary_callback() # print the timer summary diff --git a/examples/structured_1d_dgsem/elixir_euler_sedov.jl b/examples/structured_1d_dgsem/elixir_euler_sedov.jl index 9d7be21a5c1..4ffa100cc71 100644 --- a/examples/structured_1d_dgsem/elixir_euler_sedov.jl +++ b/examples/structured_1d_dgsem/elixir_euler_sedov.jl @@ -14,50 +14,50 @@ The Sedov blast wave setup based on Flash - https://flash.rochester.edu/site/flashcode/user_support/flash_ug_devel/node187.html#SECTION010114000000000000000 """ function initial_condition_sedov_blast_wave(x, t, equations::CompressibleEulerEquations1D) - # Set up polar coordinates - inicenter = SVector(0.0) - x_norm = x[1] - inicenter[1] - r = abs(x_norm) - - # Setup based on https://flash.rochester.edu/site/flashcode/user_support/flash_ug_devel/node187.html#SECTION010114000000000000000 - r0 = 0.21875 # = 3.5 * smallest dx (for domain length=4 and max-ref=6) - # r0 = 0.5 # = more reasonable setup - E = 1.0 - p0_inner = 6 * (equations.gamma - 1) * E / (3 * pi * r0) - p0_outer = 1.0e-5 # = true Sedov setup - - # Calculate primitive variables - rho = 1.0 - v1 = 0.0 - p = r > r0 ? p0_outer : p0_inner - - return prim2cons(SVector(rho, v1, p), equations) + # Set up polar coordinates + inicenter = SVector(0.0) + x_norm = x[1] - inicenter[1] + r = abs(x_norm) + + # Setup based on https://flash.rochester.edu/site/flashcode/user_support/flash_ug_devel/node187.html#SECTION010114000000000000000 + r0 = 0.21875 # = 3.5 * smallest dx (for domain length=4 and max-ref=6) + # r0 = 0.5 # = more reasonable setup + E = 1.0 + p0_inner = 6 * (equations.gamma - 1) * E / (3 * pi * r0) + p0_outer = 1.0e-5 # = true Sedov setup + + # Calculate primitive variables + rho = 1.0 + v1 = 0.0 + p = r > r0 ? p0_outer : p0_inner + + return prim2cons(SVector(rho, v1, p), equations) end initial_condition = initial_condition_sedov_blast_wave surface_flux = flux_lax_friedrichs -volume_flux = flux_ranocha +volume_flux = flux_ranocha basis = LobattoLegendreBasis(3) shock_indicator_variable = density_pressure indicator_sc = IndicatorHennemannGassner(equations, basis, - alpha_max=1.0, - alpha_min=0.001, - alpha_smooth=true, - variable=shock_indicator_variable) + alpha_max = 1.0, + alpha_min = 0.001, + alpha_smooth = true, + variable = shock_indicator_variable) volume_integral = VolumeIntegralShockCapturingHG(indicator_sc; - volume_flux_dg=volume_flux, - volume_flux_fv=surface_flux) + volume_flux_dg = volume_flux, + volume_flux_fv = surface_flux) solver = DGSEM(basis, surface_flux, volume_integral) cells_per_dimension = (64,) coordinates_min = (-2.0,) -coordinates_max = ( 2.0,) -mesh = StructuredMesh(cells_per_dimension, coordinates_min, coordinates_max, periodicity=true) +coordinates_max = (2.0,) +mesh = StructuredMesh(cells_per_dimension, coordinates_min, coordinates_max, + periodicity = true) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver) - ############################################################################### # ODE solvers, callbacks etc. @@ -67,16 +67,16 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 1000 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=100, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 100, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) -stepsize_callback = StepsizeCallback(cfl=0.5) +stepsize_callback = StepsizeCallback(cfl = 0.5) callbacks = CallbackSet(summary_callback, analysis_callback, @@ -84,11 +84,10 @@ callbacks = CallbackSet(summary_callback, save_solution, stepsize_callback) - ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=stepsize_callback(ode), # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = stepsize_callback(ode), # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/structured_1d_dgsem/elixir_euler_source_terms.jl b/examples/structured_1d_dgsem/elixir_euler_source_terms.jl index cbda7087052..97767f3e127 100644 --- a/examples/structured_1d_dgsem/elixir_euler_source_terms.jl +++ b/examples/structured_1d_dgsem/elixir_euler_source_terms.jl @@ -13,7 +13,7 @@ initial_condition = initial_condition_convergence_test # Note that the expected EOC of 5 is not reached with this flux. # Using flux_hll instead yields the expected EOC. -solver = DGSEM(polydeg=4, surface_flux=flux_lax_friedrichs) +solver = DGSEM(polydeg = 4, surface_flux = flux_lax_friedrichs) coordinates_min = (0.0,) coordinates_max = (2.0,) @@ -21,10 +21,8 @@ cells_per_dimension = (16,) mesh = StructuredMesh(cells_per_dimension, coordinates_min, coordinates_max) - semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver, - source_terms=source_terms_convergence_test) - + source_terms = source_terms_convergence_test) ############################################################################### # ODE solvers, callbacks etc. @@ -35,29 +33,28 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval, - extra_analysis_errors=(:l2_error_primitive, - :linf_error_primitive)) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval, + extra_analysis_errors = (:l2_error_primitive, + :linf_error_primitive)) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=100, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 100, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) -stepsize_callback = StepsizeCallback(cfl=0.8) +stepsize_callback = StepsizeCallback(cfl = 0.8) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, save_solution, stepsize_callback) - ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/structured_1d_dgsem/elixir_euler_source_terms_nonperiodic.jl b/examples/structured_1d_dgsem/elixir_euler_source_terms_nonperiodic.jl index 9aa5b7f4979..d5063838136 100644 --- a/examples/structured_1d_dgsem/elixir_euler_source_terms_nonperiodic.jl +++ b/examples/structured_1d_dgsem/elixir_euler_source_terms_nonperiodic.jl @@ -15,20 +15,18 @@ source_terms = source_terms_convergence_test # 1*ndims == 2 directions or you can pass a tuple containing BCs for # each direction boundary_condition = BoundaryConditionDirichlet(initial_condition) -boundary_conditions = (x_neg=boundary_condition, - x_pos=boundary_condition) +boundary_conditions = (x_neg = boundary_condition, + x_pos = boundary_condition) -solver = DGSEM(polydeg=3, surface_flux=flux_lax_friedrichs) +solver = DGSEM(polydeg = 3, surface_flux = flux_lax_friedrichs) f1() = SVector(0.0) f2() = SVector(2.0) -mesh = StructuredMesh((16,), (f1, f2), periodicity=false) - +mesh = StructuredMesh((16,), (f1, f2), periodicity = false) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver, - source_terms=source_terms, - boundary_conditions=boundary_conditions) - + source_terms = source_terms, + boundary_conditions = boundary_conditions) ############################################################################### # ODE solvers, callbacks etc. @@ -39,30 +37,29 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_restart = SaveRestartCallback(interval=100, - save_final_restart=true) +save_restart = SaveRestartCallback(interval = 100, + save_final_restart = true) -save_solution = SaveSolutionCallback(interval=100, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 100, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) -stepsize_callback = StepsizeCallback(cfl=0.8) +stepsize_callback = StepsizeCallback(cfl = 0.8) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, save_restart, save_solution, stepsize_callback) - ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/structured_2d_dgsem/elixir_advection_basic.jl b/examples/structured_2d_dgsem/elixir_advection_basic.jl index 7d2e1f49276..1d7235fc214 100644 --- a/examples/structured_2d_dgsem/elixir_advection_basic.jl +++ b/examples/structured_2d_dgsem/elixir_advection_basic.jl @@ -11,10 +11,10 @@ advection_velocity = (0.2, -0.7) equations = LinearScalarAdvectionEquation2D(advection_velocity) # Create DG solver with polynomial degree = 3 and (local) Lax-Friedrichs/Rusanov flux as surface flux -solver = DGSEM(polydeg=3, surface_flux=flux_lax_friedrichs) +solver = DGSEM(polydeg = 3, surface_flux = flux_lax_friedrichs) coordinates_min = (-1.0, -1.0) # minimum coordinates (min(x), min(y)) -coordinates_max = ( 1.0, 1.0) # maximum coordinates (max(x), max(y)) +coordinates_max = (1.0, 1.0) # maximum coordinates (max(x), max(y)) cells_per_dimension = (16, 16) @@ -22,8 +22,8 @@ cells_per_dimension = (16, 16) mesh = StructuredMesh(cells_per_dimension, coordinates_min, coordinates_max) # A semidiscretization collects data structures and functions for the spatial discretization -semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition_convergence_test, solver) - +semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition_convergence_test, + solver) ############################################################################### # ODE solvers, callbacks etc. @@ -36,26 +36,26 @@ ode = semidiscretize(semi, (0.0, 1.0)); summary_callback = SummaryCallback() # The AnalysisCallback allows to analyse the solution in regular intervals and prints the results -analysis_callback = AnalysisCallback(semi, interval=100) +analysis_callback = AnalysisCallback(semi, interval = 100) # The SaveSolutionCallback allows to save the solution to a file in regular intervals -save_solution = SaveSolutionCallback(interval=100, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 100, + solution_variables = cons2prim) # The StepsizeCallback handles the re-calculation of the maximum Δt after each time step -stepsize_callback = StepsizeCallback(cfl=1.6) +stepsize_callback = StepsizeCallback(cfl = 1.6) # Create a CallbackSet to collect all callbacks such that they can be passed to the ODE solver -callbacks = CallbackSet(summary_callback, analysis_callback, save_solution, stepsize_callback) - +callbacks = CallbackSet(summary_callback, analysis_callback, save_solution, + stepsize_callback) ############################################################################### # run the simulation # OrdinaryDiffEq's `solve` method evolves the solution in time and executes the passed callbacks -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); # Print the timer summary summary_callback() diff --git a/examples/structured_2d_dgsem/elixir_advection_coupled.jl b/examples/structured_2d_dgsem/elixir_advection_coupled.jl index 1e54e411db6..2a56d23f4c0 100644 --- a/examples/structured_2d_dgsem/elixir_advection_coupled.jl +++ b/examples/structured_2d_dgsem/elixir_advection_coupled.jl @@ -1,7 +1,6 @@ using OrdinaryDiffEq using Trixi - ############################################################################### # Coupled semidiscretization of two linear advection systems, which are connected periodically # @@ -35,11 +34,11 @@ advection_velocity = (0.2, -0.7) equations = LinearScalarAdvectionEquation2D(advection_velocity) # Create DG solver with polynomial degree = 3 and (local) Lax-Friedrichs/Rusanov flux as surface flux -solver = DGSEM(polydeg=3, surface_flux=flux_lax_friedrichs) +solver = DGSEM(polydeg = 3, surface_flux = flux_lax_friedrichs) # First mesh is the left half of a [-1,1]^2 square coordinates_min1 = (-1.0, -1.0) # minimum coordinates (min(x), min(y)) -coordinates_max1 = ( 0.0, 1.0) # maximum coordinates (max(x), max(y)) +coordinates_max1 = (0.0, 1.0) # maximum coordinates (max(x), max(y)) # Define identical resolution as a variable such that it is easier to change from `trixi_include` cells_per_dimension = (8, 16) @@ -49,32 +48,45 @@ cells_per_dimension1 = cells_per_dimension mesh1 = StructuredMesh(cells_per_dimension1, coordinates_min1, coordinates_max1) # A semidiscretization collects data structures and functions for the spatial discretization -semi1 = SemidiscretizationHyperbolic(mesh1, equations, initial_condition_convergence_test, solver, - boundary_conditions=( - # Connect left boundary with right boundary of right mesh - x_neg=BoundaryConditionCoupled(2, (:end, :i_forward), Float64), - # Connect right boundary with left boundary of right mesh - x_pos=BoundaryConditionCoupled(2, (:begin, :i_forward), Float64), - y_neg=boundary_condition_periodic, - y_pos=boundary_condition_periodic)) - +semi1 = SemidiscretizationHyperbolic(mesh1, equations, initial_condition_convergence_test, + solver, + boundary_conditions = ( + # Connect left boundary with right boundary of right mesh + x_neg = BoundaryConditionCoupled(2, + (:end, + :i_forward), + Float64), + # Connect right boundary with left boundary of right mesh + x_pos = BoundaryConditionCoupled(2, + (:begin, + :i_forward), + Float64), + y_neg = boundary_condition_periodic, + y_pos = boundary_condition_periodic)) # Second mesh is the right half of a [-1,1]^2 square coordinates_min2 = (0.0, -1.0) # minimum coordinates (min(x), min(y)) -coordinates_max2 = (1.0, 1.0) # maximum coordinates (max(x), max(y)) +coordinates_max2 = (1.0, 1.0) # maximum coordinates (max(x), max(y)) cells_per_dimension2 = cells_per_dimension mesh2 = StructuredMesh(cells_per_dimension2, coordinates_min2, coordinates_max2) -semi2 = SemidiscretizationHyperbolic(mesh2, equations, initial_condition_convergence_test, solver, - boundary_conditions=( - # Connect left boundary with right boundary of left mesh - x_neg=BoundaryConditionCoupled(1, (:end, :i_forward), Float64), - # Connect right boundary with left boundary of left mesh - x_pos=BoundaryConditionCoupled(1, (:begin, :i_forward), Float64), - y_neg=boundary_condition_periodic, - y_pos=boundary_condition_periodic)) +semi2 = SemidiscretizationHyperbolic(mesh2, equations, initial_condition_convergence_test, + solver, + boundary_conditions = ( + # Connect left boundary with right boundary of left mesh + x_neg = BoundaryConditionCoupled(1, + (:end, + :i_forward), + Float64), + # Connect right boundary with left boundary of left mesh + x_pos = BoundaryConditionCoupled(1, + (:begin, + :i_forward), + Float64), + y_neg = boundary_condition_periodic, + y_pos = boundary_condition_periodic)) # Create a semidiscretization that bundles semi1 and semi2 semi = SemidiscretizationCoupled(semi1, semi2) @@ -90,28 +102,28 @@ ode = semidiscretize(semi, (0.0, 2.0)); summary_callback = SummaryCallback() # The AnalysisCallback allows to analyse the solution in regular intervals and prints the results -analysis_callback1 = AnalysisCallback(semi1, interval=100) -analysis_callback2 = AnalysisCallback(semi2, interval=100) +analysis_callback1 = AnalysisCallback(semi1, interval = 100) +analysis_callback2 = AnalysisCallback(semi2, interval = 100) analysis_callback = AnalysisCallbackCoupled(semi, analysis_callback1, analysis_callback2) # The SaveSolutionCallback allows to save the solution to a file in regular intervals -save_solution = SaveSolutionCallback(interval=100, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 100, + solution_variables = cons2prim) # The StepsizeCallback handles the re-calculation of the maximum Δt after each time step -stepsize_callback = StepsizeCallback(cfl=1.6) +stepsize_callback = StepsizeCallback(cfl = 1.6) # Create a CallbackSet to collect all callbacks such that they can be passed to the ODE solver -callbacks = CallbackSet(summary_callback, analysis_callback, save_solution, stepsize_callback) - +callbacks = CallbackSet(summary_callback, analysis_callback, save_solution, + stepsize_callback) ############################################################################### # run the simulation # OrdinaryDiffEq's `solve` method evolves the solution in time and executes the passed callbacks -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); # Print the timer summary summary_callback() diff --git a/examples/structured_2d_dgsem/elixir_advection_extended.jl b/examples/structured_2d_dgsem/elixir_advection_extended.jl index fbaa7783d99..df7e1f375a9 100644 --- a/examples/structured_2d_dgsem/elixir_advection_extended.jl +++ b/examples/structured_2d_dgsem/elixir_advection_extended.jl @@ -18,11 +18,11 @@ initial_condition = initial_condition_convergence_test boundary_conditions = boundary_condition_periodic # Create DG solver with polynomial degree = 3 and (local) Lax-Friedrichs/Rusanov flux as surface flux -solver = DGSEM(polydeg=3, surface_flux=flux_lax_friedrichs) +solver = DGSEM(polydeg = 3, surface_flux = flux_lax_friedrichs) # The initial condition is 2-periodic coordinates_min = (-1.5, 1.3) # minimum coordinates (min(x), min(y)) -coordinates_max = ( 0.5, 5.3) # maximum coordinates (max(x), max(y)) +coordinates_max = (0.5, 5.3) # maximum coordinates (max(x), max(y)) cells_per_dimension = (19, 37) @@ -31,8 +31,7 @@ mesh = StructuredMesh(cells_per_dimension, coordinates_min, coordinates_max) # A semidiscretization collects data structures and functions for the spatial discretization semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver, - boundary_conditions=boundary_conditions) - + boundary_conditions = boundary_conditions) ############################################################################### # ODE solvers, callbacks etc. @@ -47,24 +46,24 @@ summary_callback = SummaryCallback() # The AnalysisCallback allows to analyse the solution in regular intervals and prints the results analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval, - extra_analysis_integrals=(entropy, energy_total)) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval, + extra_analysis_integrals = (entropy, energy_total)) # The AliveCallback prints short status information in regular intervals -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) # The SaveRestartCallback allows to save a file from which a Trixi.jl simulation can be restarted -save_restart = SaveRestartCallback(interval=100, - save_final_restart=true) +save_restart = SaveRestartCallback(interval = 100, + save_final_restart = true) # The SaveSolutionCallback allows to save the solution to a file in regular intervals -save_solution = SaveSolutionCallback(interval=100, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 100, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) # The StepsizeCallback handles the re-calculation of the maximum Δt after each time step -stepsize_callback = StepsizeCallback(cfl=1.6) +stepsize_callback = StepsizeCallback(cfl = 1.6) # Create a CallbackSet to collect all callbacks such that they can be passed to the ODE solver callbacks = CallbackSet(summary_callback, @@ -72,14 +71,13 @@ callbacks = CallbackSet(summary_callback, save_restart, save_solution, stepsize_callback) - ############################################################################### # run the simulation # OrdinaryDiffEq's `solve` method evolves the solution in time and executes the passed callbacks -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); # Print the timer summary summary_callback() diff --git a/examples/structured_2d_dgsem/elixir_advection_free_stream.jl b/examples/structured_2d_dgsem/elixir_advection_free_stream.jl index 155a2d19fc9..7785b4f9e18 100644 --- a/examples/structured_2d_dgsem/elixir_advection_free_stream.jl +++ b/examples/structured_2d_dgsem/elixir_advection_free_stream.jl @@ -11,21 +11,21 @@ equations = LinearScalarAdvectionEquation2D(advection_velocity) initial_condition = initial_condition_constant # Create DG solver with polynomial degree = 3 and (local) Lax-Friedrichs/Rusanov flux as surface flux -solver = DGSEM(polydeg=3, surface_flux=flux_lax_friedrichs) +solver = DGSEM(polydeg = 3, surface_flux = flux_lax_friedrichs) # Mapping as described in https://arxiv.org/abs/2012.12040, but reduced to 2D function mapping(xi_, eta_) - # Transform input variables between -1 and 1 onto [0,3] - xi = 1.5 * xi_ + 1.5 - eta = 1.5 * eta_ + 1.5 + # Transform input variables between -1 and 1 onto [0,3] + xi = 1.5 * xi_ + 1.5 + eta = 1.5 * eta_ + 1.5 - y = eta + 3/8 * (cos(1.5 * pi * (2 * xi - 3)/3) * - cos(0.5 * pi * (2 * eta - 3)/3)) + y = eta + 3 / 8 * (cos(1.5 * pi * (2 * xi - 3) / 3) * + cos(0.5 * pi * (2 * eta - 3) / 3)) - x = xi + 3/8 * (cos(0.5 * pi * (2 * xi - 3)/3) * - cos(2 * pi * (2 * y - 3)/3)) + x = xi + 3 / 8 * (cos(0.5 * pi * (2 * xi - 3) / 3) * + cos(2 * pi * (2 * y - 3) / 3)) - return SVector(x, y) + return SVector(x, y) end cells_per_dimension = (16, 16) @@ -36,7 +36,6 @@ mesh = StructuredMesh(cells_per_dimension, mapping) # A semidiscretization collects data structures and functions for the spatial discretization semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver) - ############################################################################### # ODE solvers, callbacks etc. @@ -48,30 +47,30 @@ ode = semidiscretize(semi, (0.0, 1.0)); summary_callback = SummaryCallback() # The AnalysisCallback allows to analyse the solution in regular intervals and prints the results -analysis_callback = AnalysisCallback(semi, interval=100) +analysis_callback = AnalysisCallback(semi, interval = 100) # The SaveSolutionCallback allows to save the solution to a file in regular intervals -save_solution = SaveSolutionCallback(interval=100, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 100, + solution_variables = cons2prim) # The SaveRestartCallback allows to save a file from which a Trixi.jl simulation can be restarted -save_restart = SaveRestartCallback(interval=100, - save_final_restart=true) +save_restart = SaveRestartCallback(interval = 100, + save_final_restart = true) # The StepsizeCallback handles the re-calculation of the maximum Δt after each time step -stepsize_callback = StepsizeCallback(cfl=2.0) +stepsize_callback = StepsizeCallback(cfl = 2.0) # Create a CallbackSet to collect all callbacks such that they can be passed to the ODE solver -callbacks = CallbackSet(summary_callback, analysis_callback, save_restart, save_solution, stepsize_callback) - +callbacks = CallbackSet(summary_callback, analysis_callback, save_restart, save_solution, + stepsize_callback) ############################################################################### # run the simulation # OrdinaryDiffEq's `solve` method evolves the solution in time and executes the passed callbacks -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); # Print the timer summary summary_callback() diff --git a/examples/structured_2d_dgsem/elixir_advection_nonperiodic.jl b/examples/structured_2d_dgsem/elixir_advection_nonperiodic.jl index 2aad3a01566..e2e113b168d 100644 --- a/examples/structured_2d_dgsem/elixir_advection_nonperiodic.jl +++ b/examples/structured_2d_dgsem/elixir_advection_nonperiodic.jl @@ -13,16 +13,14 @@ initial_condition = initial_condition_gauss # you can either use a single function to impose the BCs weakly in all # 2*ndims == 4 directions or you can pass a tuple containing BCs for each direction boundary_conditions = BoundaryConditionDirichlet(initial_condition) -solver = DGSEM(polydeg=3, surface_flux=flux_lax_friedrichs) +solver = DGSEM(polydeg = 3, surface_flux = flux_lax_friedrichs) coordinates_min = (-5.0, -5.0) -coordinates_max = ( 5.0, 5.0) -mesh = StructuredMesh((16, 16), coordinates_min, coordinates_max, periodicity=false) - +coordinates_max = (5.0, 5.0) +mesh = StructuredMesh((16, 16), coordinates_min, coordinates_max, periodicity = false) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver, - boundary_conditions=boundary_conditions) - + boundary_conditions = boundary_conditions) ############################################################################### # ODE solvers, callbacks etc. @@ -33,17 +31,17 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval, - extra_analysis_integrals=(entropy,)) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval, + extra_analysis_integrals = (entropy,)) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=100, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 100, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) -stepsize_callback = StepsizeCallback(cfl=1.6) +stepsize_callback = StepsizeCallback(cfl = 1.6) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, @@ -52,7 +50,7 @@ callbacks = CallbackSet(summary_callback, ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=stepsize_callback(ode), # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = stepsize_callback(ode), # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/structured_2d_dgsem/elixir_advection_parallelogram.jl b/examples/structured_2d_dgsem/elixir_advection_parallelogram.jl index b9a6d3f91ae..b70deb12318 100644 --- a/examples/structured_2d_dgsem/elixir_advection_parallelogram.jl +++ b/examples/structured_2d_dgsem/elixir_advection_parallelogram.jl @@ -7,24 +7,23 @@ using OrdinaryDiffEq using Trixi - # initial_condition_convergence_test transformed to the parallelogram function initial_condition_parallelogram(x, t, equation::LinearScalarAdvectionEquation2D) - # Transform back to unit square - x_transformed = SVector(x[1] - x[2], x[2]) - a = equation.advection_velocity - a_transformed = SVector(a[1] - a[2], a[2]) - - # Store translated coordinate for easy use of exact solution - x_translated = x_transformed - a_transformed * t - - c = 1.0 - A = 0.5 - L = 2 - f = 1/L - omega = 2 * pi * f - scalar = c + A * sin(omega * sum(x_translated)) - return SVector(scalar) + # Transform back to unit square + x_transformed = SVector(x[1] - x[2], x[2]) + a = equation.advection_velocity + a_transformed = SVector(a[1] - a[2], a[2]) + + # Store translated coordinate for easy use of exact solution + x_translated = x_transformed - a_transformed * t + + c = 1.0 + A = 0.5 + L = 2 + f = 1 / L + omega = 2 * pi * f + scalar = c + A * sin(omega * sum(x_translated)) + return SVector(scalar) end ############################################################################### @@ -35,7 +34,7 @@ advection_velocity = (-0.5, -0.7) equations = LinearScalarAdvectionEquation2D(advection_velocity) # Create DG solver with polynomial degree = 3 and (local) Lax-Friedrichs/Rusanov flux as surface flux -solver = DGSEM(polydeg=3, surface_flux=flux_lax_friedrichs) +solver = DGSEM(polydeg = 3, surface_flux = flux_lax_friedrichs) # Define faces for a parallelogram that looks like this # @@ -49,11 +48,11 @@ mapping(xi, eta) = SVector(xi + eta, eta) cells_per_dimension = (16, 16) # Create curved mesh with 16 x 16 elements, periodic in both dimensions -mesh = StructuredMesh(cells_per_dimension, mapping; periodicity=(true, true)) +mesh = StructuredMesh(cells_per_dimension, mapping; periodicity = (true, true)) # A semidiscretization collects data structures and functions for the spatial discretization -semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition_parallelogram, solver) - +semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition_parallelogram, + solver) ############################################################################### # ODE solvers, callbacks etc. @@ -66,26 +65,26 @@ ode = semidiscretize(semi, (0.0, 1.0)); summary_callback = SummaryCallback() # The AnalysisCallback allows to analyse the solution in regular intervals and prints the results -analysis_callback = AnalysisCallback(semi, interval=100) +analysis_callback = AnalysisCallback(semi, interval = 100) # The SaveSolutionCallback allows to save the solution to a file in regular intervals -save_solution = SaveSolutionCallback(interval=100, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 100, + solution_variables = cons2prim) # The StepsizeCallback handles the re-calculation of the maximum Δt after each time step -stepsize_callback = StepsizeCallback(cfl=1.6) +stepsize_callback = StepsizeCallback(cfl = 1.6) # Create a CallbackSet to collect all callbacks such that they can be passed to the ODE solver -callbacks = CallbackSet(summary_callback, analysis_callback, save_solution, stepsize_callback) - +callbacks = CallbackSet(summary_callback, analysis_callback, save_solution, + stepsize_callback) ############################################################################### # run the simulation # OrdinaryDiffEq's `solve` method evolves the solution in time and executes the passed callbacks -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); # Print the timer summary summary_callback() diff --git a/examples/structured_2d_dgsem/elixir_advection_restart.jl b/examples/structured_2d_dgsem/elixir_advection_restart.jl index 82eaa21333a..19863faae8d 100644 --- a/examples/structured_2d_dgsem/elixir_advection_restart.jl +++ b/examples/structured_2d_dgsem/elixir_advection_restart.jl @@ -10,7 +10,6 @@ restart_file = "restart_000021.h5" trixi_include(@__MODULE__, joinpath(@__DIR__, elixir_file)) - ############################################################################### # adapt the parameters that have changed compared to "elixir_advection_extended.jl" @@ -29,9 +28,9 @@ ode = semidiscretize(semi, tspan, restart_filename); # Do not overwrite the initial snapshot written by elixir_advection_extended.jl. save_solution.condition.save_initial_solution = false -integrator = init(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=dt, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +integrator = init(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = dt, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); # Get the last time index and work with that. load_timestep!(integrator, restart_filename) diff --git a/examples/structured_2d_dgsem/elixir_advection_rotated.jl b/examples/structured_2d_dgsem/elixir_advection_rotated.jl index 7dfee23a067..826c7ebaacb 100644 --- a/examples/structured_2d_dgsem/elixir_advection_rotated.jl +++ b/examples/structured_2d_dgsem/elixir_advection_rotated.jl @@ -7,7 +7,6 @@ using OrdinaryDiffEq using Trixi - # Define new structs inside a module to allow re-evaluating the file. # This module name needs to be unique among all examples, otherwise Julia will throw warnings # if multiple test cases using the same module name are run in the same session. @@ -17,40 +16,41 @@ using Trixi # initial_condition_convergence_test transformed to the rotated rectangle struct InitialConditionConvergenceTestRotated - sin_alpha::Float64 - cos_alpha::Float64 + sin_alpha::Float64 + cos_alpha::Float64 end function InitialConditionConvergenceTestRotated(alpha) - sin_alpha, cos_alpha = sincos(alpha) + sin_alpha, cos_alpha = sincos(alpha) - InitialConditionConvergenceTestRotated(sin_alpha, cos_alpha) + InitialConditionConvergenceTestRotated(sin_alpha, cos_alpha) end -function (initial_condition::InitialConditionConvergenceTestRotated)(x, t, equation::LinearScalarAdvectionEquation2D) - sin_ = initial_condition.sin_alpha - cos_ = initial_condition.cos_alpha +function (initial_condition::InitialConditionConvergenceTestRotated)(x, t, + equation::LinearScalarAdvectionEquation2D) + sin_ = initial_condition.sin_alpha + cos_ = initial_condition.cos_alpha - # Rotate back to unit square + # Rotate back to unit square - # Clockwise rotation by α and translation by 1 - # Multiply with [ cos(α) sin(α); - # -sin(α) cos(α)] - x_rot = SVector(cos_ * x[1] + sin_ * x[2], -sin_ * x[1] + cos_ * x[2]) - a = equation.advection_velocity - a_rot = SVector(cos_ * a[1] + sin_ * a[2], -sin_ * a[1] + cos_ * a[2]) + # Clockwise rotation by α and translation by 1 + # Multiply with [ cos(α) sin(α); + # -sin(α) cos(α)] + x_rot = SVector(cos_ * x[1] + sin_ * x[2], -sin_ * x[1] + cos_ * x[2]) + a = equation.advection_velocity + a_rot = SVector(cos_ * a[1] + sin_ * a[2], -sin_ * a[1] + cos_ * a[2]) - # Store translated coordinate for easy use of exact solution - x_trans = x_rot - a_rot * t + # Store translated coordinate for easy use of exact solution + x_trans = x_rot - a_rot * t - c = 1.0 - A = 0.5 - L = 2 - f = 1/L - omega = 2 * pi * f - scalar = c + A * sin(omega * sum(x_trans)) + c = 1.0 + A = 0.5 + L = 2 + f = 1 / L + omega = 2 * pi * f + scalar = c + A * sin(omega * sum(x_trans)) - return SVector(scalar) + return SVector(scalar) end end # module TrixiExtensionAdvectionRotated @@ -70,7 +70,7 @@ advection_velocity = Tuple(T * [0.2, -0.7]) equations = LinearScalarAdvectionEquation2D(advection_velocity) # Create DG solver with polynomial degree = 3 and (local) Lax-Friedrichs/Rusanov flux as surface flux -solver = DGSEM(polydeg=3, surface_flux=flux_lax_friedrichs) +solver = DGSEM(polydeg = 3, surface_flux = flux_lax_friedrichs) mapping(xi, eta) = T * SVector(xi, eta) @@ -82,7 +82,6 @@ mesh = StructuredMesh(cells_per_dimension, mapping) # A semidiscretization collects data structures and functions for the spatial discretization semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver) - ############################################################################### # ODE solvers, callbacks etc. @@ -94,26 +93,26 @@ ode = semidiscretize(semi, (0.0, 1.0)); summary_callback = SummaryCallback() # The AnalysisCallback allows to analyse the solution in regular intervals and prints the results -analysis_callback = AnalysisCallback(semi, interval=100) +analysis_callback = AnalysisCallback(semi, interval = 100) # The SaveSolutionCallback allows to save the solution to a file in regular intervals -save_solution = SaveSolutionCallback(interval=100, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 100, + solution_variables = cons2prim) # The StepsizeCallback handles the re-calculation of the maximum Δt after each time step -stepsize_callback = StepsizeCallback(cfl=1.6) +stepsize_callback = StepsizeCallback(cfl = 1.6) # Create a CallbackSet to collect all callbacks such that they can be passed to the ODE solver -callbacks = CallbackSet(summary_callback, analysis_callback, save_solution, stepsize_callback) - +callbacks = CallbackSet(summary_callback, analysis_callback, save_solution, + stepsize_callback) ############################################################################### # run the simulation # OrdinaryDiffEq's `solve` method evolves the solution in time and executes the passed callbacks -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); # Print the timer summary summary_callback() diff --git a/examples/structured_2d_dgsem/elixir_advection_waving_flag.jl b/examples/structured_2d_dgsem/elixir_advection_waving_flag.jl index d0db19ea635..50393d50a19 100644 --- a/examples/structured_2d_dgsem/elixir_advection_waving_flag.jl +++ b/examples/structured_2d_dgsem/elixir_advection_waving_flag.jl @@ -11,14 +11,14 @@ equations = LinearScalarAdvectionEquation2D(advection_velocity) initial_condition = initial_condition_convergence_test # Create DG solver with polynomial degree = 3 and (local) Lax-Friedrichs/Rusanov flux as surface flux -solver = DGSEM(polydeg=3, surface_flux=flux_lax_friedrichs) +solver = DGSEM(polydeg = 3, surface_flux = flux_lax_friedrichs) # Deformed rectangle that looks like a waving flag, # lower and upper faces are sinus curves, left and right are vertical lines. f1(s) = SVector(-1.0, s - 1.0) -f2(s) = SVector( 1.0, s + 1.0) +f2(s) = SVector(1.0, s + 1.0) f3(s) = SVector(s, -1.0 + sin(0.5 * pi * s)) -f4(s) = SVector(s, 1.0 + sin(0.5 * pi * s)) +f4(s) = SVector(s, 1.0 + sin(0.5 * pi * s)) cells_per_dimension = (16, 16) @@ -28,7 +28,6 @@ mesh = StructuredMesh(cells_per_dimension, (f1, f2, f3, f4)) # A semidiscretization collects data structures and functions for the spatial discretization semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver) - ############################################################################### # ODE solvers, callbacks etc. @@ -40,30 +39,30 @@ ode = semidiscretize(semi, (0.0, 1.0)); summary_callback = SummaryCallback() # The AnalysisCallback allows to analyse the solution in regular intervals and prints the results -analysis_callback = AnalysisCallback(semi, interval=100) +analysis_callback = AnalysisCallback(semi, interval = 100) # The SaveRestartCallback allows to save a file from which a Trixi.jl simulation can be restarted -save_restart = SaveRestartCallback(interval=100, - save_final_restart=true) +save_restart = SaveRestartCallback(interval = 100, + save_final_restart = true) # The SaveSolutionCallback allows to save the solution to a file in regular intervals -save_solution = SaveSolutionCallback(interval=100, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 100, + solution_variables = cons2prim) # The StepsizeCallback handles the re-calculation of the maximum Δt after each time step -stepsize_callback = StepsizeCallback(cfl=1.4) +stepsize_callback = StepsizeCallback(cfl = 1.4) # Create a CallbackSet to collect all callbacks such that they can be passed to the ODE solver -callbacks = CallbackSet(summary_callback, analysis_callback, save_restart, save_solution, stepsize_callback) - +callbacks = CallbackSet(summary_callback, analysis_callback, save_restart, save_solution, + stepsize_callback) ############################################################################### # run the simulation # OrdinaryDiffEq's `solve` method evolves the solution in time and executes the passed callbacks -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); # Print the timer summary summary_callback() diff --git a/examples/structured_2d_dgsem/elixir_euler_convergence_wavingflag_IDP.jl b/examples/structured_2d_dgsem/elixir_euler_convergence_wavingflag_IDP.jl index 5761e638e41..57c2d2a7801 100644 --- a/examples/structured_2d_dgsem/elixir_euler_convergence_wavingflag_IDP.jl +++ b/examples/structured_2d_dgsem/elixir_euler_convergence_wavingflag_IDP.jl @@ -14,26 +14,26 @@ volume_flux = flux_ranocha polydeg = 3 basis = LobattoLegendreBasis(polydeg) limiter_idp = SubcellLimiterIDP(equations, basis; - positivity_variables_cons=[1], - positivity_variables_nonlinear=(pressure,), - positivity_correction_factor=0.1, - spec_entropy=false, - max_iterations_newton=10, - newton_tolerances=(1.0e-12, 1.0e-14), - bar_states=true, - smoothness_indicator=false) + positivity_variables_cons = [1], + positivity_variables_nonlinear = (pressure,), + positivity_correction_factor = 0.1, + spec_entropy = false, + max_iterations_newton = 10, + newton_tolerances = (1.0e-12, 1.0e-14), + bar_states = true, + smoothness_indicator = false) volume_integral = VolumeIntegralSubcellLimiting(limiter_idp; - volume_flux_dg=volume_flux, - volume_flux_fv=surface_flux) + volume_flux_dg = volume_flux, + volume_flux_fv = surface_flux) solver = DGSEM(basis, surface_flux, volume_integral) # Deformed rectangle that looks like a waving flag, # lower and upper faces are sinus curves, left and right are vertical lines. f1(s) = SVector(-1.0, s - 1.0) -f2(s) = SVector( 1.0, s + 1.0) +f2(s) = SVector(1.0, s + 1.0) f3(s) = SVector(s, -1.0 + sin(0.5 * pi * s)) -f4(s) = SVector(s, 1.0 + sin(0.5 * pi * s)) +f4(s) = SVector(s, 1.0 + sin(0.5 * pi * s)) cells_per_dimension = (4, 4) @@ -41,7 +41,6 @@ mesh = StructuredMesh(cells_per_dimension, (f1, f2, f3, f4)) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver) - ############################################################################### # ODE solvers, callbacks etc. @@ -51,16 +50,16 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=100000, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 100000, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) -stepsize_callback = StepsizeCallback(cfl=0.9) +stepsize_callback = StepsizeCallback(cfl = 0.9) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, @@ -69,9 +68,9 @@ callbacks = CallbackSet(summary_callback, ############################################################################### # run the simulation -stage_callbacks = (SubcellLimiterIDPCorrection(), BoundsCheckCallback(save_errors=false)) +stage_callbacks = (SubcellLimiterIDPCorrection(), BoundsCheckCallback(save_errors = false)) -sol = Trixi.solve(ode, Trixi.SimpleSSPRK33(stage_callbacks=stage_callbacks); - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = Trixi.solve(ode, Trixi.SimpleSSPRK33(stage_callbacks = stage_callbacks); + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/structured_2d_dgsem/elixir_euler_convergence_wavingflag_MCL.jl b/examples/structured_2d_dgsem/elixir_euler_convergence_wavingflag_MCL.jl index fa59e5e0d37..20a20a9c20b 100644 --- a/examples/structured_2d_dgsem/elixir_euler_convergence_wavingflag_MCL.jl +++ b/examples/structured_2d_dgsem/elixir_euler_convergence_wavingflag_MCL.jl @@ -14,25 +14,26 @@ volume_flux = flux_ranocha polydeg = 3 basis = LobattoLegendreBasis(polydeg) limiter_mcl = SubcellLimiterMCL(equations, basis; - DensityLimiter=false, - DensityAlphaForAll=false, - SequentialLimiter=false, - ConservativeLimiter=false, - DensityPositivityLimiter=true, - PressurePositivityLimiterKuzmin=true, PressurePositivityLimiterKuzminExact=true, - Plotting=true) + DensityLimiter = false, + DensityAlphaForAll = false, + SequentialLimiter = false, + ConservativeLimiter = false, + DensityPositivityLimiter = true, + PressurePositivityLimiterKuzmin = true, + PressurePositivityLimiterKuzminExact = true, + Plotting = true) volume_integral = VolumeIntegralSubcellLimiting(limiter_mcl; - volume_flux_dg=volume_flux, - volume_flux_fv=surface_flux) + volume_flux_dg = volume_flux, + volume_flux_fv = surface_flux) solver = DGSEM(basis, surface_flux, volume_integral) # Deformed rectangle that looks like a waving flag, # lower and upper faces are sinus curves, left and right are vertical lines. f1(s) = SVector(-1.0, s - 1.0) -f2(s) = SVector( 1.0, s + 1.0) +f2(s) = SVector(1.0, s + 1.0) f3(s) = SVector(s, -1.0 + sin(0.5 * pi * s)) -f4(s) = SVector(s, 1.0 + sin(0.5 * pi * s)) +f4(s) = SVector(s, 1.0 + sin(0.5 * pi * s)) cells_per_dimension = (4, 4) @@ -40,7 +41,6 @@ mesh = StructuredMesh(cells_per_dimension, (f1, f2, f3, f4)) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver) - ############################################################################### # ODE solvers, callbacks etc. @@ -50,16 +50,16 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=100000, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 100000, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) -stepsize_callback = StepsizeCallback(cfl=0.9) +stepsize_callback = StepsizeCallback(cfl = 0.9) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, @@ -68,9 +68,9 @@ callbacks = CallbackSet(summary_callback, ############################################################################### # run the simulation -stage_callbacks = (BoundsCheckCallback(save_errors=false),) +stage_callbacks = (BoundsCheckCallback(save_errors = false),) -sol = Trixi.solve(ode, Trixi.SimpleSSPRK33(stage_callbacks=stage_callbacks); - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = Trixi.solve(ode, Trixi.SimpleSSPRK33(stage_callbacks = stage_callbacks); + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/structured_2d_dgsem/elixir_euler_double_mach.jl b/examples/structured_2d_dgsem/elixir_euler_double_mach.jl index 3d34e28a4f7..d306b70cb75 100644 --- a/examples/structured_2d_dgsem/elixir_euler_double_mach.jl +++ b/examples/structured_2d_dgsem/elixir_euler_double_mach.jl @@ -11,33 +11,35 @@ initial_condition = Trixi.initial_condition_double_mach_reflection boundary_condition_inflow_outflow = BoundaryConditionCharacteristic(initial_condition) -boundary_conditions = (y_neg=Trixi.boundary_condition_mixed_dirichlet_wall, - y_pos=boundary_condition_inflow_outflow, - x_pos=boundary_condition_inflow_outflow, - x_neg=boundary_condition_inflow_outflow) +boundary_conditions = (y_neg = Trixi.boundary_condition_mixed_dirichlet_wall, + y_pos = boundary_condition_inflow_outflow, + x_pos = boundary_condition_inflow_outflow, + x_neg = boundary_condition_inflow_outflow) surface_flux = flux_lax_friedrichs -volume_flux = flux_ranocha +volume_flux = flux_ranocha polydeg = 4 basis = LobattoLegendreBasis(polydeg) limiter_idp = SubcellLimiterIDP(equations, basis; - local_minmax_variables_cons=[1], - spec_entropy=true, - positivity_correction_factor=0.1, max_iterations_newton=100, - bar_states=true) + local_minmax_variables_cons = [1], + spec_entropy = true, + positivity_correction_factor = 0.1, + max_iterations_newton = 100, + bar_states = true) volume_integral = VolumeIntegralSubcellLimiting(limiter_idp; - volume_flux_dg=volume_flux, - volume_flux_fv=surface_flux) + volume_flux_dg = volume_flux, + volume_flux_fv = surface_flux) solver = DGSEM(basis, surface_flux, volume_integral) initial_refinement_level = 6 cells_per_dimension = (4 * 2^initial_refinement_level, 2^initial_refinement_level) coordinates_min = (0.0, 0.0) coordinates_max = (4.0, 1.0) -mesh = StructuredMesh(cells_per_dimension, coordinates_min, coordinates_max, periodicity=false) +mesh = StructuredMesh(cells_per_dimension, coordinates_min, coordinates_max, + periodicity = false) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver, - boundary_conditions=boundary_conditions) + boundary_conditions = boundary_conditions) ############################################################################### # ODE solvers, callbacks etc. @@ -48,17 +50,17 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 500 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval, - extra_analysis_integrals=(entropy,)) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval, + extra_analysis_integrals = (entropy,)) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=1000, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 1000, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) -stepsize_callback = StepsizeCallback(cfl=0.9) +stepsize_callback = StepsizeCallback(cfl = 0.9) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, @@ -68,9 +70,9 @@ callbacks = CallbackSet(summary_callback, ############################################################################### # run the simulation -stage_callbacks = (SubcellLimiterIDPCorrection(), BoundsCheckCallback(save_errors=false)) +stage_callbacks = (SubcellLimiterIDPCorrection(), BoundsCheckCallback(save_errors = false)) -sol = Trixi.solve(ode, Trixi.SimpleSSPRK33(stage_callbacks=stage_callbacks); - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - callback=callbacks); +sol = Trixi.solve(ode, Trixi.SimpleSSPRK33(stage_callbacks = stage_callbacks); + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/structured_2d_dgsem/elixir_euler_double_mach_MCL.jl b/examples/structured_2d_dgsem/elixir_euler_double_mach_MCL.jl index 2516d7e2054..c7df12f27af 100644 --- a/examples/structured_2d_dgsem/elixir_euler_double_mach_MCL.jl +++ b/examples/structured_2d_dgsem/elixir_euler_double_mach_MCL.jl @@ -11,37 +11,38 @@ initial_condition = Trixi.initial_condition_double_mach_reflection boundary_condition_inflow_outflow = BoundaryConditionCharacteristic(initial_condition) -boundary_conditions = (y_neg=Trixi.boundary_condition_mixed_dirichlet_wall, - y_pos=boundary_condition_inflow_outflow, - x_pos=boundary_condition_inflow_outflow, - x_neg=boundary_condition_inflow_outflow) +boundary_conditions = (y_neg = Trixi.boundary_condition_mixed_dirichlet_wall, + y_pos = boundary_condition_inflow_outflow, + x_pos = boundary_condition_inflow_outflow, + x_neg = boundary_condition_inflow_outflow) surface_flux = flux_lax_friedrichs -volume_flux = flux_ranocha +volume_flux = flux_ranocha polydeg = 4 basis = LobattoLegendreBasis(polydeg) limiter_mcl = SubcellLimiterMCL(equations, basis; - DensityLimiter=true, - DensityAlphaForAll=false, - SequentialLimiter=true, - ConservativeLimiter=false, - DensityPositivityLimiter=false, - PressurePositivityLimiterKuzmin=false, - SemiDiscEntropyLimiter=false, - Plotting=true) + DensityLimiter = true, + DensityAlphaForAll = false, + SequentialLimiter = true, + ConservativeLimiter = false, + DensityPositivityLimiter = false, + PressurePositivityLimiterKuzmin = false, + SemiDiscEntropyLimiter = false, + Plotting = true) volume_integral = VolumeIntegralSubcellLimiting(limiter_mcl; - volume_flux_dg=volume_flux, - volume_flux_fv=surface_flux) + volume_flux_dg = volume_flux, + volume_flux_fv = surface_flux) solver = DGSEM(basis, surface_flux, volume_integral) initial_refinement_level = 6 cells_per_dimension = (4 * 2^initial_refinement_level, 2^initial_refinement_level) coordinates_min = (0.0, 0.0) coordinates_max = (4.0, 1.0) -mesh = StructuredMesh(cells_per_dimension, coordinates_min, coordinates_max, periodicity=false) +mesh = StructuredMesh(cells_per_dimension, coordinates_min, coordinates_max, + periodicity = false) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver, - boundary_conditions=boundary_conditions) + boundary_conditions = boundary_conditions) ############################################################################### # ODE solvers, callbacks etc. @@ -52,17 +53,17 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 500 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval, - extra_analysis_integrals=(entropy,)) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval, + extra_analysis_integrals = (entropy,)) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=1000, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 1000, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) -stepsize_callback = StepsizeCallback(cfl=0.9) +stepsize_callback = StepsizeCallback(cfl = 0.9) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, @@ -72,9 +73,9 @@ callbacks = CallbackSet(summary_callback, ############################################################################### # run the simulation -stage_callbacks = (BoundsCheckCallback(save_errors=false),) +stage_callbacks = (BoundsCheckCallback(save_errors = false),) -sol = Trixi.solve(ode, Trixi.SimpleSSPRK33(stage_callbacks=stage_callbacks); - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - callback=callbacks); +sol = Trixi.solve(ode, Trixi.SimpleSSPRK33(stage_callbacks = stage_callbacks); + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/structured_2d_dgsem/elixir_euler_ec.jl b/examples/structured_2d_dgsem/elixir_euler_ec.jl index 2c91349ff98..29686bd3cb7 100644 --- a/examples/structured_2d_dgsem/elixir_euler_ec.jl +++ b/examples/structured_2d_dgsem/elixir_euler_ec.jl @@ -13,25 +13,25 @@ initial_condition = initial_condition_weak_blast_wave # Get the DG approximation space volume_flux = flux_ranocha -solver = DGSEM(polydeg=4, surface_flux=flux_ranocha, - volume_integral=VolumeIntegralFluxDifferencing(volume_flux)) +solver = DGSEM(polydeg = 4, surface_flux = flux_ranocha, + volume_integral = VolumeIntegralFluxDifferencing(volume_flux)) ############################################################################### # Get the curved quad mesh from a mapping function # Mapping as described in https://arxiv.org/abs/2012.12040, but reduced to 2D function mapping(xi_, eta_) - # Transform input variables between -1 and 1 onto [0,3] - xi = 1.5 * xi_ + 1.5 - eta = 1.5 * eta_ + 1.5 + # Transform input variables between -1 and 1 onto [0,3] + xi = 1.5 * xi_ + 1.5 + eta = 1.5 * eta_ + 1.5 - y = eta + 3/8 * (cos(1.5 * pi * (2 * xi - 3)/3) * - cos(0.5 * pi * (2 * eta - 3)/3)) + y = eta + 3 / 8 * (cos(1.5 * pi * (2 * xi - 3) / 3) * + cos(0.5 * pi * (2 * eta - 3) / 3)) - x = xi + 3/8 * (cos(0.5 * pi * (2 * xi - 3)/3) * - cos(2 * pi * (2 * y - 3)/3)) + x = xi + 3 / 8 * (cos(0.5 * pi * (2 * xi - 3) / 3) * + cos(2 * pi * (2 * y - 3) / 3)) - return SVector(x, y) + return SVector(x, y) end cells_per_dimension = (16, 16) @@ -53,15 +53,15 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=100, - save_initial_solution=true, - save_final_solution=true) +save_solution = SaveSolutionCallback(interval = 100, + save_initial_solution = true, + save_final_solution = true) -stepsize_callback = StepsizeCallback(cfl=1.0) +stepsize_callback = StepsizeCallback(cfl = 1.0) callbacks = CallbackSet(summary_callback, analysis_callback, @@ -72,7 +72,7 @@ callbacks = CallbackSet(summary_callback, ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/structured_2d_dgsem/elixir_euler_free_stream.jl b/examples/structured_2d_dgsem/elixir_euler_free_stream.jl index c4ddb887e5f..3aab4be979e 100644 --- a/examples/structured_2d_dgsem/elixir_euler_free_stream.jl +++ b/examples/structured_2d_dgsem/elixir_euler_free_stream.jl @@ -9,21 +9,21 @@ equations = CompressibleEulerEquations2D(1.4) initial_condition = initial_condition_constant -solver = DGSEM(polydeg=3, surface_flux=flux_lax_friedrichs) +solver = DGSEM(polydeg = 3, surface_flux = flux_lax_friedrichs) # Mapping as described in https://arxiv.org/abs/2012.12040, but reduced to 2D function mapping(xi_, eta_) - # Transform input variables between -1 and 1 onto [0,3] - xi = 1.5 * xi_ + 1.5 - eta = 1.5 * eta_ + 1.5 + # Transform input variables between -1 and 1 onto [0,3] + xi = 1.5 * xi_ + 1.5 + eta = 1.5 * eta_ + 1.5 - y = eta + 3/8 * (cos(1.5 * pi * (2 * xi - 3)/3) * - cos(0.5 * pi * (2 * eta - 3)/3)) + y = eta + 3 / 8 * (cos(1.5 * pi * (2 * xi - 3) / 3) * + cos(0.5 * pi * (2 * eta - 3) / 3)) - x = xi + 3/8 * (cos(0.5 * pi * (2 * xi - 3)/3) * - cos(2 * pi * (2 * y - 3)/3)) + x = xi + 3 / 8 * (cos(0.5 * pi * (2 * xi - 3) / 3) * + cos(2 * pi * (2 * y - 3) / 3)) - return SVector(x, y) + return SVector(x, y) end cells_per_dimension = (16, 16) @@ -32,7 +32,6 @@ mesh = StructuredMesh(cells_per_dimension, mapping) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver) - ############################################################################### # ODE solvers, callbacks etc. @@ -42,16 +41,16 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=100, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 100, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) -stepsize_callback = StepsizeCallback(cfl=2.0) +stepsize_callback = StepsizeCallback(cfl = 2.0) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, @@ -61,7 +60,7 @@ callbacks = CallbackSet(summary_callback, ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/structured_2d_dgsem/elixir_euler_free_stream_MCL.jl b/examples/structured_2d_dgsem/elixir_euler_free_stream_MCL.jl index 8999d435ecc..163cc6519a9 100644 --- a/examples/structured_2d_dgsem/elixir_euler_free_stream_MCL.jl +++ b/examples/structured_2d_dgsem/elixir_euler_free_stream_MCL.jl @@ -10,23 +10,24 @@ equations = CompressibleEulerEquations2D(1.4) initial_condition = initial_condition_constant surface_flux = flux_lax_friedrichs -volume_flux = flux_ranocha +volume_flux = flux_ranocha polydeg = 3 basis = LobattoLegendreBasis(polydeg) limiter_mcl = SubcellLimiterMCL(equations, basis; - DensityLimiter=false, - DensityAlphaForAll=false, - SequentialLimiter=false, - ConservativeLimiter=false, - PressurePositivityLimiterKuzmin=true, PressurePositivityLimiterKuzminExact=true, - DensityPositivityLimiter=true, - SemiDiscEntropyLimiter=false, - smoothness_indicator=false, - Plotting=true) + DensityLimiter = false, + DensityAlphaForAll = false, + SequentialLimiter = false, + ConservativeLimiter = false, + PressurePositivityLimiterKuzmin = true, + PressurePositivityLimiterKuzminExact = true, + DensityPositivityLimiter = true, + SemiDiscEntropyLimiter = false, + smoothness_indicator = false, + Plotting = true) volume_integral = VolumeIntegralSubcellLimiting(limiter_mcl; - volume_flux_dg=volume_flux, - volume_flux_fv=surface_flux) + volume_flux_dg = volume_flux, + volume_flux_fv = surface_flux) solver = DGSEM(basis, surface_flux, volume_integral) # Mapping as described in https://arxiv.org/abs/2012.12040 but reduced to 2D. @@ -37,21 +38,21 @@ solver = DGSEM(basis, surface_flux, volume_integral) # Mapping as described in https://arxiv.org/abs/2012.12040, but reduced to 2D function mapping(xi_, eta_) - # Transform input variables between -1 and 1 onto [0,3] - xi = 1.5 * xi_ + 1.5 - eta = 1.5 * eta_ + 1.5 + # Transform input variables between -1 and 1 onto [0,3] + xi = 1.5 * xi_ + 1.5 + eta = 1.5 * eta_ + 1.5 - y = eta + 3/8 * (cos(1.5 * pi * (2 * xi - 3)/3) * - cos(0.5 * pi * (2 * eta - 3)/3)) + y = eta + 3 / 8 * (cos(1.5 * pi * (2 * xi - 3) / 3) * + cos(0.5 * pi * (2 * eta - 3) / 3)) - x = xi + 3/8 * (cos(0.5 * pi * (2 * xi - 3)/3) * - cos(2 * pi * (2 * y - 3)/3)) + x = xi + 3 / 8 * (cos(0.5 * pi * (2 * xi - 3) / 3) * + cos(2 * pi * (2 * y - 3) / 3)) - return SVector(x, y) + return SVector(x, y) end cells_per_dimension = (32, 32) -mesh = StructuredMesh(cells_per_dimension, mapping, periodicity=true) +mesh = StructuredMesh(cells_per_dimension, mapping, periodicity = true) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver) @@ -64,29 +65,28 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=10000, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 10000, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) -stepsize_callback = StepsizeCallback(cfl=0.9) +stepsize_callback = StepsizeCallback(cfl = 0.9) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, stepsize_callback, save_solution) - ############################################################################### # run the simulation -stage_callbacks = (BoundsCheckCallback(save_errors=false),) +stage_callbacks = (BoundsCheckCallback(save_errors = false),) -sol = Trixi.solve(ode, Trixi.SimpleSSPRK33(stage_callbacks=stage_callbacks); - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = Trixi.solve(ode, Trixi.SimpleSSPRK33(stage_callbacks = stage_callbacks); + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/structured_2d_dgsem/elixir_euler_free_stream_sc_subcell.jl b/examples/structured_2d_dgsem/elixir_euler_free_stream_sc_subcell.jl index 6b70438044e..639fb928754 100644 --- a/examples/structured_2d_dgsem/elixir_euler_free_stream_sc_subcell.jl +++ b/examples/structured_2d_dgsem/elixir_euler_free_stream_sc_subcell.jl @@ -10,22 +10,22 @@ equations = CompressibleEulerEquations2D(1.4) initial_condition = initial_condition_constant surface_flux = flux_lax_friedrichs -volume_flux = flux_ranocha +volume_flux = flux_ranocha polydeg = 3 basis = LobattoLegendreBasis(polydeg) limiter_idp = SubcellLimiterIDP(equations, basis; - positivity_variables_cons=[1], - positivity_variables_nonlinear=(pressure,), - positivity_correction_factor=0.1, - spec_entropy=false, - smoothness_indicator=false, - bar_states=true, - max_iterations_newton=10, - newton_tolerances=(1.0e-12, 1.0e-14)) + positivity_variables_cons = [1], + positivity_variables_nonlinear = (pressure,), + positivity_correction_factor = 0.1, + spec_entropy = false, + smoothness_indicator = false, + bar_states = true, + max_iterations_newton = 10, + newton_tolerances = (1.0e-12, 1.0e-14)) volume_integral = VolumeIntegralSubcellLimiting(limiter_idp; - volume_flux_dg=volume_flux, - volume_flux_fv=surface_flux) + volume_flux_dg = volume_flux, + volume_flux_fv = surface_flux) solver = DGSEM(basis, surface_flux, volume_integral) # Mapping as described in https://arxiv.org/abs/2012.12040 but reduced to 2D. @@ -36,21 +36,21 @@ solver = DGSEM(basis, surface_flux, volume_integral) # Mapping as described in https://arxiv.org/abs/2012.12040, but reduced to 2D function mapping(xi_, eta_) - # Transform input variables between -1 and 1 onto [0,3] - xi = 1.5 * xi_ + 1.5 - eta = 1.5 * eta_ + 1.5 + # Transform input variables between -1 and 1 onto [0,3] + xi = 1.5 * xi_ + 1.5 + eta = 1.5 * eta_ + 1.5 - y = eta + 3/8 * (cos(1.5 * pi * (2 * xi - 3)/3) * - cos(0.5 * pi * (2 * eta - 3)/3)) + y = eta + 3 / 8 * (cos(1.5 * pi * (2 * xi - 3) / 3) * + cos(0.5 * pi * (2 * eta - 3) / 3)) - x = xi + 3/8 * (cos(0.5 * pi * (2 * xi - 3)/3) * - cos(2 * pi * (2 * y - 3)/3)) + x = xi + 3 / 8 * (cos(0.5 * pi * (2 * xi - 3) / 3) * + cos(2 * pi * (2 * y - 3) / 3)) - return SVector(x, y) + return SVector(x, y) end cells_per_dimension = (32, 32) -mesh = StructuredMesh(cells_per_dimension, mapping, periodicity=true) +mesh = StructuredMesh(cells_per_dimension, mapping, periodicity = true) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver) @@ -63,29 +63,28 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=10000, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 10000, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) -stepsize_callback = StepsizeCallback(cfl=0.9) +stepsize_callback = StepsizeCallback(cfl = 0.9) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, stepsize_callback, save_solution) - ############################################################################### # run the simulation -stage_callbacks = (SubcellLimiterIDPCorrection(), BoundsCheckCallback(save_errors=false)) +stage_callbacks = (SubcellLimiterIDPCorrection(), BoundsCheckCallback(save_errors = false)) -sol = Trixi.solve(ode, Trixi.SimpleSSPRK33(stage_callbacks=stage_callbacks); - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = Trixi.solve(ode, Trixi.SimpleSSPRK33(stage_callbacks = stage_callbacks); + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/structured_2d_dgsem/elixir_euler_rayleigh_taylor_instability.jl b/examples/structured_2d_dgsem/elixir_euler_rayleigh_taylor_instability.jl index bb5870ab9d5..6c254e8bd8b 100644 --- a/examples/structured_2d_dgsem/elixir_euler_rayleigh_taylor_instability.jl +++ b/examples/structured_2d_dgsem/elixir_euler_rayleigh_taylor_instability.jl @@ -29,40 +29,40 @@ defined below. """ @inline function initial_condition_rayleigh_taylor_instability(x, t, equations::CompressibleEulerEquations2D, - slope=1000) - tol = 1e2*eps() - - if x[2] < 0.5 - p = 2*x[2] + 1 - else - p = x[2] + 3/2 - end - - # smooth the discontinuity to avoid ambiguity at element interfaces - smoothed_heaviside(x, left, right) = left + 0.5*(1 + tanh(slope * x)) * (right-left) - rho = smoothed_heaviside(x[2] - 0.5, 2.0, 1.0) - - c = sqrt(equations.gamma * p / rho) - # the velocity is multiplied by sin(pi*y)^6 as in Remacle et al. 2003 to ensure that the - # initial condition satisfies reflective boundary conditions at the top/bottom boundaries. - v = -0.025 * c * cos(8*pi*x[1]) * sin(pi*x[2])^6 - u = 0.0 - - return prim2cons(SVector(rho, u, v, p), equations) + slope = 1000) + tol = 1e2 * eps() + + if x[2] < 0.5 + p = 2 * x[2] + 1 + else + p = x[2] + 3 / 2 + end + + # smooth the discontinuity to avoid ambiguity at element interfaces + smoothed_heaviside(x, left, right) = left + 0.5 * (1 + tanh(slope * x)) * (right - left) + rho = smoothed_heaviside(x[2] - 0.5, 2.0, 1.0) + + c = sqrt(equations.gamma * p / rho) + # the velocity is multiplied by sin(pi*y)^6 as in Remacle et al. 2003 to ensure that the + # initial condition satisfies reflective boundary conditions at the top/bottom boundaries. + v = -0.025 * c * cos(8 * pi * x[1]) * sin(pi * x[2])^6 + u = 0.0 + + return prim2cons(SVector(rho, u, v, p), equations) end @inline function source_terms_rayleigh_taylor_instability(u, x, t, equations::CompressibleEulerEquations2D) - g = 1.0 - rho, rho_v1, rho_v2, rho_e = u + g = 1.0 + rho, rho_v1, rho_v2, rho_e = u - return SVector(0.0, 0.0, g*rho, g*rho_v2) + return SVector(0.0, 0.0, g * rho, g * rho_v2) end # numerical parameters volume_flux = flux_ranocha -solver = DGSEM(polydeg=3, surface_flux=flux_hll, - volume_integral=VolumeIntegralFluxDifferencing(volume_flux)) +solver = DGSEM(polydeg = 3, surface_flux = flux_hll, + volume_integral = VolumeIntegralFluxDifferencing(volume_flux)) # The domain is [0, 0.25] x [0, 1] mapping(xi, eta) = SVector(0.25 * 0.5 * (1.0 + xi), 0.5 * (1.0 + eta)) @@ -72,12 +72,10 @@ cells_per_dimension = (num_elements_per_dimension, num_elements_per_dimension * mesh = StructuredMesh(cells_per_dimension, mapping) initial_condition = initial_condition_rayleigh_taylor_instability -boundary_conditions = ( - x_neg=boundary_condition_slip_wall, - x_pos=boundary_condition_slip_wall, - y_neg=boundary_condition_slip_wall, - y_pos=boundary_condition_slip_wall, - ) +boundary_conditions = (x_neg = boundary_condition_slip_wall, + x_pos = boundary_condition_slip_wall, + y_neg = boundary_condition_slip_wall, + y_pos = boundary_condition_slip_wall) # # Alternative setup: left/right periodic BCs and Dirichlet BCs on the top/bottom. # boundary_conditions = ( @@ -88,8 +86,8 @@ boundary_conditions = ( # ) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver; - source_terms=source_terms_rayleigh_taylor_instability, - boundary_conditions=boundary_conditions) + source_terms = source_terms_rayleigh_taylor_instability, + boundary_conditions = boundary_conditions) ############################################################################### # ODE solvers, callbacks etc. @@ -100,9 +98,9 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) callbacks = CallbackSet(summary_callback, analysis_callback, @@ -111,7 +109,7 @@ callbacks = CallbackSet(summary_callback, ############################################################################### # run the simulation -sol = solve(ode, RDPK3SpFSAL49(); abstol=1.0e-6, reltol=1.0e-6, - ode_default_options()..., callback=callbacks); +sol = solve(ode, RDPK3SpFSAL49(); abstol = 1.0e-6, reltol = 1.0e-6, + ode_default_options()..., callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/structured_2d_dgsem/elixir_euler_sedov.jl b/examples/structured_2d_dgsem/elixir_euler_sedov.jl index efc3b6627c0..42094d7191c 100644 --- a/examples/structured_2d_dgsem/elixir_euler_sedov.jl +++ b/examples/structured_2d_dgsem/elixir_euler_sedov.jl @@ -14,25 +14,25 @@ The Sedov blast wave setup based on Flash - https://flash.rochester.edu/site/flashcode/user_support/flash_ug_devel/node187.html#SECTION010114000000000000000 """ function initial_condition_sedov_blast_wave(x, t, equations::CompressibleEulerEquations2D) - # Set up polar coordinates - inicenter = SVector(0.0, 0.0) - x_norm = x[1] - inicenter[1] - y_norm = x[2] - inicenter[2] - r = sqrt(x_norm^2 + y_norm^2) - - # Setup based on https://flash.rochester.edu/site/flashcode/user_support/flash_ug_devel/node187.html#SECTION010114000000000000000 - r0 = 0.21875 # = 3.5 * smallest dx (for domain length=4 and max-ref=6) - E = 1.0 - p0_inner = 3 * (equations.gamma - 1) * E / (3 * pi * r0^2) - p0_outer = 1.0e-5 # = true Sedov setup - - # Calculate primitive variables - rho = 1.0 - v1 = 0.0 - v2 = 0.0 - p = r > r0 ? p0_outer : p0_inner - - return prim2cons(SVector(rho, v1, v2, p), equations) + # Set up polar coordinates + inicenter = SVector(0.0, 0.0) + x_norm = x[1] - inicenter[1] + y_norm = x[2] - inicenter[2] + r = sqrt(x_norm^2 + y_norm^2) + + # Setup based on https://flash.rochester.edu/site/flashcode/user_support/flash_ug_devel/node187.html#SECTION010114000000000000000 + r0 = 0.21875 # = 3.5 * smallest dx (for domain length=4 and max-ref=6) + E = 1.0 + p0_inner = 3 * (equations.gamma - 1) * E / (3 * pi * r0^2) + p0_outer = 1.0e-5 # = true Sedov setup + + # Calculate primitive variables + rho = 1.0 + v1 = 0.0 + v2 = 0.0 + p = r > r0 ? p0_outer : p0_inner + + return prim2cons(SVector(rho, v1, v2, p), equations) end initial_condition = initial_condition_sedov_blast_wave @@ -43,29 +43,30 @@ volume_flux = flux_ranocha polydeg = 4 basis = LobattoLegendreBasis(polydeg) indicator_sc = IndicatorHennemannGassner(equations, basis, - alpha_max=1.0, - alpha_min=0.001, - alpha_smooth=true, - variable=density_pressure) + alpha_max = 1.0, + alpha_min = 0.001, + alpha_smooth = true, + variable = density_pressure) volume_integral = VolumeIntegralShockCapturingHG(indicator_sc; - volume_flux_dg=volume_flux, - volume_flux_fv=surface_flux) + volume_flux_dg = volume_flux, + volume_flux_fv = surface_flux) -solver = DGSEM(polydeg=polydeg, surface_flux=surface_flux, volume_integral=volume_integral) +solver = DGSEM(polydeg = polydeg, surface_flux = surface_flux, + volume_integral = volume_integral) # Get the curved quad mesh from a mapping function # Mapping as described in https://arxiv.org/abs/2012.12040 function mapping(xi, eta) - y = eta + 0.125 * (cos(1.5 * pi * xi) * cos(0.5 * pi * eta)) + y = eta + 0.125 * (cos(1.5 * pi * xi) * cos(0.5 * pi * eta)) - x = xi + 0.125 * (cos(0.5 * pi * xi) * cos(2 * pi * y)) + x = xi + 0.125 * (cos(0.5 * pi * xi) * cos(2 * pi * y)) - return SVector(x, y) + return SVector(x, y) end cells_per_dimension = (16, 16) -mesh = StructuredMesh(cells_per_dimension, mapping, periodicity=true) +mesh = StructuredMesh(cells_per_dimension, mapping, periodicity = true) # create the semidiscretization semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver) @@ -79,15 +80,15 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 300 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=300, - save_initial_solution=true, - save_final_solution=true) +save_solution = SaveSolutionCallback(interval = 300, + save_initial_solution = true, + save_final_solution = true) -stepsize_callback = StepsizeCallback(cfl=0.5) +stepsize_callback = StepsizeCallback(cfl = 0.5) callbacks = CallbackSet(summary_callback, analysis_callback, @@ -98,7 +99,7 @@ callbacks = CallbackSet(summary_callback, ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/structured_2d_dgsem/elixir_euler_shock_upstream_MCL.jl b/examples/structured_2d_dgsem/elixir_euler_shock_upstream_MCL.jl index 2d4f8f608a1..06eaceb4f7c 100644 --- a/examples/structured_2d_dgsem/elixir_euler_shock_upstream_MCL.jl +++ b/examples/structured_2d_dgsem/elixir_euler_shock_upstream_MCL.jl @@ -17,37 +17,38 @@ A version of the classical Kelvin-Helmholtz instability based on [arXiv: 2102.06017](https://arxiv.org/abs/2102.06017) """ function initial_condition_inviscid_bow(x, t, equations::CompressibleEulerEquations2D) - rho = 1.4 - p = 1.0 - v1 = 4.0 - v2 = 0.0 - return prim2cons(SVector(rho, v1, v2, p), equations) + rho = 1.4 + p = 1.0 + v1 = 4.0 + v2 = 0.0 + return prim2cons(SVector(rho, v1, v2, p), equations) end initial_condition = initial_condition_inviscid_bow boundary_condition = BoundaryConditionCharacteristic(initial_condition) -boundary_conditions = (x_neg=boundary_condition, - x_pos=boundary_condition_slip_wall, - y_neg=boundary_condition, - y_pos=boundary_condition) +boundary_conditions = (x_neg = boundary_condition, + x_pos = boundary_condition_slip_wall, + y_neg = boundary_condition, + y_pos = boundary_condition) surface_flux = flux_lax_friedrichs -volume_flux = flux_ranocha +volume_flux = flux_ranocha polydeg = 5 basis = LobattoLegendreBasis(polydeg) limiter_mcl = SubcellLimiterMCL(equations, basis; - DensityLimiter=true, - DensityAlphaForAll=false, - SequentialLimiter=true, - ConservativeLimiter=false, - PressurePositivityLimiterKuzmin=false, PressurePositivityLimiterKuzminExact=false, - DensityPositivityLimiter=false, - SemiDiscEntropyLimiter=false, - Plotting=true) + DensityLimiter = true, + DensityAlphaForAll = false, + SequentialLimiter = true, + ConservativeLimiter = false, + PressurePositivityLimiterKuzmin = false, + PressurePositivityLimiterKuzminExact = false, + DensityPositivityLimiter = false, + SemiDiscEntropyLimiter = false, + Plotting = true) volume_integral = VolumeIntegralSubcellLimiting(limiter_mcl; - volume_flux_dg=volume_flux, - volume_flux_fv=surface_flux) + volume_flux_dg = volume_flux, + volume_flux_fv = surface_flux) solver = DGSEM(basis, surface_flux, volume_integral) # domain @@ -68,19 +69,21 @@ alpha = acos(3.85 / 5.9) l = (pi / 4) / (pi / 2 + 1) f1(s) = SVector(5.9 * cos(pi - s * alpha) + 3.85, 5.9 * sin(pi - s * alpha)) # left function f2(s) # right - t = 0.5 * s + 0.5 # in [0,1] - if 0 <= t <= l - beta = t / l # in [0,1] - return SVector(0.5 * cos(1.5 * pi - beta * 0.5 * pi), 0.5 * sin(1.5 * pi - beta * 0.5 * pi) - 0.5) - elseif l < t <= 1 - l # 0 <= t - l <= 1-2l - beta = (t - l) / (1 - 2 * l) # in [0,1] - return SVector(-0.5, -0.5 + beta) - else # 1 - l < t <= 1 - beta = (t + l - 1) / l # in [0,1] - return SVector(0.5 * cos(pi - beta * 0.5 * pi), 0.5 * sin(pi - beta * 0.5 * pi) + 0.5) - end + t = 0.5 * s + 0.5 # in [0,1] + if 0 <= t <= l + beta = t / l # in [0,1] + return SVector(0.5 * cos(1.5 * pi - beta * 0.5 * pi), + 0.5 * sin(1.5 * pi - beta * 0.5 * pi) - 0.5) + elseif l < t <= 1 - l # 0 <= t - l <= 1-2l + beta = (t - l) / (1 - 2 * l) # in [0,1] + return SVector(-0.5, -0.5 + beta) + else # 1 - l < t <= 1 + beta = (t + l - 1) / l # in [0,1] + return SVector(0.5 * cos(pi - beta * 0.5 * pi), + 0.5 * sin(pi - beta * 0.5 * pi) + 0.5) + end end -f3(s) = SVector(0.0, (a - 1.0) * 0.5 * (s + 1.0) - a) # bottom +f3(s) = SVector(0.0, (a - 1.0) * 0.5 * (s + 1.0) - a) # bottom f4(s) = SVector(0.0, -(a - 1.0) * 0.5 * (s + 1.0) + a) # top faces = (f1, f2, f3, f4) @@ -89,21 +92,22 @@ Trixi.validate_faces(faces) mapping_bow = Trixi.transfinite_mapping(faces) mapping_as_string = "a = sqrt(5.9^2 - 3.85^2); alpha = acos(3.85 / 5.9); l = (pi / 4) / (pi / 2 + 1); " * - "f1(s) = SVector(5.9 * cos(pi - s * alpha) + 3.85, 5.9 * sin(pi - s * alpha)); " * - "function f2(s); t = 0.5 * s + 0.5; " * - "if 0 <= t <= l; beta = t / l; return SVector(0.5 * cos(1.5 * pi - beta * 0.5 * pi), 0.5 * sin(1.5 * pi - beta * 0.5 * pi) - 0.5); " * - "elseif l < t <= 1 - l; beta = (t - l) / (1 - 2 * l); return SVector(-0.5, -0.5 + beta); " * - "else beta = (t + l - 1) / l; return SVector(0.5 * cos(pi - beta * 0.5 * pi), 0.5 * sin(pi - beta * 0.5 * pi) + 0.5); end; end; " * - "f3(s) = SVector(0.0, (a - 1.0) * 0.5 * (s + 1.0) - a); " * - "f4(s) = SVector(0.0, -(a - 1.0) * 0.5 * (s + 1.0) + a); " * - "faces = (f1, f2, f3, f4); mapping = Trixi.transfinite_mapping(faces)" + "f1(s) = SVector(5.9 * cos(pi - s * alpha) + 3.85, 5.9 * sin(pi - s * alpha)); " * + "function f2(s); t = 0.5 * s + 0.5; " * + "if 0 <= t <= l; beta = t / l; return SVector(0.5 * cos(1.5 * pi - beta * 0.5 * pi), 0.5 * sin(1.5 * pi - beta * 0.5 * pi) - 0.5); " * + "elseif l < t <= 1 - l; beta = (t - l) / (1 - 2 * l); return SVector(-0.5, -0.5 + beta); " * + "else beta = (t + l - 1) / l; return SVector(0.5 * cos(pi - beta * 0.5 * pi), 0.5 * sin(pi - beta * 0.5 * pi) + 0.5); end; end; " * + "f3(s) = SVector(0.0, (a - 1.0) * 0.5 * (s + 1.0) - a); " * + "f4(s) = SVector(0.0, -(a - 1.0) * 0.5 * (s + 1.0) + a); " * + "faces = (f1, f2, f3, f4); mapping = Trixi.transfinite_mapping(faces)" cells_per_dimension = (24, 36) -mesh = StructuredMesh(cells_per_dimension, mapping_bow, mapping_as_string=mapping_as_string, periodicity=false) +mesh = StructuredMesh(cells_per_dimension, mapping_bow, + mapping_as_string = mapping_as_string, periodicity = false) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver, - boundary_conditions=boundary_conditions) + boundary_conditions = boundary_conditions) ############################################################################### # ODE solvers, callbacks etc. @@ -114,29 +118,28 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 1000 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=2000, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 2000, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) -stepsize_callback = StepsizeCallback(cfl=0.9) +stepsize_callback = StepsizeCallback(cfl = 0.9) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, stepsize_callback, save_solution) - ############################################################################### # run the simulation -stage_callbacks = (BoundsCheckCallback(save_errors=false),) +stage_callbacks = (BoundsCheckCallback(save_errors = false),) -sol = Trixi.solve(ode, Trixi.SimpleSSPRK33(stage_callbacks=stage_callbacks); - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - callback=callbacks); +sol = Trixi.solve(ode, Trixi.SimpleSSPRK33(stage_callbacks = stage_callbacks); + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/structured_2d_dgsem/elixir_euler_shock_upstream_sc_subcell.jl b/examples/structured_2d_dgsem/elixir_euler_shock_upstream_sc_subcell.jl index 5d266629764..def69ecc282 100644 --- a/examples/structured_2d_dgsem/elixir_euler_shock_upstream_sc_subcell.jl +++ b/examples/structured_2d_dgsem/elixir_euler_shock_upstream_sc_subcell.jl @@ -17,33 +17,33 @@ A version of the classical Kelvin-Helmholtz instability based on [arXiv: 2102.06017](https://arxiv.org/abs/2102.06017) """ function initial_condition_inviscid_bow(x, t, equations::CompressibleEulerEquations2D) - rho = 1.4 - p = 1.0 - v1 = 4.0 - v2 = 0.0 - return prim2cons(SVector(rho, v1, v2, p), equations) + rho = 1.4 + p = 1.0 + v1 = 4.0 + v2 = 0.0 + return prim2cons(SVector(rho, v1, v2, p), equations) end initial_condition = initial_condition_inviscid_bow boundary_condition = BoundaryConditionCharacteristic(initial_condition) -boundary_conditions = (x_neg=boundary_condition, - x_pos=boundary_condition_slip_wall, - y_neg=boundary_condition, - y_pos=boundary_condition) +boundary_conditions = (x_neg = boundary_condition, + x_pos = boundary_condition_slip_wall, + y_neg = boundary_condition, + y_pos = boundary_condition) surface_flux = flux_lax_friedrichs -volume_flux = flux_ranocha +volume_flux = flux_ranocha polydeg = 5 basis = LobattoLegendreBasis(polydeg) limiter_idp = SubcellLimiterIDP(equations, basis; - local_minmax_variables_cons=[1], - spec_entropy=true, - max_iterations_newton=100, - bar_states=true) + local_minmax_variables_cons = [1], + spec_entropy = true, + max_iterations_newton = 100, + bar_states = true) volume_integral = VolumeIntegralSubcellLimiting(limiter_idp; - volume_flux_dg=volume_flux, - volume_flux_fv=surface_flux) + volume_flux_dg = volume_flux, + volume_flux_fv = surface_flux) solver = DGSEM(basis, surface_flux, volume_integral) # domain @@ -64,19 +64,21 @@ alpha = acos(3.85 / 5.9) l = (pi / 4) / (pi / 2 + 1) f1(s) = SVector(5.9 * cos(pi - s * alpha) + 3.85, 5.9 * sin(pi - s * alpha)) # left function f2(s) # right - t = 0.5 * s + 0.5 # in [0,1] - if 0 <= t <= l - beta = t / l # in [0,1] - return SVector(0.5 * cos(1.5 * pi - beta * 0.5 * pi), 0.5 * sin(1.5 * pi - beta * 0.5 * pi) - 0.5) - elseif l < t <= 1 - l # 0 <= t - l <= 1-2l - beta = (t - l) / (1 - 2 * l) # in [0,1] - return SVector(-0.5, -0.5 + beta) - else # 1 - l < t <= 1 - beta = (t + l - 1) / l # in [0,1] - return SVector(0.5 * cos(pi - beta * 0.5 * pi), 0.5 * sin(pi - beta * 0.5 * pi) + 0.5) - end + t = 0.5 * s + 0.5 # in [0,1] + if 0 <= t <= l + beta = t / l # in [0,1] + return SVector(0.5 * cos(1.5 * pi - beta * 0.5 * pi), + 0.5 * sin(1.5 * pi - beta * 0.5 * pi) - 0.5) + elseif l < t <= 1 - l # 0 <= t - l <= 1-2l + beta = (t - l) / (1 - 2 * l) # in [0,1] + return SVector(-0.5, -0.5 + beta) + else # 1 - l < t <= 1 + beta = (t + l - 1) / l # in [0,1] + return SVector(0.5 * cos(pi - beta * 0.5 * pi), + 0.5 * sin(pi - beta * 0.5 * pi) + 0.5) + end end -f3(s) = SVector(0.0, (a - 1.0) * 0.5 * (s + 1.0) - a) # bottom +f3(s) = SVector(0.0, (a - 1.0) * 0.5 * (s + 1.0) - a) # bottom f4(s) = SVector(0.0, -(a - 1.0) * 0.5 * (s + 1.0) + a) # top faces = (f1, f2, f3, f4) @@ -85,21 +87,22 @@ Trixi.validate_faces(faces) mapping_bow = Trixi.transfinite_mapping(faces) mapping_as_string = "a = sqrt(5.9^2 - 3.85^2); alpha = acos(3.85 / 5.9); l = (pi / 4) / (pi / 2 + 1); " * - "f1(s) = SVector(5.9 * cos(pi - s * alpha) + 3.85, 5.9 * sin(pi - s * alpha)); " * - "function f2(s); t = 0.5 * s + 0.5; " * - "if 0 <= t <= l; beta = t / l; return SVector(0.5 * cos(1.5 * pi - beta * 0.5 * pi), 0.5 * sin(1.5 * pi - beta * 0.5 * pi) - 0.5); " * - "elseif l < t <= 1 - l; beta = (t - l) / (1 - 2 * l); return SVector(-0.5, -0.5 + beta); " * - "else beta = (t + l - 1) / l; return SVector(0.5 * cos(pi - beta * 0.5 * pi), 0.5 * sin(pi - beta * 0.5 * pi) + 0.5); end; end; " * - "f3(s) = SVector(0.0, (a - 1.0) * 0.5 * (s + 1.0) - a); " * - "f4(s) = SVector(0.0, -(a - 1.0) * 0.5 * (s + 1.0) + a); " * - "faces = (f1, f2, f3, f4); mapping = Trixi.transfinite_mapping(faces)" + "f1(s) = SVector(5.9 * cos(pi - s * alpha) + 3.85, 5.9 * sin(pi - s * alpha)); " * + "function f2(s); t = 0.5 * s + 0.5; " * + "if 0 <= t <= l; beta = t / l; return SVector(0.5 * cos(1.5 * pi - beta * 0.5 * pi), 0.5 * sin(1.5 * pi - beta * 0.5 * pi) - 0.5); " * + "elseif l < t <= 1 - l; beta = (t - l) / (1 - 2 * l); return SVector(-0.5, -0.5 + beta); " * + "else beta = (t + l - 1) / l; return SVector(0.5 * cos(pi - beta * 0.5 * pi), 0.5 * sin(pi - beta * 0.5 * pi) + 0.5); end; end; " * + "f3(s) = SVector(0.0, (a - 1.0) * 0.5 * (s + 1.0) - a); " * + "f4(s) = SVector(0.0, -(a - 1.0) * 0.5 * (s + 1.0) + a); " * + "faces = (f1, f2, f3, f4); mapping = Trixi.transfinite_mapping(faces)" cells_per_dimension = (24, 36) -mesh = StructuredMesh(cells_per_dimension, mapping_bow, mapping_as_string=mapping_as_string, periodicity=false) +mesh = StructuredMesh(cells_per_dimension, mapping_bow, + mapping_as_string = mapping_as_string, periodicity = false) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver, - boundary_conditions=boundary_conditions) + boundary_conditions = boundary_conditions) ############################################################################### # ODE solvers, callbacks etc. @@ -110,29 +113,28 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 1000 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=2000, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 2000, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) -stepsize_callback = StepsizeCallback(cfl=0.9) +stepsize_callback = StepsizeCallback(cfl = 0.9) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, stepsize_callback, save_solution) - ############################################################################### # run the simulation -stage_callbacks = (SubcellLimiterIDPCorrection(), BoundsCheckCallback(save_errors=false)) +stage_callbacks = (SubcellLimiterIDPCorrection(), BoundsCheckCallback(save_errors = false)) -sol = Trixi.solve(ode, Trixi.SimpleSSPRK33(stage_callbacks=stage_callbacks); - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - callback=callbacks); +sol = Trixi.solve(ode, Trixi.SimpleSSPRK33(stage_callbacks = stage_callbacks); + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/structured_2d_dgsem/elixir_euler_source_terms.jl b/examples/structured_2d_dgsem/elixir_euler_source_terms.jl index 70d3e060dd0..6827848e185 100644 --- a/examples/structured_2d_dgsem/elixir_euler_source_terms.jl +++ b/examples/structured_2d_dgsem/elixir_euler_source_terms.jl @@ -11,7 +11,7 @@ equations = CompressibleEulerEquations2D(1.4) initial_condition = initial_condition_convergence_test -solver = DGSEM(polydeg=3, surface_flux=flux_lax_friedrichs) +solver = DGSEM(polydeg = 3, surface_flux = flux_lax_friedrichs) coordinates_min = (0.0, 0.0) coordinates_max = (2.0, 2.0) @@ -20,10 +20,8 @@ cells_per_dimension = (16, 16) mesh = StructuredMesh(cells_per_dimension, coordinates_min, coordinates_max) - semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver, - source_terms=source_terms_convergence_test) - + source_terms = source_terms_convergence_test) ############################################################################### # ODE solvers, callbacks etc. @@ -34,16 +32,16 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=100, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 100, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) -stepsize_callback = StepsizeCallback(cfl=1.0) +stepsize_callback = StepsizeCallback(cfl = 1.0) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, @@ -53,7 +51,7 @@ callbacks = CallbackSet(summary_callback, ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/structured_2d_dgsem/elixir_euler_source_terms_nonperiodic.jl b/examples/structured_2d_dgsem/elixir_euler_source_terms_nonperiodic.jl index 94537ecef0d..f42d223611a 100644 --- a/examples/structured_2d_dgsem/elixir_euler_source_terms_nonperiodic.jl +++ b/examples/structured_2d_dgsem/elixir_euler_source_terms_nonperiodic.jl @@ -12,21 +12,20 @@ initial_condition = initial_condition_convergence_test # you can either use a single function to impose the BCs weakly in all # 2*ndims == 4 directions or you can pass a tuple containing BCs for each direction boundary_condition = BoundaryConditionDirichlet(initial_condition) -boundary_conditions = (x_neg=boundary_condition, - x_pos=boundary_condition, - y_neg=boundary_condition, - y_pos=boundary_condition,) +boundary_conditions = (x_neg = boundary_condition, + x_pos = boundary_condition, + y_neg = boundary_condition, + y_pos = boundary_condition) -solver = DGSEM(polydeg=3, surface_flux=flux_lax_friedrichs) +solver = DGSEM(polydeg = 3, surface_flux = flux_lax_friedrichs) coordinates_min = (0.0, 0.0) coordinates_max = (2.0, 2.0) -mesh = StructuredMesh((16, 16), coordinates_min, coordinates_max, periodicity=false) +mesh = StructuredMesh((16, 16), coordinates_min, coordinates_max, periodicity = false) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver, - source_terms=source_terms_convergence_test, - boundary_conditions=boundary_conditions) - + source_terms = source_terms_convergence_test, + boundary_conditions = boundary_conditions) ############################################################################### # ODE solvers, callbacks etc. @@ -37,19 +36,19 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_restart = SaveRestartCallback(interval=100, - save_final_restart=true) +save_restart = SaveRestartCallback(interval = 100, + save_final_restart = true) -save_solution = SaveSolutionCallback(interval=100, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 100, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) -stepsize_callback = StepsizeCallback(cfl=1.0) +stepsize_callback = StepsizeCallback(cfl = 1.0) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, @@ -58,7 +57,7 @@ callbacks = CallbackSet(summary_callback, ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/structured_2d_dgsem/elixir_euler_source_terms_parallelogram.jl b/examples/structured_2d_dgsem/elixir_euler_source_terms_parallelogram.jl index a9c08049f41..5d6b0908389 100644 --- a/examples/structured_2d_dgsem/elixir_euler_source_terms_parallelogram.jl +++ b/examples/structured_2d_dgsem/elixir_euler_source_terms_parallelogram.jl @@ -9,7 +9,7 @@ equations = CompressibleEulerEquations2D(1.4) initial_condition = initial_condition_convergence_test -solver = DGSEM(polydeg=3, surface_flux=flux_lax_friedrichs) +solver = DGSEM(polydeg = 3, surface_flux = flux_lax_friedrichs) # Define faces for a parallelogram that looks like this # @@ -24,10 +24,8 @@ cells_per_dimension = (16, 16) mesh = StructuredMesh(cells_per_dimension, mapping) - semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver, - source_terms=source_terms_convergence_test) - + source_terms = source_terms_convergence_test) ############################################################################### # ODE solvers, callbacks etc. @@ -38,16 +36,16 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=100, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 100, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) -stepsize_callback = StepsizeCallback(cfl=0.5) +stepsize_callback = StepsizeCallback(cfl = 0.5) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, @@ -57,7 +55,7 @@ callbacks = CallbackSet(summary_callback, ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/structured_2d_dgsem/elixir_euler_source_terms_rotated.jl b/examples/structured_2d_dgsem/elixir_euler_source_terms_rotated.jl index fdd189ffb55..f2e3c448893 100644 --- a/examples/structured_2d_dgsem/elixir_euler_source_terms_rotated.jl +++ b/examples/structured_2d_dgsem/elixir_euler_source_terms_rotated.jl @@ -2,7 +2,6 @@ using OrdinaryDiffEq using Trixi - # Define new structs inside a module to allow re-evaluating the file. # This module name needs to be unique among all examples, otherwise Julia will throw warnings # if multiple test cases using the same module name are run in the same session. @@ -12,68 +11,69 @@ using Trixi # initial_condition_convergence_test transformed to the rotated rectangle struct InitialConditionSourceTermsRotated - sin_alpha::Float64 - cos_alpha::Float64 + sin_alpha::Float64 + cos_alpha::Float64 end function InitialConditionSourceTermsRotated(alpha) - sin_alpha, cos_alpha = sincos(alpha) + sin_alpha, cos_alpha = sincos(alpha) - InitialConditionSourceTermsRotated(sin_alpha, cos_alpha) + InitialConditionSourceTermsRotated(sin_alpha, cos_alpha) end -function (initial_condition::InitialConditionSourceTermsRotated)(x, t, equations::CompressibleEulerEquations2D) - sin_ = initial_condition.sin_alpha - cos_ = initial_condition.cos_alpha +function (initial_condition::InitialConditionSourceTermsRotated)(x, t, + equations::CompressibleEulerEquations2D) + sin_ = initial_condition.sin_alpha + cos_ = initial_condition.cos_alpha - # Rotate back to unit square and translate from [-1, 1]^2 to [0, 2]^2 + # Rotate back to unit square and translate from [-1, 1]^2 to [0, 2]^2 - # Clockwise rotation by α and translation by 1 - # Multiply with [ cos(α) sin(α); - # -sin(α) cos(α)] - x1 = cos_ * x[1] + sin_ * x[2] + 1 - x2 = -sin_ * x[1] + cos_ * x[2] + 1 + # Clockwise rotation by α and translation by 1 + # Multiply with [ cos(α) sin(α); + # -sin(α) cos(α)] + x1 = cos_ * x[1] + sin_ * x[2] + 1 + x2 = -sin_ * x[1] + cos_ * x[2] + 1 - rho, rho_v1, rho_v2, rho_e = initial_condition_convergence_test(SVector(x1, x2), t, equations) + rho, rho_v1, rho_v2, rho_e = initial_condition_convergence_test(SVector(x1, x2), t, + equations) - # Rotate velocity vector counterclockwise - # Multiply with [ cos(α) -sin(α); - # sin(α) cos(α)] - rho_v1_rot = cos_ * rho_v1 - sin_ * rho_v2 - rho_v2_rot = sin_ * rho_v1 + cos_ * rho_v2 + # Rotate velocity vector counterclockwise + # Multiply with [ cos(α) -sin(α); + # sin(α) cos(α)] + rho_v1_rot = cos_ * rho_v1 - sin_ * rho_v2 + rho_v2_rot = sin_ * rho_v1 + cos_ * rho_v2 - return SVector(rho, rho_v1_rot, rho_v2_rot, rho_e) + return SVector(rho, rho_v1_rot, rho_v2_rot, rho_e) end +@inline function (source_terms::InitialConditionSourceTermsRotated)(u, x, t, + equations::CompressibleEulerEquations2D) + sin_ = source_terms.sin_alpha + cos_ = source_terms.cos_alpha -@inline function (source_terms::InitialConditionSourceTermsRotated)(u, x, t, equations::CompressibleEulerEquations2D) - sin_ = source_terms.sin_alpha - cos_ = source_terms.cos_alpha - - # Rotate back to unit square and translate from [-1, 1]^2 to [0, 2]^2 + # Rotate back to unit square and translate from [-1, 1]^2 to [0, 2]^2 - # Clockwise rotation by α and translation by 1 - # Multiply with [ cos(α) sin(α); - # -sin(α) cos(α)] - x1 = cos_ * x[1] + sin_ * x[2] + 1 - x2 = -sin_ * x[1] + cos_ * x[2] + 1 + # Clockwise rotation by α and translation by 1 + # Multiply with [ cos(α) sin(α); + # -sin(α) cos(α)] + x1 = cos_ * x[1] + sin_ * x[2] + 1 + x2 = -sin_ * x[1] + cos_ * x[2] + 1 - du1, du2, du3, du4 = source_terms_convergence_test(u, SVector(x1, x2), t, equations) + du1, du2, du3, du4 = source_terms_convergence_test(u, SVector(x1, x2), t, equations) - # Rotate velocity vector counterclockwise - # Multiply with [ cos(α) -sin(α); - # sin(α) cos(α)] - du2_rotated = cos_ * du2 - sin_ * du3 - du3_rotated = sin_ * du2 + cos_ * du3 + # Rotate velocity vector counterclockwise + # Multiply with [ cos(α) -sin(α); + # sin(α) cos(α)] + du2_rotated = cos_ * du2 - sin_ * du3 + du3_rotated = sin_ * du2 + cos_ * du3 - return SVector(du1, du2_rotated, du3_rotated, du4) + return SVector(du1, du2_rotated, du3_rotated, du4) end end # module TrixiExtensionEulerRotated import .TrixiExtensionEulerRotated - ############################################################################### # semidiscretization of the compressible Euler equations @@ -85,8 +85,7 @@ sin_ = initial_condition_source_terms.sin_alpha cos_ = initial_condition_source_terms.cos_alpha T = [cos_ -sin_; sin_ cos_] - -solver = DGSEM(polydeg=3, surface_flux=flux_lax_friedrichs) +solver = DGSEM(polydeg = 3, surface_flux = flux_lax_friedrichs) mapping(xi, eta) = T * SVector(xi, eta) @@ -94,10 +93,8 @@ cells_per_dimension = (16, 16) mesh = StructuredMesh(cells_per_dimension, mapping) - semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition_source_terms, solver, - source_terms=initial_condition_source_terms) - + source_terms = initial_condition_source_terms) ############################################################################### # ODE solvers, callbacks etc. @@ -108,16 +105,16 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=100, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 100, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) -stepsize_callback = StepsizeCallback(cfl=1.0) +stepsize_callback = StepsizeCallback(cfl = 1.0) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, @@ -127,7 +124,7 @@ callbacks = CallbackSet(summary_callback, ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/structured_2d_dgsem/elixir_euler_source_terms_sc_subcell.jl b/examples/structured_2d_dgsem/elixir_euler_source_terms_sc_subcell.jl index 13ed29db2ba..53c07261c36 100644 --- a/examples/structured_2d_dgsem/elixir_euler_source_terms_sc_subcell.jl +++ b/examples/structured_2d_dgsem/elixir_euler_source_terms_sc_subcell.jl @@ -16,26 +16,26 @@ volume_flux = flux_ranocha polydeg = 3 basis = LobattoLegendreBasis(polydeg) limiter_idp = SubcellLimiterIDP(equations, basis; - local_minmax_variables_cons=[1], - spec_entropy=true, - bar_states=false) + local_minmax_variables_cons = [1], + spec_entropy = true, + bar_states = false) volume_integral = VolumeIntegralSubcellLimiting(limiter_idp; - volume_flux_dg=volume_flux, - volume_flux_fv=surface_flux) + volume_flux_dg = volume_flux, + volume_flux_fv = surface_flux) solver = DGSEM(basis, surface_flux, volume_integral) # Waving flag f1(s) = SVector(-1.0, s - 1.0) -f2(s) = SVector( 1.0, s + 1.0) +f2(s) = SVector(1.0, s + 1.0) f3(s) = SVector(s, -1.0 + sin(0.5 * pi * s)) -f4(s) = SVector(s, 1.0 + sin(0.5 * pi * s)) +f4(s) = SVector(s, 1.0 + sin(0.5 * pi * s)) mapping = Trixi.transfinite_mapping((f1, f2, f3, f4)) cells_per_dimension = (16, 16) -mesh = StructuredMesh(cells_per_dimension, mapping, periodicity=true) +mesh = StructuredMesh(cells_per_dimension, mapping, periodicity = true) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver, - source_terms=source_terms) + source_terms = source_terms) ############################################################################### # ODE solvers, callbacks etc. @@ -46,16 +46,16 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=100, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 100, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) -stepsize_callback = StepsizeCallback(cfl=0.5) +stepsize_callback = StepsizeCallback(cfl = 0.5) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, @@ -65,9 +65,9 @@ callbacks = CallbackSet(summary_callback, ############################################################################### # run the simulation -stage_callbacks = (SubcellLimiterIDPCorrection(), BoundsCheckCallback(save_errors=false)) +stage_callbacks = (SubcellLimiterIDPCorrection(), BoundsCheckCallback(save_errors = false)) -sol = Trixi.solve(ode, Trixi.SimpleSSPRK33(stage_callbacks=stage_callbacks); - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = Trixi.solve(ode, Trixi.SimpleSSPRK33(stage_callbacks = stage_callbacks); + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/structured_2d_dgsem/elixir_euler_source_terms_waving_flag.jl b/examples/structured_2d_dgsem/elixir_euler_source_terms_waving_flag.jl index 505e28ecd8d..4a78b65ae0b 100644 --- a/examples/structured_2d_dgsem/elixir_euler_source_terms_waving_flag.jl +++ b/examples/structured_2d_dgsem/elixir_euler_source_terms_waving_flag.jl @@ -9,23 +9,21 @@ equations = CompressibleEulerEquations2D(1.4) initial_condition = initial_condition_convergence_test -solver = DGSEM(polydeg=3, surface_flux=flux_lax_friedrichs) +solver = DGSEM(polydeg = 3, surface_flux = flux_lax_friedrichs) # Deformed rectangle that looks like a waving flag, # lower and upper faces are sinus curves, left and right are vertical lines. f1(s) = SVector(-1.0, s - 1.0) -f2(s) = SVector( 1.0, s + 1.0) +f2(s) = SVector(1.0, s + 1.0) f3(s) = SVector(s, -1.0 + sin(0.5 * pi * s)) -f4(s) = SVector(s, 1.0 + sin(0.5 * pi * s)) +f4(s) = SVector(s, 1.0 + sin(0.5 * pi * s)) cells_per_dimension = (16, 16) mesh = StructuredMesh(cells_per_dimension, (f1, f2, f3, f4)) - semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver, - source_terms=source_terms_convergence_test) - + source_terms = source_terms_convergence_test) ############################################################################### # ODE solvers, callbacks etc. @@ -36,16 +34,16 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=100, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 100, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) -stepsize_callback = StepsizeCallback(cfl=0.8) +stepsize_callback = StepsizeCallback(cfl = 0.8) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, @@ -55,7 +53,7 @@ callbacks = CallbackSet(summary_callback, ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/structured_2d_dgsem/elixir_eulerpolytropic_ec.jl b/examples/structured_2d_dgsem/elixir_eulerpolytropic_ec.jl index de15f6b2bc3..b96f1d3cd68 100644 --- a/examples/structured_2d_dgsem/elixir_eulerpolytropic_ec.jl +++ b/examples/structured_2d_dgsem/elixir_eulerpolytropic_ec.jl @@ -15,25 +15,25 @@ initial_condition = initial_condition_weak_blast_wave # Get the DG approximation space volume_flux = flux_winters_etal -solver = DGSEM(polydeg=4, surface_flux=flux_winters_etal, - volume_integral=VolumeIntegralFluxDifferencing(volume_flux)) +solver = DGSEM(polydeg = 4, surface_flux = flux_winters_etal, + volume_integral = VolumeIntegralFluxDifferencing(volume_flux)) ############################################################################### # Get the curved quad mesh from a mapping function # Mapping as described in https://arxiv.org/abs/2012.12040, but reduced to 2D function mapping(xi_, eta_) - # Transform input variables between -1 and 1 onto [0,3] - xi = 1.5 * xi_ + 1.5 - eta = 1.5 * eta_ + 1.5 + # Transform input variables between -1 and 1 onto [0,3] + xi = 1.5 * xi_ + 1.5 + eta = 1.5 * eta_ + 1.5 - y = eta + 3/8 * (cos(1.5 * pi * (2 * xi - 3)/3) * - cos(0.5 * pi * (2 * eta - 3)/3)) + y = eta + 3 / 8 * (cos(1.5 * pi * (2 * xi - 3) / 3) * + cos(0.5 * pi * (2 * eta - 3) / 3)) - x = xi + 3/8 * (cos(0.5 * pi * (2 * xi - 3)/3) * - cos(2 * pi * (2 * y - 3)/3)) + x = xi + 3 / 8 * (cos(0.5 * pi * (2 * xi - 3) / 3) * + cos(2 * pi * (2 * y - 3) / 3)) - return SVector(x, y) + return SVector(x, y) end cells_per_dimension = (16, 16) @@ -55,15 +55,15 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=100, - save_initial_solution=true, - save_final_solution=true) +save_solution = SaveSolutionCallback(interval = 100, + save_initial_solution = true, + save_final_solution = true) -stepsize_callback = StepsizeCallback(cfl=1.0) +stepsize_callback = StepsizeCallback(cfl = 1.0) callbacks = CallbackSet(summary_callback, analysis_callback, @@ -74,7 +74,7 @@ callbacks = CallbackSet(summary_callback, ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/structured_2d_dgsem/elixir_hypdiff_harmonic_nonperiodic.jl b/examples/structured_2d_dgsem/elixir_hypdiff_harmonic_nonperiodic.jl index 6730b1c4beb..ccb74fa4b68 100644 --- a/examples/structured_2d_dgsem/elixir_hypdiff_harmonic_nonperiodic.jl +++ b/examples/structured_2d_dgsem/elixir_hypdiff_harmonic_nonperiodic.jl @@ -7,43 +7,42 @@ using Trixi equations = HyperbolicDiffusionEquations2D() -@inline function initial_condition_harmonic_nonperiodic(x, t, equations::HyperbolicDiffusionEquations2D) - # elliptic equation: -ν Δϕ = 0 in Ω, u = g on ∂Ω - if t == 0.0 - phi = 1.0 - q1 = 1.0 - q2 = 1.0 - else - C = inv(sinh(pi)) - sinpi_x1, cospi_x1 = sincos(pi*x[1]) - sinpi_x2, cospi_x2 = sincos(pi*x[2]) - sinh_pix1 = sinh(pi*x[1]) - cosh_pix1 = cosh(pi*x[1]) - sinh_pix2 = sinh(pi*x[2]) - cosh_pix2 = cosh(pi*x[2]) - phi = C * (sinh_pix1 * sinpi_x2 + sinh_pix2 * sinpi_x1) - q1 = C * pi * (cosh_pix1 * sinpi_x2 + sinh_pix2 * cospi_x1) - q2 = C * pi * (sinh_pix1 * cospi_x2 + cosh_pix2 * sinpi_x1) - end - return SVector(phi, q1, q2) +@inline function initial_condition_harmonic_nonperiodic(x, t, + equations::HyperbolicDiffusionEquations2D) + # elliptic equation: -ν Δϕ = 0 in Ω, u = g on ∂Ω + if t == 0.0 + phi = 1.0 + q1 = 1.0 + q2 = 1.0 + else + C = inv(sinh(pi)) + sinpi_x1, cospi_x1 = sincos(pi * x[1]) + sinpi_x2, cospi_x2 = sincos(pi * x[2]) + sinh_pix1 = sinh(pi * x[1]) + cosh_pix1 = cosh(pi * x[1]) + sinh_pix2 = sinh(pi * x[2]) + cosh_pix2 = cosh(pi * x[2]) + phi = C * (sinh_pix1 * sinpi_x2 + sinh_pix2 * sinpi_x1) + q1 = C * pi * (cosh_pix1 * sinpi_x2 + sinh_pix2 * cospi_x1) + q2 = C * pi * (sinh_pix1 * cospi_x2 + cosh_pix2 * sinpi_x1) + end + return SVector(phi, q1, q2) end initial_condition = initial_condition_harmonic_nonperiodic boundary_conditions = BoundaryConditionDirichlet(initial_condition) -solver = DGSEM(polydeg=4, surface_flux=flux_godunov) +solver = DGSEM(polydeg = 4, surface_flux = flux_godunov) coordinates_min = (0.0, 0.0) coordinates_max = (1.0, 1.0) cells_per_dimension = (8, 8) mesh = StructuredMesh(cells_per_dimension, coordinates_min, coordinates_max, - periodicity=false) - + periodicity = false) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver, - boundary_conditions=boundary_conditions, - source_terms=source_terms_harmonic) - + boundary_conditions = boundary_conditions, + source_terms = source_terms_harmonic) ############################################################################### # ODE solvers, callbacks etc. @@ -54,30 +53,29 @@ ode = semidiscretize(semi, tspan); summary_callback = SummaryCallback() resid_tol = 5.0e-12 -steady_state_callback = SteadyStateCallback(abstol=resid_tol, reltol=0.0) +steady_state_callback = SteadyStateCallback(abstol = resid_tol, reltol = 0.0) analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=100, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 100, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) -stepsize_callback = StepsizeCallback(cfl=1.0) +stepsize_callback = StepsizeCallback(cfl = 1.0) callbacks = CallbackSet(summary_callback, steady_state_callback, analysis_callback, alive_callback, save_solution, stepsize_callback) - ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/structured_2d_dgsem/elixir_hypdiff_nonperiodic.jl b/examples/structured_2d_dgsem/elixir_hypdiff_nonperiodic.jl index ba77dca9a99..681b3bd781b 100644 --- a/examples/structured_2d_dgsem/elixir_hypdiff_nonperiodic.jl +++ b/examples/structured_2d_dgsem/elixir_hypdiff_nonperiodic.jl @@ -9,40 +9,38 @@ equations = HyperbolicDiffusionEquations2D() initial_condition = initial_condition_poisson_nonperiodic -solver = DGSEM(polydeg=6, surface_flux=flux_lax_friedrichs) +solver = DGSEM(polydeg = 6, surface_flux = flux_lax_friedrichs) -boundary_conditions = (x_neg=boundary_condition_poisson_nonperiodic, - x_pos=boundary_condition_poisson_nonperiodic, - y_neg=boundary_condition_periodic, - y_pos=boundary_condition_periodic) +boundary_conditions = (x_neg = boundary_condition_poisson_nonperiodic, + x_pos = boundary_condition_poisson_nonperiodic, + y_neg = boundary_condition_periodic, + y_pos = boundary_condition_periodic) ############################################################################### # Get the curved quad mesh from a mapping function # # Mapping as described in https://arxiv.org/abs/2012.12040, but reduced to 2D function mapping(xi_, eta_) - # Transform input variables between -1 and 1 onto [0,3] - xi = 1.5 * xi_ + 1.5 - eta = 1.5 * eta_ + 1.5 + # Transform input variables between -1 and 1 onto [0,3] + xi = 1.5 * xi_ + 1.5 + eta = 1.5 * eta_ + 1.5 - y = eta + 3/8 * (cos(1.5 * pi * (2 * xi - 3)/3) * - cos(0.5 * pi * (2 * eta - 3)/3)) + y = eta + 3 / 8 * (cos(1.5 * pi * (2 * xi - 3) / 3) * + cos(0.5 * pi * (2 * eta - 3) / 3)) - x = xi + 3/8 * (cos(0.5 * pi * (2 * xi - 3)/3) * - cos(2 * pi * (2 * y - 3)/3)) + x = xi + 3 / 8 * (cos(0.5 * pi * (2 * xi - 3) / 3) * + cos(2 * pi * (2 * y - 3) / 3)) - return SVector(x, y) + return SVector(x, y) end # Create curved mesh with 8 x 8 elements cells_per_dimension = (8, 8) -mesh = StructuredMesh(cells_per_dimension, mapping, periodicity=(false, true)) - +mesh = StructuredMesh(cells_per_dimension, mapping, periodicity = (false, true)) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver, - source_terms=source_terms_poisson_nonperiodic, - boundary_conditions=boundary_conditions) - + source_terms = source_terms_poisson_nonperiodic, + boundary_conditions = boundary_conditions) ############################################################################### # ODE solvers, callbacks etc. @@ -53,31 +51,30 @@ ode = semidiscretize(semi, tspan); summary_callback = SummaryCallback() resid_tol = 5.0e-12 -steady_state_callback = SteadyStateCallback(abstol=resid_tol, reltol=0.0) +steady_state_callback = SteadyStateCallback(abstol = resid_tol, reltol = 0.0) analysis_interval = 4000 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval, - extra_analysis_integrals=(entropy, energy_total)) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval, + extra_analysis_integrals = (entropy, energy_total)) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=4000, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 4000, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) -stepsize_callback = StepsizeCallback(cfl=1.9) +stepsize_callback = StepsizeCallback(cfl = 1.9) callbacks = CallbackSet(summary_callback, steady_state_callback, analysis_callback, alive_callback, save_solution, stepsize_callback) - ############################################################################### # run the simulation sol = Trixi.solve(ode, Trixi.HypDiffN3Erk3Sstar52(), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/structured_2d_dgsem/elixir_mhd_alfven_wave.jl b/examples/structured_2d_dgsem/elixir_mhd_alfven_wave.jl index 259875050c6..e8f2b2ecc3a 100644 --- a/examples/structured_2d_dgsem/elixir_mhd_alfven_wave.jl +++ b/examples/structured_2d_dgsem/elixir_mhd_alfven_wave.jl @@ -5,31 +5,34 @@ using Trixi ############################################################################### # semidiscretization of the compressible ideal GLM-MHD equations -gamma = 5/3 +gamma = 5 / 3 equations = IdealGlmMhdEquations2D(gamma) initial_condition = initial_condition_convergence_test # Get the DG approximation space volume_flux = (flux_central, flux_nonconservative_powell) -solver = DGSEM(polydeg=3, surface_flux=(flux_lax_friedrichs, flux_nonconservative_powell), - volume_integral=VolumeIntegralFluxDifferencing(volume_flux)) +solver = DGSEM(polydeg = 3, + surface_flux = (flux_lax_friedrichs, flux_nonconservative_powell), + volume_integral = VolumeIntegralFluxDifferencing(volume_flux)) # Get the curved quad mesh from a mapping function # Mapping as described in https://arxiv.org/abs/1809.01178 function mapping(xi_, eta_) - # Transform input variables between -1 and 1 onto [0, sqrt(2)] - # Note, we use the domain [0, sqrt(2)]^2 for the Alfvén wave convergence test case - xi = 0.5 * sqrt(2) * xi_ + 0.5 * sqrt(2) - eta = 0.5 * sqrt(2) * eta_ + 0.5 * sqrt(2) + # Transform input variables between -1 and 1 onto [0, sqrt(2)] + # Note, we use the domain [0, sqrt(2)]^2 for the Alfvén wave convergence test case + xi = 0.5 * sqrt(2) * xi_ + 0.5 * sqrt(2) + eta = 0.5 * sqrt(2) * eta_ + 0.5 * sqrt(2) - y = eta + sqrt(2)/12 * (cos(1.5 * pi * (2 * xi - sqrt(2))/sqrt(2)) * - cos(0.5 * pi * (2 * eta - sqrt(2))/sqrt(2))) + y = eta + + sqrt(2) / 12 * (cos(1.5 * pi * (2 * xi - sqrt(2)) / sqrt(2)) * + cos(0.5 * pi * (2 * eta - sqrt(2)) / sqrt(2))) - x = xi + sqrt(2)/12 * (cos(0.5 * pi * (2 * xi - sqrt(2))/sqrt(2)) * - cos(2 * pi * (2 * y - sqrt(2))/sqrt(2))) + x = xi + + sqrt(2) / 12 * (cos(0.5 * pi * (2 * xi - sqrt(2)) / sqrt(2)) * + cos(2 * pi * (2 * y - sqrt(2)) / sqrt(2))) - return SVector(x, y) + return SVector(x, y) end cells_per_dimension = (4, 4) @@ -47,21 +50,24 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval, save_analysis=false, - extra_analysis_integrals=(entropy, energy_total, - energy_kinetic, energy_internal, - energy_magnetic, cross_helicity)) - -alive_callback = AliveCallback(analysis_interval=analysis_interval) - -save_solution = SaveSolutionCallback(interval=100, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval, + save_analysis = false, + extra_analysis_integrals = (entropy, energy_total, + energy_kinetic, + energy_internal, + energy_magnetic, + cross_helicity)) + +alive_callback = AliveCallback(analysis_interval = analysis_interval) + +save_solution = SaveSolutionCallback(interval = 100, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) cfl = 2.0 -stepsize_callback = StepsizeCallback(cfl=cfl) +stepsize_callback = StepsizeCallback(cfl = cfl) -glm_speed_callback = GlmSpeedCallback(glm_scale=0.5, cfl=cfl) +glm_speed_callback = GlmSpeedCallback(glm_scale = 0.5, cfl = cfl) callbacks = CallbackSet(summary_callback, analysis_callback, @@ -73,7 +79,7 @@ callbacks = CallbackSet(summary_callback, ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/structured_2d_dgsem/elixir_mhd_ec.jl b/examples/structured_2d_dgsem/elixir_mhd_ec.jl index 634738e5c8b..a6c31744ca5 100644 --- a/examples/structured_2d_dgsem/elixir_mhd_ec.jl +++ b/examples/structured_2d_dgsem/elixir_mhd_ec.jl @@ -8,45 +8,46 @@ using Trixi equations = IdealGlmMhdEquations2D(1.4) function initial_condition_shifted_weak_blast_wave(x, t, equations::IdealGlmMhdEquations2D) - # Adapted MHD version of the weak blast wave from Hennemann & Gassner JCP paper 2020 (Sec. 6.3) - # Same discontinuity in the velocities but with magnetic fields - # Set up polar coordinates - inicenter = (1.5, 1.5) - x_norm = x[1] - inicenter[1] - y_norm = x[2] - inicenter[2] - r = sqrt(x_norm^2 + y_norm^2) - phi = atan(y_norm, x_norm) - - # Calculate primitive variables - rho = r > 0.5 ? 1.0 : 1.1691 - v1 = r > 0.5 ? 0.0 : 0.1882 * cos(phi) - v2 = r > 0.5 ? 0.0 : 0.1882 * sin(phi) - p = r > 0.5 ? 1.0 : 1.245 - - return prim2cons(SVector(rho, v1, v2, 0.0, p, 1.0, 1.0, 1.0, 0.0), equations) + # Adapted MHD version of the weak blast wave from Hennemann & Gassner JCP paper 2020 (Sec. 6.3) + # Same discontinuity in the velocities but with magnetic fields + # Set up polar coordinates + inicenter = (1.5, 1.5) + x_norm = x[1] - inicenter[1] + y_norm = x[2] - inicenter[2] + r = sqrt(x_norm^2 + y_norm^2) + phi = atan(y_norm, x_norm) + + # Calculate primitive variables + rho = r > 0.5 ? 1.0 : 1.1691 + v1 = r > 0.5 ? 0.0 : 0.1882 * cos(phi) + v2 = r > 0.5 ? 0.0 : 0.1882 * sin(phi) + p = r > 0.5 ? 1.0 : 1.245 + + return prim2cons(SVector(rho, v1, v2, 0.0, p, 1.0, 1.0, 1.0, 0.0), equations) end initial_condition = initial_condition_shifted_weak_blast_wave # Get the DG approximation space volume_flux = (flux_hindenlang_gassner, flux_nonconservative_powell) -solver = DGSEM(polydeg=5, surface_flux=(flux_hindenlang_gassner, flux_nonconservative_powell), - volume_integral=VolumeIntegralFluxDifferencing(volume_flux)) +solver = DGSEM(polydeg = 5, + surface_flux = (flux_hindenlang_gassner, flux_nonconservative_powell), + volume_integral = VolumeIntegralFluxDifferencing(volume_flux)) # Get the curved quad mesh from a mapping function # Mapping as described in https://arxiv.org/abs/2012.12040, but reduced to 2D function mapping(xi_, eta_) - # Transform input variables between -1 and 1 onto [0,3] - xi = 1.5 * xi_ + 1.5 - eta = 1.5 * eta_ + 1.5 + # Transform input variables between -1 and 1 onto [0,3] + xi = 1.5 * xi_ + 1.5 + eta = 1.5 * eta_ + 1.5 - y = eta + 3/8 * (cos(1.5 * pi * (2 * xi - 3)/3) * - cos(0.5 * pi * (2 * eta - 3)/3)) + y = eta + 3 / 8 * (cos(1.5 * pi * (2 * xi - 3) / 3) * + cos(0.5 * pi * (2 * eta - 3) / 3)) - x = xi + 3/8 * (cos(0.5 * pi * (2 * xi - 3)/3) * - cos(2 * pi * (2 * y - 3)/3)) + x = xi + 3 / 8 * (cos(0.5 * pi * (2 * xi - 3) / 3) * + cos(2 * pi * (2 * y - 3) / 3)) - return SVector(x, y) + return SVector(x, y) end # Create curved mesh with 8 x 8 elements @@ -65,21 +66,24 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval, save_analysis=false, - extra_analysis_integrals=(entropy, energy_total, - energy_kinetic, energy_internal, - energy_magnetic, cross_helicity)) - -alive_callback = AliveCallback(analysis_interval=analysis_interval) - -save_solution = SaveSolutionCallback(interval=100, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval, + save_analysis = false, + extra_analysis_integrals = (entropy, energy_total, + energy_kinetic, + energy_internal, + energy_magnetic, + cross_helicity)) + +alive_callback = AliveCallback(analysis_interval = analysis_interval) + +save_solution = SaveSolutionCallback(interval = 100, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) cfl = 1.0 -stepsize_callback = StepsizeCallback(cfl=cfl) +stepsize_callback = StepsizeCallback(cfl = cfl) -glm_speed_callback = GlmSpeedCallback(glm_scale=0.5, cfl=cfl) +glm_speed_callback = GlmSpeedCallback(glm_scale = 0.5, cfl = cfl) callbacks = CallbackSet(summary_callback, analysis_callback, @@ -91,7 +95,7 @@ callbacks = CallbackSet(summary_callback, ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/structured_2d_dgsem/elixir_mhd_ec_shockcapturing.jl b/examples/structured_2d_dgsem/elixir_mhd_ec_shockcapturing.jl index 084aeca90b9..6668014a0b6 100644 --- a/examples/structured_2d_dgsem/elixir_mhd_ec_shockcapturing.jl +++ b/examples/structured_2d_dgsem/elixir_mhd_ec_shockcapturing.jl @@ -2,7 +2,6 @@ using OrdinaryDiffEq using Trixi - ############################################################################### # semidiscretization of the compressible ideal GLM-MHD equations equations = IdealGlmMhdEquations2D(1.4) @@ -10,17 +9,17 @@ equations = IdealGlmMhdEquations2D(1.4) initial_condition = initial_condition_weak_blast_wave surface_flux = (flux_hindenlang_gassner, flux_nonconservative_powell) -volume_flux = (flux_hindenlang_gassner, flux_nonconservative_powell) +volume_flux = (flux_hindenlang_gassner, flux_nonconservative_powell) polydeg = 4 basis = LobattoLegendreBasis(polydeg) indicator_sc = IndicatorHennemannGassner(equations, basis, - alpha_max=0.5, - alpha_min=0.001, - alpha_smooth=true, - variable=density_pressure) + alpha_max = 0.5, + alpha_min = 0.001, + alpha_smooth = true, + variable = density_pressure) volume_integral = VolumeIntegralShockCapturingHG(indicator_sc; - volume_flux_dg=volume_flux, - volume_flux_fv=surface_flux) + volume_flux_dg = volume_flux, + volume_flux_fv = surface_flux) solver = DGSEM(basis, surface_flux, volume_integral) # Get the curved quad mesh from a mapping function @@ -31,16 +30,14 @@ function mapping(xi, eta) x = 2.0 * xi + 1.0 / 6.0 * (cos(0.5 * pi * xi) * cos(2 * pi * y)) return SVector(x, y) - end +end cells_per_dimension = (16, 16) -mesh = StructuredMesh(cells_per_dimension, mapping, periodicity=true) - +mesh = StructuredMesh(cells_per_dimension, mapping, periodicity = true) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver) - ############################################################################### # ODE solvers, callbacks etc. @@ -50,14 +47,14 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) cfl = 1.0 -stepsize_callback = StepsizeCallback(cfl=cfl) +stepsize_callback = StepsizeCallback(cfl = cfl) -glm_speed_callback = GlmSpeedCallback(glm_scale=0.5, cfl=cfl) +glm_speed_callback = GlmSpeedCallback(glm_scale = 0.5, cfl = cfl) callbacks = CallbackSet(summary_callback, analysis_callback, @@ -68,7 +65,7 @@ callbacks = CallbackSet(summary_callback, ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/structured_2d_dgsem/elixir_shallowwater_conical_island.jl b/examples/structured_2d_dgsem/elixir_shallowwater_conical_island.jl index 44bc7a12b35..e65ed19221e 100644 --- a/examples/structured_2d_dgsem/elixir_shallowwater_conical_island.jl +++ b/examples/structured_2d_dgsem/elixir_shallowwater_conical_island.jl @@ -2,12 +2,12 @@ using OrdinaryDiffEq using Trixi - ############################################################################### - # Semidiscretization of the shallow water equations +############################################################################### +# Semidiscretization of the shallow water equations # # TODO: TrixiShallowWater: wet/dry example elixir -equations = ShallowWaterEquations2D(gravity_constant=9.81, H0=1.4) +equations = ShallowWaterEquations2D(gravity_constant = 9.81, H0 = 1.4) """ initial_condition_conical_island(x, t, equations::ShallowWaterEquations2D) @@ -20,29 +20,29 @@ discontinuous water height is smoothed by a logistic function. This simulation u boundary conditions. """ function initial_condition_conical_island(x, t, equations::ShallowWaterEquations2D) - # Set the background values + # Set the background values - v1 = 0.0 - v2 = 0.0 + v1 = 0.0 + v2 = 0.0 - x1, x2 = x - b = max(0.1, 1.0 - 4.0 * sqrt(x1^2 + x2^2)) + x1, x2 = x + b = max(0.1, 1.0 - 4.0 * sqrt(x1^2 + x2^2)) - # use a logistic function to transfer water height value smoothly - L = equations.H0 # maximum of function - x0 = 0.3 # center point of function - k = -25.0 # sharpness of transfer + # use a logistic function to transfer water height value smoothly + L = equations.H0 # maximum of function + x0 = 0.3 # center point of function + k = -25.0 # sharpness of transfer - H = max(b, L/(1.0 + exp(-k*(sqrt(x1^2+x2^2) - x0)))) + H = max(b, L / (1.0 + exp(-k * (sqrt(x1^2 + x2^2) - x0)))) - # It is mandatory to shift the water level at dry areas to make sure the water height h - # stays positive. The system would not be stable for h set to a hard 0 due to division by h in - # the computation of velocity, e.g., (h v1) / h. Therefore, a small dry state threshold - # with a default value of 500*eps() ≈ 1e-13 in double precision, is set in the constructor above - # for the ShallowWaterEquations and added to the initial condition if h = 0. - # This default value can be changed within the constructor call depending on the simulation setup. - H = max(H, b + equations.threshold_limiter) - return prim2cons(SVector(H, v1, v2, b), equations) + # It is mandatory to shift the water level at dry areas to make sure the water height h + # stays positive. The system would not be stable for h set to a hard 0 due to division by h in + # the computation of velocity, e.g., (h v1) / h. Therefore, a small dry state threshold + # with a default value of 500*eps() ≈ 1e-13 in double precision, is set in the constructor above + # for the ShallowWaterEquations and added to the initial condition if h = 0. + # This default value can be changed within the constructor call depending on the simulation setup. + H = max(H, b + equations.threshold_limiter) + return prim2cons(SVector(H, v1, v2, b), equations) end initial_condition = initial_condition_conical_island @@ -51,19 +51,20 @@ initial_condition = initial_condition_conical_island # Get the DG approximation space volume_flux = (flux_wintermeyer_etal, flux_nonconservative_wintermeyer_etal) -surface_flux = (FluxHydrostaticReconstruction(flux_hll_chen_noelle, hydrostatic_reconstruction_chen_noelle), +surface_flux = (FluxHydrostaticReconstruction(flux_hll_chen_noelle, + hydrostatic_reconstruction_chen_noelle), flux_nonconservative_chen_noelle) basis = LobattoLegendreBasis(4) indicator_sc = IndicatorHennemannGassnerShallowWater(equations, basis, - alpha_max=0.5, - alpha_min=0.001, - alpha_smooth=true, - variable=waterheight_pressure) + alpha_max = 0.5, + alpha_min = 0.001, + alpha_smooth = true, + variable = waterheight_pressure) volume_integral = VolumeIntegralShockCapturingHG(indicator_sc; - volume_flux_dg=volume_flux, - volume_flux_fv=surface_flux) + volume_flux_dg = volume_flux, + volume_flux_fv = surface_flux) solver = DGSEM(basis, surface_flux, volume_integral) @@ -71,7 +72,7 @@ solver = DGSEM(basis, surface_flux, volume_integral) # Get the StructuredMesh and setup a periodic mesh coordinates_min = (-1.0, -1.0) -coordinates_max = (1.0, 1.0) +coordinates_max = (1.0, 1.0) cells_per_dimension = (16, 16) @@ -92,22 +93,22 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 1000 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=100, - save_initial_solution=true, - save_final_solution=true) +save_solution = SaveSolutionCallback(interval = 100, + save_initial_solution = true, + save_final_solution = true) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, save_solution) ############################################################################### # run the simulation -stage_limiter! = PositivityPreservingLimiterShallowWater(variables=(Trixi.waterheight,)) +stage_limiter! = PositivityPreservingLimiterShallowWater(variables = (Trixi.waterheight,)) sol = solve(ode, SSPRK43(stage_limiter!); - ode_default_options()..., callback=callbacks); + ode_default_options()..., callback = callbacks); -summary_callback() # print the timer summary \ No newline at end of file +summary_callback() # print the timer summary diff --git a/examples/structured_2d_dgsem/elixir_shallowwater_parabolic_bowl.jl b/examples/structured_2d_dgsem/elixir_shallowwater_parabolic_bowl.jl index 15cfe6698fc..bc198f18835 100644 --- a/examples/structured_2d_dgsem/elixir_shallowwater_parabolic_bowl.jl +++ b/examples/structured_2d_dgsem/elixir_shallowwater_parabolic_bowl.jl @@ -7,7 +7,7 @@ using Trixi # # TODO: TrixiShallowWater: wet/dry example elixir -equations = ShallowWaterEquations2D(gravity_constant=9.81) +equations = ShallowWaterEquations2D(gravity_constant = 9.81) """ initial_condition_parabolic_bowl(x, t, equations:: ShallowWaterEquations2D) @@ -28,53 +28,52 @@ The particular setup below is taken from Section 6.2 of curvilinear meshes with wet/dry fronts accelerated by GPUs [DOI: 10.1016/j.jcp.2018.08.038](https://doi.org/10.1016/j.jcp.2018.08.038). """ -function initial_condition_parabolic_bowl(x, t, equations:: ShallowWaterEquations2D) - a = 1.0 - h_0 = 0.1 - sigma = 0.5 - ω = sqrt(2 * equations.gravity * h_0) / a - - v1 = -sigma * ω * sin(ω * t) - v2 = sigma * ω * cos(ω * t) - - b = h_0 * ((x[1])^2 + (x[2])^2) / a^2 - - H = sigma * h_0 / a^2 * (2 * x[1] * cos(ω * t) + 2 * x[2] * sin(ω * t) - sigma) + h_0 - - # It is mandatory to shift the water level at dry areas to make sure the water height h - # stays positive. The system would not be stable for h set to a hard 0 due to division by h in - # the computation of velocity, e.g., (h v1) / h. Therefore, a small dry state threshold - # with a default value of 500*eps() ≈ 1e-13 in double precision, is set in the constructor above - # for the ShallowWaterEquations and added to the initial condition if h = 0. - # This default value can be changed within the constructor call depending on the simulation setup. - H = max(H, b + equations.threshold_limiter) - return prim2cons(SVector(H, v1, v2, b), equations) +function initial_condition_parabolic_bowl(x, t, equations::ShallowWaterEquations2D) + a = 1.0 + h_0 = 0.1 + sigma = 0.5 + ω = sqrt(2 * equations.gravity * h_0) / a + + v1 = -sigma * ω * sin(ω * t) + v2 = sigma * ω * cos(ω * t) + + b = h_0 * ((x[1])^2 + (x[2])^2) / a^2 + + H = sigma * h_0 / a^2 * (2 * x[1] * cos(ω * t) + 2 * x[2] * sin(ω * t) - sigma) + h_0 + + # It is mandatory to shift the water level at dry areas to make sure the water height h + # stays positive. The system would not be stable for h set to a hard 0 due to division by h in + # the computation of velocity, e.g., (h v1) / h. Therefore, a small dry state threshold + # with a default value of 500*eps() ≈ 1e-13 in double precision, is set in the constructor above + # for the ShallowWaterEquations and added to the initial condition if h = 0. + # This default value can be changed within the constructor call depending on the simulation setup. + H = max(H, b + equations.threshold_limiter) + return prim2cons(SVector(H, v1, v2, b), equations) end initial_condition = initial_condition_parabolic_bowl - ############################################################################### # Get the DG approximation space volume_flux = (flux_wintermeyer_etal, flux_nonconservative_wintermeyer_etal) -surface_flux = (FluxHydrostaticReconstruction(flux_hll_chen_noelle, hydrostatic_reconstruction_chen_noelle), +surface_flux = (FluxHydrostaticReconstruction(flux_hll_chen_noelle, + hydrostatic_reconstruction_chen_noelle), flux_nonconservative_chen_noelle) basis = LobattoLegendreBasis(4) indicator_sc = IndicatorHennemannGassnerShallowWater(equations, basis, - alpha_max=0.6, - alpha_min=0.001, - alpha_smooth=true, - variable=waterheight_pressure) + alpha_max = 0.6, + alpha_min = 0.001, + alpha_smooth = true, + variable = waterheight_pressure) volume_integral = VolumeIntegralShockCapturingHG(indicator_sc; - volume_flux_dg=volume_flux, - volume_flux_fv=surface_flux) + volume_flux_dg = volume_flux, + volume_flux_fv = surface_flux) solver = DGSEM(basis, surface_flux, volume_integral) - ############################################################################### coordinates_min = (-2.0, -2.0) @@ -96,24 +95,25 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 1000 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval, save_analysis=false, - extra_analysis_integrals=(energy_kinetic, - energy_internal)) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval, + save_analysis = false, + extra_analysis_integrals = (energy_kinetic, + energy_internal)) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=100, - save_initial_solution=true, - save_final_solution=true) +save_solution = SaveSolutionCallback(interval = 100, + save_initial_solution = true, + save_final_solution = true) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, save_solution) -stage_limiter! = PositivityPreservingLimiterShallowWater(variables=(Trixi.waterheight,)) +stage_limiter! = PositivityPreservingLimiterShallowWater(variables = (Trixi.waterheight,)) ############################################################################### # run the simulation sol = solve(ode, SSPRK43(stage_limiter!); - ode_default_options()..., callback=callbacks); + ode_default_options()..., callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/structured_2d_dgsem/elixir_shallowwater_source_terms.jl b/examples/structured_2d_dgsem/elixir_shallowwater_source_terms.jl index 18f48080850..48fe37b9996 100644 --- a/examples/structured_2d_dgsem/elixir_shallowwater_source_terms.jl +++ b/examples/structured_2d_dgsem/elixir_shallowwater_source_terms.jl @@ -5,13 +5,14 @@ using Trixi ############################################################################### # semidiscretization of the shallow water equations -equations = ShallowWaterEquations2D(gravity_constant=9.81) +equations = ShallowWaterEquations2D(gravity_constant = 9.81) initial_condition = initial_condition_convergence_test volume_flux = (flux_wintermeyer_etal, flux_nonconservative_wintermeyer_etal) -solver = DGSEM(polydeg=3, surface_flux=(flux_lax_friedrichs, flux_nonconservative_fjordholm_etal), - volume_integral=VolumeIntegralFluxDifferencing(volume_flux)) +solver = DGSEM(polydeg = 3, + surface_flux = (flux_lax_friedrichs, flux_nonconservative_fjordholm_etal), + volume_integral = VolumeIntegralFluxDifferencing(volume_flux)) coordinates_min = (0.0, 0.0) coordinates_max = (sqrt(2.0), sqrt(2.0)) @@ -20,10 +21,8 @@ cells_per_dimension = (8, 8) mesh = StructuredMesh(cells_per_dimension, coordinates_min, coordinates_max) - semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver, - source_terms=source_terms_convergence_test) - + source_terms = source_terms_convergence_test) ############################################################################### # ODE solvers, callbacks etc. @@ -34,16 +33,16 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=100, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 100, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) -stepsize_callback = StepsizeCallback(cfl=2.0) +stepsize_callback = StepsizeCallback(cfl = 2.0) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, @@ -53,7 +52,7 @@ callbacks = CallbackSet(summary_callback, ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/structured_2d_dgsem/elixir_shallowwater_well_balanced.jl b/examples/structured_2d_dgsem/elixir_shallowwater_well_balanced.jl index 17836fa6b8f..61dd252fd83 100644 --- a/examples/structured_2d_dgsem/elixir_shallowwater_well_balanced.jl +++ b/examples/structured_2d_dgsem/elixir_shallowwater_well_balanced.jl @@ -7,21 +7,21 @@ using Trixi # semidiscretization of the shallow water equations with a discontinuous # bottom topography function (set in the initial conditions) -equations = ShallowWaterEquations2D(gravity_constant=9.81, H0=3.0) +equations = ShallowWaterEquations2D(gravity_constant = 9.81, H0 = 3.0) # An initial condition with constant total water height and zero velocities to test well-balancedness. # Note, this routine is used to compute errors in the analysis callback but the initialization is # overwritten by `initial_condition_discontinuous_well_balancedness` below. function initial_condition_well_balancedness(x, t, equations::ShallowWaterEquations2D) - # Set the background values - H = equations.H0 - v1 = 0.0 - v2 = 0.0 - # bottom topography taken from Pond.control in [HOHQMesh](https://github.com/trixi-framework/HOHQMesh) - x1, x2 = x - b = ( 1.5 / exp( 0.5 * ((x1 - 1.0)^2 + (x2 - 1.0)^2) ) - + 0.75 / exp( 0.5 * ((x1 + 1.0)^2 + (x2 + 1.0)^2) ) ) - return prim2cons(SVector(H, v1, v2, b), equations) + # Set the background values + H = equations.H0 + v1 = 0.0 + v2 = 0.0 + # bottom topography taken from Pond.control in [HOHQMesh](https://github.com/trixi-framework/HOHQMesh) + x1, x2 = x + b = (1.5 / exp(0.5 * ((x1 - 1.0)^2 + (x2 - 1.0)^2)) + + 0.75 / exp(0.5 * ((x1 + 1.0)^2 + (x2 + 1.0)^2))) + return prim2cons(SVector(H, v1, v2, b), equations) end initial_condition = initial_condition_well_balancedness @@ -30,16 +30,17 @@ initial_condition = initial_condition_well_balancedness # Get the DG approximation space volume_flux = (flux_wintermeyer_etal, flux_nonconservative_wintermeyer_etal) -surface_flux = (FluxHydrostaticReconstruction(flux_lax_friedrichs, hydrostatic_reconstruction_audusse_etal), +surface_flux = (FluxHydrostaticReconstruction(flux_lax_friedrichs, + hydrostatic_reconstruction_audusse_etal), flux_nonconservative_audusse_etal) -solver = DGSEM(polydeg=4, surface_flux=surface_flux, - volume_integral=VolumeIntegralFluxDifferencing(volume_flux)) +solver = DGSEM(polydeg = 4, surface_flux = surface_flux, + volume_integral = VolumeIntegralFluxDifferencing(volume_flux)) ############################################################################### # This setup a structured periodic mesh coordinates_min = (-2.0, -2.0) -coordinates_max = ( 2.0, 2.0) +coordinates_max = (2.0, 2.0) cells_per_dimension = (4, 4) @@ -64,30 +65,33 @@ ode = semidiscretize(semi, tspan) # In contrast to the usual signature of initial conditions, this one get passed the # `element_id` explicitly. In particular, this initial conditions works as intended # only for the specific mesh loaded above! -function initial_condition_discontinuous_well_balancedness(x, t, element_id, equations::ShallowWaterEquations2D) - # Set the background values - H = equations.H0 - v1 = 0.0 - v2 = 0.0 - b = 0.0 - - # Setup a discontinuous bottom topography using the element id number - if element_id == 7 - b = 2.0 + 0.5 * sin(2.0 * pi * x[1]) + 0.5 * cos(2.0 * pi * x[2]) - end - - return prim2cons(SVector(H, v1, v2, b), equations) +function initial_condition_discontinuous_well_balancedness(x, t, element_id, + equations::ShallowWaterEquations2D) + # Set the background values + H = equations.H0 + v1 = 0.0 + v2 = 0.0 + b = 0.0 + + # Setup a discontinuous bottom topography using the element id number + if element_id == 7 + b = 2.0 + 0.5 * sin(2.0 * pi * x[1]) + 0.5 * cos(2.0 * pi * x[2]) + end + + return prim2cons(SVector(H, v1, v2, b), equations) end # point to the data we want to augment u = Trixi.wrap_array(ode.u0, semi) # reset the initial condition for element in eachelement(semi.solver, semi.cache) - for j in eachnode(semi.solver), i in eachnode(semi.solver) - x_node = Trixi.get_node_coords(semi.cache.elements.node_coordinates, equations, semi.solver, i, j, element) - u_node = initial_condition_discontinuous_well_balancedness(x_node, first(tspan), element, equations) - Trixi.set_node_vars!(u, u_node, equations, semi.solver, i, j, element) - end + for j in eachnode(semi.solver), i in eachnode(semi.solver) + x_node = Trixi.get_node_coords(semi.cache.elements.node_coordinates, equations, + semi.solver, i, j, element) + u_node = initial_condition_discontinuous_well_balancedness(x_node, first(tspan), + element, equations) + Trixi.set_node_vars!(u, u_node, equations, semi.solver, i, j, element) + end end ############################################################################### @@ -96,16 +100,16 @@ end summary_callback = SummaryCallback() analysis_interval = 1000 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval, - extra_analysis_integrals=(lake_at_rest_error,)) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval, + extra_analysis_integrals = (lake_at_rest_error,)) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=1000, - save_initial_solution=true, - save_final_solution=true) +save_solution = SaveSolutionCallback(interval = 1000, + save_initial_solution = true, + save_final_solution = true) -stepsize_callback = StepsizeCallback(cfl=3.0) +stepsize_callback = StepsizeCallback(cfl = 3.0) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, save_solution, stepsize_callback) @@ -113,7 +117,7 @@ callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, sav ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/structured_2d_dgsem/elixir_shallowwater_well_balanced_wet_dry.jl b/examples/structured_2d_dgsem/elixir_shallowwater_well_balanced_wet_dry.jl index b18b02e0b4c..8e492b1ba05 100644 --- a/examples/structured_2d_dgsem/elixir_shallowwater_well_balanced_wet_dry.jl +++ b/examples/structured_2d_dgsem/elixir_shallowwater_well_balanced_wet_dry.jl @@ -8,8 +8,7 @@ using Printf: @printf, @sprintf # # TODO: TrixiShallowWater: wet/dry example elixir - -equations = ShallowWaterEquations2D(gravity_constant=9.812) +equations = ShallowWaterEquations2D(gravity_constant = 9.812) """ initial_condition_well_balanced_chen_noelle(x, t, equations:: ShallowWaterEquations2D) @@ -24,29 +23,30 @@ The initial condition is taken from Section 5.2 of the paper: A new hydrostatic reconstruction scheme based on subcell reconstructions [DOI:10.1137/15M1053074](https://dx.doi.org/10.1137/15M1053074) """ -function initial_condition_complex_bottom_well_balanced(x, t, equations:: ShallowWaterEquations2D) - v1 = 0 - v2 = 0 - b = sin(4 * pi * x[1]) + 3 - - if x[1] >= 0.5 - b = sin(4 * pi * x[1]) + 1 - end - - H = max(b, 2.5) - - if x[1] >= 0.5 - H = max(b, 1.5) - end - - # It is mandatory to shift the water level at dry areas to make sure the water height h - # stays positive. The system would not be stable for h set to a hard 0 due to division by h in - # the computation of velocity, e.g., (h v1) / h. Therefore, a small dry state threshold - # with a default value of 500*eps() ≈ 1e-13 in double precision, is set in the constructor above - # for the ShallowWaterEquations and added to the initial condition if h = 0. - # This default value can be changed within the constructor call depending on the simulation setup. - H = max(H, b + equations.threshold_limiter) - return prim2cons(SVector(H, v1, v2, b), equations) +function initial_condition_complex_bottom_well_balanced(x, t, + equations::ShallowWaterEquations2D) + v1 = 0 + v2 = 0 + b = sin(4 * pi * x[1]) + 3 + + if x[1] >= 0.5 + b = sin(4 * pi * x[1]) + 1 + end + + H = max(b, 2.5) + + if x[1] >= 0.5 + H = max(b, 1.5) + end + + # It is mandatory to shift the water level at dry areas to make sure the water height h + # stays positive. The system would not be stable for h set to a hard 0 due to division by h in + # the computation of velocity, e.g., (h v1) / h. Therefore, a small dry state threshold + # with a default value of 500*eps() ≈ 1e-13 in double precision, is set in the constructor above + # for the ShallowWaterEquations and added to the initial condition if h = 0. + # This default value can be changed within the constructor call depending on the simulation setup. + H = max(H, b + equations.threshold_limiter) + return prim2cons(SVector(H, v1, v2, b), equations) end initial_condition = initial_condition_complex_bottom_well_balanced @@ -56,23 +56,23 @@ initial_condition = initial_condition_complex_bottom_well_balanced volume_flux = (flux_wintermeyer_etal, flux_nonconservative_wintermeyer_etal) -surface_flux = (FluxHydrostaticReconstruction(flux_hll_chen_noelle, hydrostatic_reconstruction_chen_noelle), +surface_flux = (FluxHydrostaticReconstruction(flux_hll_chen_noelle, + hydrostatic_reconstruction_chen_noelle), flux_nonconservative_chen_noelle) basis = LobattoLegendreBasis(3) indicator_sc = IndicatorHennemannGassnerShallowWater(equations, basis, - alpha_max=0.5, - alpha_min=0.001, - alpha_smooth=true, - variable=waterheight_pressure) + alpha_max = 0.5, + alpha_min = 0.001, + alpha_smooth = true, + variable = waterheight_pressure) volume_integral = VolumeIntegralShockCapturingHG(indicator_sc; - volume_flux_dg=volume_flux, - volume_flux_fv=surface_flux) + volume_flux_dg = volume_flux, + volume_flux_fv = surface_flux) solver = DGSEM(basis, surface_flux, volume_integral) - ############################################################################### # Create the StructuredMesh for the domain [0, 1]^2 @@ -83,7 +83,6 @@ cells_per_dimension = (16, 16) mesh = StructuredMesh(cells_per_dimension, coordinates_min, coordinates_max) - # create the semi discretization object semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver) @@ -107,18 +106,20 @@ ode = semidiscretize(semi, tspan) u = Trixi.wrap_array(ode.u0, semi) # reset the initial condition for element in eachelement(semi.solver, semi.cache) - for j in eachnode(semi.solver), i in eachnode(semi.solver) - x_node = Trixi.get_node_coords(semi.cache.elements.node_coordinates, equations, semi.solver, i, j, element) - # We know that the discontinuity is a vertical line. Slightly augment the x value by a factor - # of unit roundoff to avoid the repeted value from the LGL nodes at at interface. - if i == 1 - x_node = SVector(nextfloat(x_node[1]) , x_node[2]) - elseif i == nnodes(semi.solver) - x_node = SVector(prevfloat(x_node[1]) , x_node[2]) + for j in eachnode(semi.solver), i in eachnode(semi.solver) + x_node = Trixi.get_node_coords(semi.cache.elements.node_coordinates, equations, + semi.solver, i, j, element) + # We know that the discontinuity is a vertical line. Slightly augment the x value by a factor + # of unit roundoff to avoid the repeted value from the LGL nodes at at interface. + if i == 1 + x_node = SVector(nextfloat(x_node[1]), x_node[2]) + elseif i == nnodes(semi.solver) + x_node = SVector(prevfloat(x_node[1]), x_node[2]) + end + u_node = initial_condition_complex_bottom_well_balanced(x_node, first(tspan), + equations) + Trixi.set_node_vars!(u, u_node, equations, semi.solver, i, j, element) end - u_node = initial_condition_complex_bottom_well_balanced(x_node, first(tspan), equations) - Trixi.set_node_vars!(u, u_node, equations, semi.solver, i, j, element) - end end ############################################################################### @@ -127,25 +128,27 @@ end summary_callback = SummaryCallback() analysis_interval = 1000 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval, save_analysis=false) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval, + save_analysis = false) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=1000, - save_initial_solution=true, - save_final_solution=true) +save_solution = SaveSolutionCallback(interval = 1000, + save_initial_solution = true, + save_final_solution = true) -stepsize_callback = StepsizeCallback(cfl=1.0) +stepsize_callback = StepsizeCallback(cfl = 1.0) -callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, save_solution, stepsize_callback) +callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, save_solution, + stepsize_callback) -stage_limiter! = PositivityPreservingLimiterShallowWater(variables=(Trixi.waterheight,)) +stage_limiter! = PositivityPreservingLimiterShallowWater(variables = (Trixi.waterheight,)) ############################################################################### # run the simulation -sol = solve(ode, SSPRK43(stage_limiter!); dt=1.0, - ode_default_options()..., callback=callbacks, adaptive=false); +sol = solve(ode, SSPRK43(stage_limiter!); dt = 1.0, + ode_default_options()..., callback = callbacks, adaptive = false); summary_callback() # print the timer summary @@ -160,39 +163,43 @@ summary_callback() # print the timer summary function lake_at_rest_error_two_level(u, x, equations::ShallowWaterEquations2D) h, _, _, b = u - # For well-balancedness testing with possible wet/dry regions the reference - # water height `H0` accounts for the possibility that the bottom topography - # can emerge out of the water as well as for the threshold offset to avoid - # division by a "hard" zero water heights as well. - if x[1] < 0.5 - H0_wet_dry = max( 2.5 , b + equations.threshold_limiter ) - else - H0_wet_dry = max( 1.5 , b + equations.threshold_limiter ) - end - - return abs(H0_wet_dry - (h + b)) + # For well-balancedness testing with possible wet/dry regions the reference + # water height `H0` accounts for the possibility that the bottom topography + # can emerge out of the water as well as for the threshold offset to avoid + # division by a "hard" zero water heights as well. + if x[1] < 0.5 + H0_wet_dry = max(2.5, b + equations.threshold_limiter) + else + H0_wet_dry = max(1.5, b + equations.threshold_limiter) + end + + return abs(H0_wet_dry - (h + b)) end # point to the data we want to analyze u = Trixi.wrap_array(sol[end], semi) # Perform the actual integration of the well-balancedness error over the domain -l1_well_balance_error = Trixi.integrate_via_indices(u, mesh, equations, semi.solver, semi.cache; normalize=true) do u, i, j, element, equations, solver - x_node = Trixi.get_node_coords(semi.cache.elements.node_coordinates, equations, solver, i, j, element) - # We know that the discontinuity is a vertical line. Slightly augment the x value by a factor - # of unit roundoff to avoid the repeted value from the LGL nodes at at interface. - if i == 1 - x_node = SVector(nextfloat(x_node[1]) , x_node[2]) - elseif i == nnodes(semi.solver) - x_node = SVector(prevfloat(x_node[1]) , x_node[2]) - end - u_local = Trixi.get_node_vars(u, equations, solver, i, j, element) - return lake_at_rest_error_two_level(u_local, x_node, equations) +l1_well_balance_error = Trixi.integrate_via_indices(u, mesh, equations, semi.solver, + semi.cache; + normalize = true) do u, i, j, element, + equations, solver + x_node = Trixi.get_node_coords(semi.cache.elements.node_coordinates, equations, solver, + i, j, element) + # We know that the discontinuity is a vertical line. Slightly augment the x value by a factor + # of unit roundoff to avoid the repeted value from the LGL nodes at at interface. + if i == 1 + x_node = SVector(nextfloat(x_node[1]), x_node[2]) + elseif i == nnodes(semi.solver) + x_node = SVector(prevfloat(x_node[1]), x_node[2]) + end + u_local = Trixi.get_node_vars(u, equations, solver, i, j, element) + return lake_at_rest_error_two_level(u_local, x_node, equations) end # report the well-balancedness lake-at-rest error to the screen println("─"^100) println(" Lake-at-rest error for '", Trixi.get_name(equations), "' with ", summary(solver), - " at final time " * @sprintf("%10.8e", tspan[end])) + " at final time " * @sprintf("%10.8e", tspan[end])) @printf(" %-12s:", Trixi.pretty_form_utf(lake_at_rest_error)) @printf(" % 10.8e", l1_well_balance_error) diff --git a/examples/structured_3d_dgsem/elixir_advection_basic.jl b/examples/structured_3d_dgsem/elixir_advection_basic.jl index 47ae6352485..5b0bb371fe8 100644 --- a/examples/structured_3d_dgsem/elixir_advection_basic.jl +++ b/examples/structured_3d_dgsem/elixir_advection_basic.jl @@ -11,18 +11,18 @@ advection_velocity = (0.2, -0.7, 0.5) equations = LinearScalarAdvectionEquation3D(advection_velocity) # Create DG solver with polynomial degree = 3 and (local) Lax-Friedrichs/Rusanov flux as surface flux -solver = DGSEM(polydeg=3, surface_flux=flux_lax_friedrichs) +solver = DGSEM(polydeg = 3, surface_flux = flux_lax_friedrichs) coordinates_min = (-1.0, -1.0, -1.0) # minimum coordinates (min(x), min(y), min(z)) -coordinates_max = ( 1.0, 1.0, 1.0) # maximum coordinates (max(x), max(y), max(z)) +coordinates_max = (1.0, 1.0, 1.0) # maximum coordinates (max(x), max(y), max(z)) cells_per_dimension = (8, 8, 8) # Create curved mesh with 8 x 8 x 8 elements mesh = StructuredMesh(cells_per_dimension, coordinates_min, coordinates_max) # A semidiscretization collects data structures and functions for the spatial discretization -semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition_convergence_test, solver) - +semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition_convergence_test, + solver) ############################################################################### # ODE solvers, callbacks etc. @@ -35,30 +35,30 @@ ode = semidiscretize(semi, (0.0, 1.0)); summary_callback = SummaryCallback() # The AnalysisCallback allows to analyse the solution in regular intervals and prints the results -analysis_callback = AnalysisCallback(semi, interval=100) +analysis_callback = AnalysisCallback(semi, interval = 100) # The SaveSolutionCallback allows to save the solution to a file in regular intervals -save_solution = SaveSolutionCallback(interval=100, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 100, + solution_variables = cons2prim) # The SaveRestartCallback allows to save a file from which a Trixi.jl simulation can be restarted -save_restart = SaveRestartCallback(interval=100, - save_final_restart=true) +save_restart = SaveRestartCallback(interval = 100, + save_final_restart = true) # The StepsizeCallback handles the re-calculation of the maximum Δt after each time step -stepsize_callback = StepsizeCallback(cfl=1.2) +stepsize_callback = StepsizeCallback(cfl = 1.2) # Create a CallbackSet to collect all callbacks such that they can be passed to the ODE solver -callbacks = CallbackSet(summary_callback, analysis_callback, save_solution, save_restart, stepsize_callback) - +callbacks = CallbackSet(summary_callback, analysis_callback, save_solution, save_restart, + stepsize_callback) ############################################################################### # run the simulation # OrdinaryDiffEq's `solve` method evolves the solution in time and executes the passed callbacks -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); # Print the timer summary summary_callback() diff --git a/examples/structured_3d_dgsem/elixir_advection_free_stream.jl b/examples/structured_3d_dgsem/elixir_advection_free_stream.jl index 749233b8c68..12d52f15160 100644 --- a/examples/structured_3d_dgsem/elixir_advection_free_stream.jl +++ b/examples/structured_3d_dgsem/elixir_advection_free_stream.jl @@ -13,24 +13,27 @@ solver = DGSEM(3, flux_lax_friedrichs) # Mapping as described in https://arxiv.org/abs/2012.12040 function mapping(xi_, eta_, zeta_) - # Transform input variables between -1 and 1 onto [0,3] - xi = 1.5 * xi_ + 1.5 - eta = 1.5 * eta_ + 1.5 - zeta = 1.5 * zeta_ + 1.5 - - y = eta + 3/8 * (cos(1.5 * pi * (2 * xi - 3)/3) * - cos(0.5 * pi * (2 * eta - 3)/3) * - cos(0.5 * pi * (2 * zeta - 3)/3)) - - x = xi + 3/8 * (cos(0.5 * pi * (2 * xi - 3)/3) * - cos(2 * pi * (2 * y - 3)/3) * - cos(0.5 * pi * (2 * zeta - 3)/3)) - - z = zeta + 3/8 * (cos(0.5 * pi * (2 * x - 3)/3) * - cos(pi * (2 * y - 3)/3) * - cos(0.5 * pi * (2 * zeta - 3)/3)) - - return SVector(x, y, z) + # Transform input variables between -1 and 1 onto [0,3] + xi = 1.5 * xi_ + 1.5 + eta = 1.5 * eta_ + 1.5 + zeta = 1.5 * zeta_ + 1.5 + + y = eta + + 3 / 8 * (cos(1.5 * pi * (2 * xi - 3) / 3) * + cos(0.5 * pi * (2 * eta - 3) / 3) * + cos(0.5 * pi * (2 * zeta - 3) / 3)) + + x = xi + + 3 / 8 * (cos(0.5 * pi * (2 * xi - 3) / 3) * + cos(2 * pi * (2 * y - 3) / 3) * + cos(0.5 * pi * (2 * zeta - 3) / 3)) + + z = zeta + + 3 / 8 * (cos(0.5 * pi * (2 * x - 3) / 3) * + cos(pi * (2 * y - 3) / 3) * + cos(0.5 * pi * (2 * zeta - 3) / 3)) + + return SVector(x, y, z) end cells_per_dimension = (8, 8, 8) @@ -41,7 +44,6 @@ mesh = StructuredMesh(cells_per_dimension, mapping) # A semidiscretization collects data structures and functions for the spatial discretization semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition_constant, solver) - ############################################################################### # ODE solvers, callbacks etc. @@ -53,26 +55,26 @@ ode = semidiscretize(semi, (0.0, 1.0)); summary_callback = SummaryCallback() # The AnalysisCallback allows to analyse the solution in regular intervals and prints the results -analysis_callback = AnalysisCallback(semi, interval=100) +analysis_callback = AnalysisCallback(semi, interval = 100) # The SaveSolutionCallback allows to save the solution to a file in regular intervals -save_solution = SaveSolutionCallback(interval=100, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 100, + solution_variables = cons2prim) # The StepsizeCallback handles the re-calculation of the maximum Δt after each time step -stepsize_callback = StepsizeCallback(cfl=2.0) +stepsize_callback = StepsizeCallback(cfl = 2.0) # Create a CallbackSet to collect all callbacks such that they can be passed to the ODE solver -callbacks = CallbackSet(summary_callback, analysis_callback, save_solution, stepsize_callback) - +callbacks = CallbackSet(summary_callback, analysis_callback, save_solution, + stepsize_callback) ############################################################################### # run the simulation # OrdinaryDiffEq's `solve` method evolves the solution in time and executes the passed callbacks -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); # Print the timer summary summary_callback() diff --git a/examples/structured_3d_dgsem/elixir_advection_nonperiodic_curved.jl b/examples/structured_3d_dgsem/elixir_advection_nonperiodic_curved.jl index fa8ae756566..1a20a9c8533 100644 --- a/examples/structured_3d_dgsem/elixir_advection_nonperiodic_curved.jl +++ b/examples/structured_3d_dgsem/elixir_advection_nonperiodic_curved.jl @@ -11,36 +11,38 @@ equations = LinearScalarAdvectionEquation3D(advection_velocity) initial_condition = initial_condition_convergence_test boundary_conditions = BoundaryConditionDirichlet(initial_condition) -solver = DGSEM(polydeg=3, surface_flux=flux_lax_friedrichs) +solver = DGSEM(polydeg = 3, surface_flux = flux_lax_friedrichs) # Mapping as described in https://arxiv.org/abs/2012.12040 but with less warping. function mapping(xi, eta, zeta) - # Don't transform input variables between -1 and 1 onto [0,3] to obtain curved boundaries - # xi = 1.5 * xi_ + 1.5 - # eta = 1.5 * eta_ + 1.5 - # zeta = 1.5 * zeta_ + 1.5 - - y = eta + 1/6 * (cos(1.5 * pi * (2 * xi - 3)/3) * - cos(0.5 * pi * (2 * eta - 3)/3) * - cos(0.5 * pi * (2 * zeta - 3)/3)) - - x = xi + 1/6 * (cos(0.5 * pi * (2 * xi - 3)/3) * - cos(2 * pi * (2 * y - 3)/3) * - cos(0.5 * pi * (2 * zeta - 3)/3)) - - z = zeta + 1/6 * (cos(0.5 * pi * (2 * x - 3)/3) * - cos(pi * (2 * y - 3)/3) * - cos(0.5 * pi * (2 * zeta - 3)/3)) - - return SVector(x, y, z) + # Don't transform input variables between -1 and 1 onto [0,3] to obtain curved boundaries + # xi = 1.5 * xi_ + 1.5 + # eta = 1.5 * eta_ + 1.5 + # zeta = 1.5 * zeta_ + 1.5 + + y = eta + + 1 / 6 * (cos(1.5 * pi * (2 * xi - 3) / 3) * + cos(0.5 * pi * (2 * eta - 3) / 3) * + cos(0.5 * pi * (2 * zeta - 3) / 3)) + + x = xi + + 1 / 6 * (cos(0.5 * pi * (2 * xi - 3) / 3) * + cos(2 * pi * (2 * y - 3) / 3) * + cos(0.5 * pi * (2 * zeta - 3) / 3)) + + z = zeta + + 1 / 6 * (cos(0.5 * pi * (2 * x - 3) / 3) * + cos(pi * (2 * y - 3) / 3) * + cos(0.5 * pi * (2 * zeta - 3) / 3)) + + return SVector(x, y, z) end cells_per_dimension = (8, 8, 8) -mesh = StructuredMesh(cells_per_dimension, mapping, periodicity=false) +mesh = StructuredMesh(cells_per_dimension, mapping, periodicity = false) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver, - boundary_conditions=boundary_conditions) - + boundary_conditions = boundary_conditions) ############################################################################### # ODE solvers, callbacks etc. @@ -51,20 +53,20 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval, - extra_analysis_integrals=(entropy,)) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval, + extra_analysis_integrals = (entropy,)) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_restart = SaveRestartCallback(interval=100, - save_final_restart=true) +save_restart = SaveRestartCallback(interval = 100, + save_final_restart = true) -save_solution = SaveSolutionCallback(interval=100, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 100, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) -stepsize_callback = StepsizeCallback(cfl=1.2) +stepsize_callback = StepsizeCallback(cfl = 1.2) callbacks = CallbackSet(summary_callback, analysis_callback, @@ -76,7 +78,7 @@ callbacks = CallbackSet(summary_callback, ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/structured_3d_dgsem/elixir_advection_restart.jl b/examples/structured_3d_dgsem/elixir_advection_restart.jl index 921c5310340..e81ad5d6430 100644 --- a/examples/structured_3d_dgsem/elixir_advection_restart.jl +++ b/examples/structured_3d_dgsem/elixir_advection_restart.jl @@ -6,8 +6,7 @@ using Trixi # create a restart file trixi_include(@__MODULE__, joinpath(@__DIR__, "elixir_advection_basic.jl"), - cells_per_dimension=(4, 4, 4)) - + cells_per_dimension = (4, 4, 4)) ############################################################################### # adapt the parameters that have changed compared to "elixir_advection_extended.jl" @@ -18,7 +17,8 @@ trixi_include(@__MODULE__, joinpath(@__DIR__, "elixir_advection_basic.jl"), restart_filename = joinpath("out", "restart_000010.h5") mesh = load_mesh(restart_filename) -semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition_convergence_test, solver) +semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition_convergence_test, + solver) tspan = (load_time(restart_filename), 2.0) dt = load_dt(restart_filename) @@ -27,14 +27,13 @@ ode = semidiscretize(semi, tspan, restart_filename); # Do not overwrite the initial snapshot written by elixir_advection_extended.jl. save_solution.condition.save_initial_solution = false -integrator = init(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=dt, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +integrator = init(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = dt, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); # Get the last time index and work with that. load_timestep!(integrator, restart_filename) - ############################################################################### # run the simulation diff --git a/examples/structured_3d_dgsem/elixir_euler_ec.jl b/examples/structured_3d_dgsem/elixir_euler_ec.jl index 0009eb31180..1330006760e 100644 --- a/examples/structured_3d_dgsem/elixir_euler_ec.jl +++ b/examples/structured_3d_dgsem/elixir_euler_ec.jl @@ -5,7 +5,7 @@ using Trixi ############################################################################### # semidiscretization of the compressible Euler equations -equations = CompressibleEulerEquations3D(5/3) +equations = CompressibleEulerEquations3D(5 / 3) initial_condition = initial_condition_weak_blast_wave @@ -13,32 +13,35 @@ initial_condition = initial_condition_weak_blast_wave # Get the DG approximation space volume_flux = flux_ranocha -solver = DGSEM(polydeg=5, surface_flux=flux_ranocha, - volume_integral=VolumeIntegralFluxDifferencing(volume_flux)) +solver = DGSEM(polydeg = 5, surface_flux = flux_ranocha, + volume_integral = VolumeIntegralFluxDifferencing(volume_flux)) ############################################################################### # Get the curved quad mesh from a file # Mapping as described in https://arxiv.org/abs/2012.12040 function mapping(xi_, eta_, zeta_) - # Transform input variables between -1 and 1 onto [0,3] - xi = 1.5 * xi_ + 1.5 - eta = 1.5 * eta_ + 1.5 - zeta = 1.5 * zeta_ + 1.5 - - y = eta + 3/8 * (cos(1.5 * pi * (2 * xi - 3)/3) * - cos(0.5 * pi * (2 * eta - 3)/3) * - cos(0.5 * pi * (2 * zeta - 3)/3)) - - x = xi + 3/8 * (cos(0.5 * pi * (2 * xi - 3)/3) * - cos(2 * pi * (2 * y - 3)/3) * - cos(0.5 * pi * (2 * zeta - 3)/3)) - - z = zeta + 3/8 * (cos(0.5 * pi * (2 * x - 3)/3) * - cos(pi * (2 * y - 3)/3) * - cos(0.5 * pi * (2 * zeta - 3)/3)) - - return SVector(x, y, z) + # Transform input variables between -1 and 1 onto [0,3] + xi = 1.5 * xi_ + 1.5 + eta = 1.5 * eta_ + 1.5 + zeta = 1.5 * zeta_ + 1.5 + + y = eta + + 3 / 8 * (cos(1.5 * pi * (2 * xi - 3) / 3) * + cos(0.5 * pi * (2 * eta - 3) / 3) * + cos(0.5 * pi * (2 * zeta - 3) / 3)) + + x = xi + + 3 / 8 * (cos(0.5 * pi * (2 * xi - 3) / 3) * + cos(2 * pi * (2 * y - 3) / 3) * + cos(0.5 * pi * (2 * zeta - 3) / 3)) + + z = zeta + + 3 / 8 * (cos(0.5 * pi * (2 * x - 3) / 3) * + cos(pi * (2 * y - 3) / 3) * + cos(0.5 * pi * (2 * zeta - 3) / 3)) + + return SVector(x, y, z) end cells_per_dimension = (4, 4, 4) @@ -59,15 +62,15 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=100, - save_initial_solution=true, - save_final_solution=true) +save_solution = SaveSolutionCallback(interval = 100, + save_initial_solution = true, + save_final_solution = true) -stepsize_callback = StepsizeCallback(cfl=1.0) +stepsize_callback = StepsizeCallback(cfl = 1.0) callbacks = CallbackSet(summary_callback, analysis_callback, @@ -78,7 +81,7 @@ callbacks = CallbackSet(summary_callback, ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/structured_3d_dgsem/elixir_euler_free_stream.jl b/examples/structured_3d_dgsem/elixir_euler_free_stream.jl index b0e71435767..1b01287100e 100644 --- a/examples/structured_3d_dgsem/elixir_euler_free_stream.jl +++ b/examples/structured_3d_dgsem/elixir_euler_free_stream.jl @@ -9,29 +9,32 @@ equations = CompressibleEulerEquations3D(1.4) initial_condition = initial_condition_constant -solver = DGSEM(polydeg=3, surface_flux=flux_lax_friedrichs, - volume_integral=VolumeIntegralWeakForm()) +solver = DGSEM(polydeg = 3, surface_flux = flux_lax_friedrichs, + volume_integral = VolumeIntegralWeakForm()) # Mapping as described in https://arxiv.org/abs/2012.12040 function mapping(xi_, eta_, zeta_) - # Transform input variables between -1 and 1 onto [0,3] - xi = 1.5 * xi_ + 1.5 - eta = 1.5 * eta_ + 1.5 - zeta = 1.5 * zeta_ + 1.5 - - y = eta + 3/8 * (cos(1.5 * pi * (2 * xi - 3)/3) * - cos(0.5 * pi * (2 * eta - 3)/3) * - cos(0.5 * pi * (2 * zeta - 3)/3)) - - x = xi + 3/8 * (cos(0.5 * pi * (2 * xi - 3)/3) * - cos(2 * pi * (2 * y - 3)/3) * - cos(0.5 * pi * (2 * zeta - 3)/3)) - - z = zeta + 3/8 * (cos(0.5 * pi * (2 * x - 3)/3) * - cos(pi * (2 * y - 3)/3) * - cos(0.5 * pi * (2 * zeta - 3)/3)) - - return SVector(x, y, z) + # Transform input variables between -1 and 1 onto [0,3] + xi = 1.5 * xi_ + 1.5 + eta = 1.5 * eta_ + 1.5 + zeta = 1.5 * zeta_ + 1.5 + + y = eta + + 3 / 8 * (cos(1.5 * pi * (2 * xi - 3) / 3) * + cos(0.5 * pi * (2 * eta - 3) / 3) * + cos(0.5 * pi * (2 * zeta - 3) / 3)) + + x = xi + + 3 / 8 * (cos(0.5 * pi * (2 * xi - 3) / 3) * + cos(2 * pi * (2 * y - 3) / 3) * + cos(0.5 * pi * (2 * zeta - 3) / 3)) + + z = zeta + + 3 / 8 * (cos(0.5 * pi * (2 * x - 3) / 3) * + cos(pi * (2 * y - 3) / 3) * + cos(0.5 * pi * (2 * zeta - 3) / 3)) + + return SVector(x, y, z) end cells_per_dimension = (4, 4, 4) @@ -40,7 +43,6 @@ mesh = StructuredMesh(cells_per_dimension, mapping) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver) - ############################################################################### # ODE solvers, callbacks etc. @@ -50,30 +52,29 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_restart = SaveRestartCallback(interval=100, - save_final_restart=true) +save_restart = SaveRestartCallback(interval = 100, + save_final_restart = true) -save_solution = SaveSolutionCallback(interval=100, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 100, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) -stepsize_callback = StepsizeCallback(cfl=1.3) +stepsize_callback = StepsizeCallback(cfl = 1.3) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, save_restart, save_solution, stepsize_callback) - ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/structured_3d_dgsem/elixir_euler_sedov.jl b/examples/structured_3d_dgsem/elixir_euler_sedov.jl index e0595437c99..1f2d9d2eeb6 100644 --- a/examples/structured_3d_dgsem/elixir_euler_sedov.jl +++ b/examples/structured_3d_dgsem/elixir_euler_sedov.jl @@ -14,28 +14,29 @@ The Sedov blast wave setup based on Flash - https://flash.rochester.edu/site/flashcode/user_support/flash_ug_devel/node187.html#SECTION010114000000000000000 with smaller strength of the initial discontinuity. """ -function initial_condition_medium_sedov_blast_wave(x, t, equations::CompressibleEulerEquations3D) - # Set up polar coordinates - inicenter = SVector(0.0, 0.0, 0.0) - x_norm = x[1] - inicenter[1] - y_norm = x[2] - inicenter[2] - z_norm = x[3] - inicenter[3] - r = sqrt(x_norm^2 + y_norm^2 + z_norm^2) - - # Setup based on https://flash.rochester.edu/site/flashcode/user_support/flash_ug_devel/node187.html#SECTION010114000000000000000 - r0 = 0.21875 # = 3.5 * smallest dx (for domain length=4 and max-ref=6) - E = 1.0 - p0_inner = 3 * (equations.gamma - 1) * E / (4 * pi * r0^2) - p0_outer = 1.0e-3 - - # Calculate primitive variables - rho = 1.0 - v1 = 0.0 - v2 = 0.0 - v3 = 0.0 - p = r > r0 ? p0_outer : p0_inner - - return prim2cons(SVector(rho, v1, v2, v3, p), equations) +function initial_condition_medium_sedov_blast_wave(x, t, + equations::CompressibleEulerEquations3D) + # Set up polar coordinates + inicenter = SVector(0.0, 0.0, 0.0) + x_norm = x[1] - inicenter[1] + y_norm = x[2] - inicenter[2] + z_norm = x[3] - inicenter[3] + r = sqrt(x_norm^2 + y_norm^2 + z_norm^2) + + # Setup based on https://flash.rochester.edu/site/flashcode/user_support/flash_ug_devel/node187.html#SECTION010114000000000000000 + r0 = 0.21875 # = 3.5 * smallest dx (for domain length=4 and max-ref=6) + E = 1.0 + p0_inner = 3 * (equations.gamma - 1) * E / (4 * pi * r0^2) + p0_outer = 1.0e-3 + + # Calculate primitive variables + rho = 1.0 + v1 = 0.0 + v2 = 0.0 + v3 = 0.0 + p = r > r0 ? p0_outer : p0_inner + + return prim2cons(SVector(rho, v1, v2, v3, p), equations) end initial_condition = initial_condition_medium_sedov_blast_wave @@ -45,30 +46,31 @@ volume_flux = flux_ranocha polydeg = 3 basis = LobattoLegendreBasis(polydeg) indicator_sc = IndicatorHennemannGassner(equations, basis, - alpha_max=1.0, - alpha_min=0.001, - alpha_smooth=true, - variable=density_pressure) + alpha_max = 1.0, + alpha_min = 0.001, + alpha_smooth = true, + variable = density_pressure) volume_integral = VolumeIntegralShockCapturingHG(indicator_sc; - volume_flux_dg=volume_flux, - volume_flux_fv=surface_flux) + volume_flux_dg = volume_flux, + volume_flux_fv = surface_flux) -solver = DGSEM(polydeg=polydeg, surface_flux=surface_flux, volume_integral=volume_integral) +solver = DGSEM(polydeg = polydeg, surface_flux = surface_flux, + volume_integral = volume_integral) # Mapping as described in https://arxiv.org/abs/2012.12040 function mapping(xi, eta, zeta) - y = eta + 0.125 * (cos(1.5 * pi * xi) * cos(0.5 * pi * eta) * cos(0.5 * pi * zeta)) + y = eta + 0.125 * (cos(1.5 * pi * xi) * cos(0.5 * pi * eta) * cos(0.5 * pi * zeta)) - x = xi + 0.125 * (cos(0.5 * pi * xi) * cos(2 * pi * y) * cos(0.5 * pi * zeta)) + x = xi + 0.125 * (cos(0.5 * pi * xi) * cos(2 * pi * y) * cos(0.5 * pi * zeta)) - z = zeta + 0.125 * (cos(0.5 * pi * x) * cos(pi * y) * cos(0.5 * pi * zeta)) + z = zeta + 0.125 * (cos(0.5 * pi * x) * cos(pi * y) * cos(0.5 * pi * zeta)) - return SVector(x, y, z) + return SVector(x, y, z) end cells_per_dimension = (4, 4, 4) -mesh = StructuredMesh(cells_per_dimension, mapping, periodicity=true) +mesh = StructuredMesh(cells_per_dimension, mapping, periodicity = true) # create the semi discretization object semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver) @@ -82,15 +84,15 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=100, - save_initial_solution=true, - save_final_solution=true) +save_solution = SaveSolutionCallback(interval = 100, + save_initial_solution = true, + save_final_solution = true) -stepsize_callback = StepsizeCallback(cfl=0.5) +stepsize_callback = StepsizeCallback(cfl = 0.5) callbacks = CallbackSet(summary_callback, analysis_callback, @@ -101,7 +103,7 @@ callbacks = CallbackSet(summary_callback, ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/structured_3d_dgsem/elixir_euler_source_terms.jl b/examples/structured_3d_dgsem/elixir_euler_source_terms.jl index d8c6ea4bb83..ebf1336c12c 100644 --- a/examples/structured_3d_dgsem/elixir_euler_source_terms.jl +++ b/examples/structured_3d_dgsem/elixir_euler_source_terms.jl @@ -11,8 +11,8 @@ equations = CompressibleEulerEquations3D(1.4) initial_condition = initial_condition_convergence_test -solver = DGSEM(polydeg=3, surface_flux=flux_lax_friedrichs, - volume_integral=VolumeIntegralWeakForm()) +solver = DGSEM(polydeg = 3, surface_flux = flux_lax_friedrichs, + volume_integral = VolumeIntegralWeakForm()) # coordinates_min = (0.0, 0.0, 0.0) # coordinates_max = (2.0, 2.0, 2.0) @@ -28,8 +28,7 @@ cells_per_dimension = (4, 4, 4) mesh = StructuredMesh(cells_per_dimension, (f1, f2, f3, f4, f5, f6)) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver, - source_terms=source_terms_convergence_test) - + source_terms = source_terms_convergence_test) ############################################################################### # ODE solvers, callbacks etc. @@ -40,27 +39,26 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=100, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 100, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) -stepsize_callback = StepsizeCallback(cfl=0.6) +stepsize_callback = StepsizeCallback(cfl = 0.6) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, save_solution, stepsize_callback) - ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/structured_3d_dgsem/elixir_euler_source_terms_nonperiodic_curved.jl b/examples/structured_3d_dgsem/elixir_euler_source_terms_nonperiodic_curved.jl index 8ddfd426553..eb358fa5da1 100644 --- a/examples/structured_3d_dgsem/elixir_euler_source_terms_nonperiodic_curved.jl +++ b/examples/structured_3d_dgsem/elixir_euler_source_terms_nonperiodic_curved.jl @@ -12,46 +12,48 @@ initial_condition = initial_condition_convergence_test # you can either use a single function to impose the BCs weakly in all # 2*ndims == 4 directions or you can pass a tuple containing BCs for each direction boundary_condition = BoundaryConditionDirichlet(initial_condition) -boundary_conditions = (x_neg=boundary_condition, - x_pos=boundary_condition, - y_neg=boundary_condition, - y_pos=boundary_condition, - z_neg=boundary_condition, - z_pos=boundary_condition,) +boundary_conditions = (x_neg = boundary_condition, + x_pos = boundary_condition, + y_neg = boundary_condition, + y_pos = boundary_condition, + z_neg = boundary_condition, + z_pos = boundary_condition) -solver = DGSEM(polydeg=3, surface_flux=flux_lax_friedrichs, - volume_integral=VolumeIntegralWeakForm()) +solver = DGSEM(polydeg = 3, surface_flux = flux_lax_friedrichs, + volume_integral = VolumeIntegralWeakForm()) # Mapping as described in https://arxiv.org/abs/2012.12040 but with less warping. function mapping(xi, eta, zeta) - # Don't transform input variables between -1 and 1 onto [0,3] to obtain curved boundaries - # xi = 1.5 * xi_ + 1.5 - # eta = 1.5 * eta_ + 1.5 - # zeta = 1.5 * zeta_ + 1.5 - - y = eta + 1/6 * (cos(1.5 * pi * (2 * xi - 3)/3) * - cos(0.5 * pi * (2 * eta - 3)/3) * - cos(0.5 * pi * (2 * zeta - 3)/3)) - - x = xi + 1/6 * (cos(0.5 * pi * (2 * xi - 3)/3) * - cos(2 * pi * (2 * y - 3)/3) * - cos(0.5 * pi * (2 * zeta - 3)/3)) - - z = zeta + 1/6 * (cos(0.5 * pi * (2 * x - 3)/3) * - cos(pi * (2 * y - 3)/3) * - cos(0.5 * pi * (2 * zeta - 3)/3)) - - # Transform the weird deformed cube to be approximately the cube [0,2]^3 - return SVector(x + 1, y + 1, z + 1) + # Don't transform input variables between -1 and 1 onto [0,3] to obtain curved boundaries + # xi = 1.5 * xi_ + 1.5 + # eta = 1.5 * eta_ + 1.5 + # zeta = 1.5 * zeta_ + 1.5 + + y = eta + + 1 / 6 * (cos(1.5 * pi * (2 * xi - 3) / 3) * + cos(0.5 * pi * (2 * eta - 3) / 3) * + cos(0.5 * pi * (2 * zeta - 3) / 3)) + + x = xi + + 1 / 6 * (cos(0.5 * pi * (2 * xi - 3) / 3) * + cos(2 * pi * (2 * y - 3) / 3) * + cos(0.5 * pi * (2 * zeta - 3) / 3)) + + z = zeta + + 1 / 6 * (cos(0.5 * pi * (2 * x - 3) / 3) * + cos(pi * (2 * y - 3) / 3) * + cos(0.5 * pi * (2 * zeta - 3) / 3)) + + # Transform the weird deformed cube to be approximately the cube [0,2]^3 + return SVector(x + 1, y + 1, z + 1) end cells_per_dimension = (4, 4, 4) -mesh = StructuredMesh(cells_per_dimension, mapping, periodicity=false) +mesh = StructuredMesh(cells_per_dimension, mapping, periodicity = false) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver, - source_terms=source_terms_convergence_test, - boundary_conditions=boundary_conditions) - + source_terms = source_terms_convergence_test, + boundary_conditions = boundary_conditions) ############################################################################### # ODE solvers, callbacks etc. @@ -62,27 +64,26 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=100, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 100, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) -stepsize_callback = StepsizeCallback(cfl=0.6) +stepsize_callback = StepsizeCallback(cfl = 0.6) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, save_solution, stepsize_callback) - ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/structured_3d_dgsem/elixir_mhd_alfven_wave.jl b/examples/structured_3d_dgsem/elixir_mhd_alfven_wave.jl index f4da8ee9470..6eb35078ef4 100644 --- a/examples/structured_3d_dgsem/elixir_mhd_alfven_wave.jl +++ b/examples/structured_3d_dgsem/elixir_mhd_alfven_wave.jl @@ -5,13 +5,13 @@ using Trixi ############################################################################### # semidiscretization of the compressible ideal GLM-MHD equations -equations = IdealGlmMhdEquations3D(5/3) +equations = IdealGlmMhdEquations3D(5 / 3) initial_condition = initial_condition_convergence_test volume_flux = (flux_central, flux_nonconservative_powell) -solver = DGSEM(polydeg=5, surface_flux=(flux_hll, flux_nonconservative_powell), - volume_integral=VolumeIntegralFluxDifferencing(volume_flux)) +solver = DGSEM(polydeg = 5, surface_flux = (flux_hll, flux_nonconservative_powell), + volume_integral = VolumeIntegralFluxDifferencing(volume_flux)) # Create the mesh # Note, we use the domain [-1, 1]^3 for the Alfvén wave convergence test case so the @@ -19,13 +19,13 @@ solver = DGSEM(polydeg=5, surface_flux=(flux_hll, flux_nonconservative_powell), # Mapping as described in https://arxiv.org/abs/2012.12040 function mapping(xi, eta, zeta) - y = eta + 0.125 * (cos(1.5 * pi * xi) * cos(0.5 * pi * eta) * cos(0.5 * pi * zeta)) + y = eta + 0.125 * (cos(1.5 * pi * xi) * cos(0.5 * pi * eta) * cos(0.5 * pi * zeta)) - x = xi + 0.125 * (cos(0.5 * pi * xi) * cos(2 * pi * y) * cos(0.5 * pi * zeta)) + x = xi + 0.125 * (cos(0.5 * pi * xi) * cos(2 * pi * y) * cos(0.5 * pi * zeta)) - z = zeta + 0.125 * (cos(0.5 * pi * x) * cos(pi * y) * cos(0.5 * pi * zeta)) + z = zeta + 0.125 * (cos(0.5 * pi * x) * cos(pi * y) * cos(0.5 * pi * zeta)) - return SVector(x, y, z) + return SVector(x, y, z) end cells_per_dimension = (4, 4, 4) @@ -43,18 +43,18 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=100, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 100, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) cfl = 1.2 -stepsize_callback = StepsizeCallback(cfl=cfl) +stepsize_callback = StepsizeCallback(cfl = cfl) -glm_speed_callback = GlmSpeedCallback(glm_scale=0.5, cfl=cfl) +glm_speed_callback = GlmSpeedCallback(glm_scale = 0.5, cfl = cfl) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, @@ -62,11 +62,10 @@ callbacks = CallbackSet(summary_callback, stepsize_callback, glm_speed_callback) - ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/structured_3d_dgsem/elixir_mhd_ec.jl b/examples/structured_3d_dgsem/elixir_mhd_ec.jl index a8c2288e811..5b3cd6f3718 100644 --- a/examples/structured_3d_dgsem/elixir_mhd_ec.jl +++ b/examples/structured_3d_dgsem/elixir_mhd_ec.jl @@ -10,31 +10,35 @@ equations = IdealGlmMhdEquations3D(1.4) initial_condition = initial_condition_weak_blast_wave volume_flux = (flux_hindenlang_gassner, flux_nonconservative_powell) -solver = DGSEM(polydeg=3, surface_flux=(flux_hindenlang_gassner, flux_nonconservative_powell), - volume_integral=VolumeIntegralFluxDifferencing(volume_flux)) +solver = DGSEM(polydeg = 3, + surface_flux = (flux_hindenlang_gassner, flux_nonconservative_powell), + volume_integral = VolumeIntegralFluxDifferencing(volume_flux)) # Create a heavily warped curved mesh # Mapping as described in https://arxiv.org/abs/2012.12040 function mapping(xi_, eta_, zeta_) - # Transform input variables between -1 and 1 onto [0,3] - xi = 1.5 * xi_ + 1.5 - eta = 1.5 * eta_ + 1.5 - zeta = 1.5 * zeta_ + 1.5 - - y = eta + 3/8 * (cos(1.5 * pi * (2 * xi - 3)/3) * - cos(0.5 * pi * (2 * eta - 3)/3) * - cos(0.5 * pi * (2 * zeta - 3)/3)) - - x = xi + 3/8 * (cos(0.5 * pi * (2 * xi - 3)/3) * - cos(2 * pi * (2 * y - 3)/3) * - cos(0.5 * pi * (2 * zeta - 3)/3)) - - z = zeta + 3/8 * (cos(0.5 * pi * (2 * x - 3)/3) * - cos(pi * (2 * y - 3)/3) * - cos(0.5 * pi * (2 * zeta - 3)/3)) - - return SVector(x, y, z) + # Transform input variables between -1 and 1 onto [0,3] + xi = 1.5 * xi_ + 1.5 + eta = 1.5 * eta_ + 1.5 + zeta = 1.5 * zeta_ + 1.5 + + y = eta + + 3 / 8 * (cos(1.5 * pi * (2 * xi - 3) / 3) * + cos(0.5 * pi * (2 * eta - 3) / 3) * + cos(0.5 * pi * (2 * zeta - 3) / 3)) + + x = xi + + 3 / 8 * (cos(0.5 * pi * (2 * xi - 3) / 3) * + cos(2 * pi * (2 * y - 3) / 3) * + cos(0.5 * pi * (2 * zeta - 3) / 3)) + + z = zeta + + 3 / 8 * (cos(0.5 * pi * (2 * x - 3) / 3) * + cos(pi * (2 * y - 3) / 3) * + cos(0.5 * pi * (2 * zeta - 3) / 3)) + + return SVector(x, y, z) end cells_per_dimension = (4, 4, 4) @@ -52,19 +56,19 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=100, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 100, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) cfl = 1.4 -stepsize_callback = StepsizeCallback(cfl=cfl) +stepsize_callback = StepsizeCallback(cfl = cfl) -glm_speed_callback = GlmSpeedCallback(glm_scale=0.5, cfl=cfl) +glm_speed_callback = GlmSpeedCallback(glm_scale = 0.5, cfl = cfl) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, @@ -72,11 +76,10 @@ callbacks = CallbackSet(summary_callback, stepsize_callback, glm_speed_callback) - ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/structured_3d_dgsem/elixir_mhd_ec_shockcapturing.jl b/examples/structured_3d_dgsem/elixir_mhd_ec_shockcapturing.jl index d669c2350a5..084e2ee962a 100644 --- a/examples/structured_3d_dgsem/elixir_mhd_ec_shockcapturing.jl +++ b/examples/structured_3d_dgsem/elixir_mhd_ec_shockcapturing.jl @@ -10,42 +10,46 @@ equations = IdealGlmMhdEquations3D(1.4) initial_condition = initial_condition_weak_blast_wave surface_flux = (flux_hindenlang_gassner, flux_nonconservative_powell) -volume_flux = (flux_hindenlang_gassner, flux_nonconservative_powell) +volume_flux = (flux_hindenlang_gassner, flux_nonconservative_powell) polydeg = 4 basis = LobattoLegendreBasis(polydeg) indicator_sc = IndicatorHennemannGassner(equations, basis, - alpha_max=0.5, - alpha_min=0.001, - alpha_smooth=true, - variable=density_pressure) + alpha_max = 0.5, + alpha_min = 0.001, + alpha_smooth = true, + variable = density_pressure) volume_integral = VolumeIntegralShockCapturingHG(indicator_sc; - volume_flux_dg=volume_flux, - volume_flux_fv=surface_flux) + volume_flux_dg = volume_flux, + volume_flux_fv = surface_flux) -solver = DGSEM(polydeg=polydeg, surface_flux=surface_flux, volume_integral=volume_integral) +solver = DGSEM(polydeg = polydeg, surface_flux = surface_flux, + volume_integral = volume_integral) # Create a heavily warped curved mesh # Mapping as described in https://arxiv.org/abs/2012.12040 function mapping(xi_, eta_, zeta_) - # Transform input variables between -1 and 1 onto [0,3] - xi = 1.5 * xi_ + 1.5 - eta = 1.5 * eta_ + 1.5 - zeta = 1.5 * zeta_ + 1.5 - - y = eta + 3/8 * (cos(1.5 * pi * (2 * xi - 3)/3) * - cos(0.5 * pi * (2 * eta - 3)/3) * - cos(0.5 * pi * (2 * zeta - 3)/3)) - - x = xi + 3/8 * (cos(0.5 * pi * (2 * xi - 3)/3) * - cos(2 * pi * (2 * y - 3)/3) * - cos(0.5 * pi * (2 * zeta - 3)/3)) - - z = zeta + 3/8 * (cos(0.5 * pi * (2 * x - 3)/3) * - cos(pi * (2 * y - 3)/3) * - cos(0.5 * pi * (2 * zeta - 3)/3)) - - return SVector(x, y, z) + # Transform input variables between -1 and 1 onto [0,3] + xi = 1.5 * xi_ + 1.5 + eta = 1.5 * eta_ + 1.5 + zeta = 1.5 * zeta_ + 1.5 + + y = eta + + 3 / 8 * (cos(1.5 * pi * (2 * xi - 3) / 3) * + cos(0.5 * pi * (2 * eta - 3) / 3) * + cos(0.5 * pi * (2 * zeta - 3) / 3)) + + x = xi + + 3 / 8 * (cos(0.5 * pi * (2 * xi - 3) / 3) * + cos(2 * pi * (2 * y - 3) / 3) * + cos(0.5 * pi * (2 * zeta - 3) / 3)) + + z = zeta + + 3 / 8 * (cos(0.5 * pi * (2 * x - 3) / 3) * + cos(pi * (2 * y - 3) / 3) * + cos(0.5 * pi * (2 * zeta - 3) / 3)) + + return SVector(x, y, z) end cells_per_dimension = (8, 8, 8) @@ -63,25 +67,24 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) cfl = 1.4 -stepsize_callback = StepsizeCallback(cfl=cfl) +stepsize_callback = StepsizeCallback(cfl = cfl) -glm_speed_callback = GlmSpeedCallback(glm_scale=0.5, cfl=cfl) +glm_speed_callback = GlmSpeedCallback(glm_scale = 0.5, cfl = cfl) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, stepsize_callback, glm_speed_callback) - ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/t8code_2d_dgsem/elixir_eulergravity_convergence.jl b/examples/t8code_2d_dgsem/elixir_eulergravity_convergence.jl index 32649eacff4..6d6bb27e0c3 100644 --- a/examples/t8code_2d_dgsem/elixir_eulergravity_convergence.jl +++ b/examples/t8code_2d_dgsem/elixir_eulergravity_convergence.jl @@ -22,9 +22,9 @@ mesh = T8codeMesh(trees_per_dimension, polydeg = 1, mapping = mapping, initial_refinement_level = 2) -semi_euler = SemidiscretizationHyperbolic(mesh, equations_euler, initial_condition, solver_euler, - source_terms=source_terms_eoc_test_coupled_euler_gravity) - +semi_euler = SemidiscretizationHyperbolic(mesh, equations_euler, initial_condition, + solver_euler, + source_terms = source_terms_eoc_test_coupled_euler_gravity) ############################################################################### # semidiscretization of the hyperbolic diffusion equations @@ -32,24 +32,23 @@ equations_gravity = HyperbolicDiffusionEquations2D() solver_gravity = DGSEM(polydeg, flux_lax_friedrichs) -semi_gravity = SemidiscretizationHyperbolic(mesh, equations_gravity, initial_condition, solver_gravity, - source_terms=source_terms_harmonic) - +semi_gravity = SemidiscretizationHyperbolic(mesh, equations_gravity, initial_condition, + solver_gravity, + source_terms = source_terms_harmonic) ############################################################################### # combining both semidiscretizations for Euler + self-gravity -parameters = ParametersEulerGravity(background_density=2.0, # aka rho0 +parameters = ParametersEulerGravity(background_density = 2.0, # aka rho0 # rho0 is (ab)used to add a "+8π" term to the source terms # for the manufactured solution - gravitational_constant=1.0, # aka G - cfl=1.1, - resid_tol=1.0e-10, - n_iterations_max=1000, - timestep_gravity=timestep_gravity_erk52_3Sstar!) + gravitational_constant = 1.0, # aka G + cfl = 1.1, + resid_tol = 1.0e-10, + n_iterations_max = 1000, + timestep_gravity = timestep_gravity_erk52_3Sstar!) semi = SemidiscretizationEulerGravity(semi_euler, semi_gravity, parameters) - ############################################################################### # ODE solvers, callbacks etc. tspan = (0.0, 0.5) @@ -57,21 +56,21 @@ ode = semidiscretize(semi, tspan); summary_callback = SummaryCallback() -stepsize_callback = StepsizeCallback(cfl=0.8) +stepsize_callback = StepsizeCallback(cfl = 0.8) analysis_interval = 100 -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -analysis_callback = AnalysisCallback(semi_euler, interval=analysis_interval, - save_analysis=true) +analysis_callback = AnalysisCallback(semi_euler, interval = analysis_interval, + save_analysis = true) callbacks = CallbackSet(summary_callback, stepsize_callback, analysis_callback, alive_callback) ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary println("Number of gravity subcycles: ", semi.gravity_counter.ncalls_since_readout) diff --git a/examples/t8code_2d_dgsem/elixir_mhd_alfven_wave.jl b/examples/t8code_2d_dgsem/elixir_mhd_alfven_wave.jl index 463f916fa2e..8040f79cafd 100644 --- a/examples/t8code_2d_dgsem/elixir_mhd_alfven_wave.jl +++ b/examples/t8code_2d_dgsem/elixir_mhd_alfven_wave.jl @@ -4,26 +4,26 @@ using Trixi ############################################################################### # Semidiscretization of the compressible ideal GLM-MHD equations. -gamma = 5/3 +gamma = 5 / 3 equations = IdealGlmMhdEquations2D(gamma) initial_condition = initial_condition_convergence_test # Get the DG approximation space volume_flux = (flux_central, flux_nonconservative_powell) -solver = DGSEM(polydeg=4, surface_flux=(flux_hll, flux_nonconservative_powell), - volume_integral=VolumeIntegralFluxDifferencing(volume_flux)) +solver = DGSEM(polydeg = 4, surface_flux = (flux_hll, flux_nonconservative_powell), + volume_integral = VolumeIntegralFluxDifferencing(volume_flux)) -coordinates_min = (0.0 , 0.0 ) +coordinates_min = (0.0, 0.0) coordinates_max = (sqrt(2.0), sqrt(2.0)) mapping = Trixi.coordinates2mapping(coordinates_min, coordinates_max) trees_per_dimension = (8, 8) -mesh = T8codeMesh(trees_per_dimension, polydeg=3, - mapping=mapping, - initial_refinement_level=0, periodicity=true) +mesh = T8codeMesh(trees_per_dimension, polydeg = 3, + mapping = mapping, + initial_refinement_level = 0, periodicity = true) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver) @@ -36,14 +36,14 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) cfl = 0.9 -stepsize_callback = StepsizeCallback(cfl=cfl) +stepsize_callback = StepsizeCallback(cfl = cfl) -glm_speed_callback = GlmSpeedCallback(glm_scale=0.5, cfl=cfl) +glm_speed_callback = GlmSpeedCallback(glm_scale = 0.5, cfl = cfl) callbacks = CallbackSet(summary_callback, analysis_callback, @@ -54,7 +54,7 @@ callbacks = CallbackSet(summary_callback, ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/t8code_2d_dgsem/elixir_shallowwater_source_terms.jl b/examples/t8code_2d_dgsem/elixir_shallowwater_source_terms.jl index c19f440ebc7..b2d5097036f 100644 --- a/examples/t8code_2d_dgsem/elixir_shallowwater_source_terms.jl +++ b/examples/t8code_2d_dgsem/elixir_shallowwater_source_terms.jl @@ -4,17 +4,17 @@ using Trixi ############################################################################### # Semidiscretization of the shallow water equations. -equations = ShallowWaterEquations2D(gravity_constant=9.81) +equations = ShallowWaterEquations2D(gravity_constant = 9.81) initial_condition = initial_condition_convergence_test # MMS EOC test - ############################################################################### # Get the DG approximation space volume_flux = (flux_wintermeyer_etal, flux_nonconservative_wintermeyer_etal) -solver = DGSEM(polydeg=3, surface_flux=(flux_lax_friedrichs, flux_nonconservative_fjordholm_etal), - volume_integral=VolumeIntegralFluxDifferencing(volume_flux)) +solver = DGSEM(polydeg = 3, + surface_flux = (flux_lax_friedrichs, flux_nonconservative_fjordholm_etal), + volume_integral = VolumeIntegralFluxDifferencing(volume_flux)) ############################################################################### # Get the P4estMesh and setup a periodic mesh @@ -26,14 +26,13 @@ mapping = Trixi.coordinates2mapping(coordinates_min, coordinates_max) trees_per_dimension = (8, 8) -mesh = T8codeMesh(trees_per_dimension, polydeg=3, - mapping=mapping, - initial_refinement_level=1) +mesh = T8codeMesh(trees_per_dimension, polydeg = 3, + mapping = mapping, + initial_refinement_level = 1) # A semidiscretization collects data structures and functions for the spatial discretization semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver, - source_terms=source_terms_convergence_test) - + source_terms = source_terms_convergence_test) ############################################################################### # ODE solvers, callbacks etc. @@ -45,9 +44,9 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 500 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback) @@ -55,6 +54,6 @@ callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback) # run the simulation # use a Runge-Kutta method with automatic (error based) time step size control -sol = solve(ode, RDPK3SpFSAL49(); abstol=1.0e-8, reltol=1.0e-8, - ode_default_options()..., callback=callbacks); +sol = solve(ode, RDPK3SpFSAL49(); abstol = 1.0e-8, reltol = 1.0e-8, + ode_default_options()..., callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/tree_1d_dgsem/elixir_advection_amr.jl b/examples/tree_1d_dgsem/elixir_advection_amr.jl index dc371233bc8..1071c98ab7e 100644 --- a/examples/tree_1d_dgsem/elixir_advection_amr.jl +++ b/examples/tree_1d_dgsem/elixir_advection_amr.jl @@ -10,18 +10,16 @@ equations = LinearScalarAdvectionEquation1D(advection_velocity) initial_condition = initial_condition_gauss -solver = DGSEM(polydeg=3, surface_flux=flux_lax_friedrichs) +solver = DGSEM(polydeg = 3, surface_flux = flux_lax_friedrichs) coordinates_min = (-5.0,) -coordinates_max = ( 5.0,) +coordinates_max = (5.0,) mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=4, - n_cells_max=30_000) - + initial_refinement_level = 4, + n_cells_max = 30_000) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver) - ############################################################################### # ODE solvers, callbacks etc. @@ -31,37 +29,36 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval, - extra_analysis_integrals=(entropy,)) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval, + extra_analysis_integrals = (entropy,)) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=100, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 100, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) -amr_controller = ControllerThreeLevel(semi, IndicatorMax(semi, variable=first), - base_level=4, - med_level=5, med_threshold=0.1, - max_level=6, max_threshold=0.6) +amr_controller = ControllerThreeLevel(semi, IndicatorMax(semi, variable = first), + base_level = 4, + med_level = 5, med_threshold = 0.1, + max_level = 6, max_threshold = 0.6) amr_callback = AMRCallback(semi, amr_controller, - interval=5, - adapt_initial_condition=true, - adapt_initial_condition_only_refine=true) + interval = 5, + adapt_initial_condition = true, + adapt_initial_condition_only_refine = true) -stepsize_callback = StepsizeCallback(cfl=1.6) +stepsize_callback = StepsizeCallback(cfl = 1.6) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, save_solution, amr_callback, stepsize_callback) - ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/tree_1d_dgsem/elixir_advection_amr_nonperiodic.jl b/examples/tree_1d_dgsem/elixir_advection_amr_nonperiodic.jl index 098deedb9d6..ff62e905429 100644 --- a/examples/tree_1d_dgsem/elixir_advection_amr_nonperiodic.jl +++ b/examples/tree_1d_dgsem/elixir_advection_amr_nonperiodic.jl @@ -11,21 +11,19 @@ equations = LinearScalarAdvectionEquation1D(advection_velocity) initial_condition = initial_condition_gauss boundary_conditions = BoundaryConditionDirichlet(initial_condition) -solver = DGSEM(polydeg=3, surface_flux=flux_lax_friedrichs) +solver = DGSEM(polydeg = 3, surface_flux = flux_lax_friedrichs) coordinates_min = (0.0,) coordinates_max = (5.0,) mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=4, - n_cells_max=10_000, - periodicity=false) - + initial_refinement_level = 4, + n_cells_max = 10_000, + periodicity = false) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver, - boundary_conditions=boundary_conditions) - + boundary_conditions = boundary_conditions) ############################################################################### # ODE solvers, callbacks etc. @@ -36,40 +34,39 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval, - extra_analysis_integrals=(entropy,)) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval, + extra_analysis_integrals = (entropy,)) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_restart = SaveRestartCallback(interval=100, - save_final_restart=true) +save_restart = SaveRestartCallback(interval = 100, + save_final_restart = true) -save_solution = SaveSolutionCallback(interval=100, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 100, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) -amr_controller = ControllerThreeLevel(semi, IndicatorMax(semi, variable=first), - base_level=4, - med_level=5, med_threshold=0.1, - max_level=6, max_threshold=0.6) +amr_controller = ControllerThreeLevel(semi, IndicatorMax(semi, variable = first), + base_level = 4, + med_level = 5, med_threshold = 0.1, + max_level = 6, max_threshold = 0.6) amr_callback = AMRCallback(semi, amr_controller, - interval=5, - adapt_initial_condition=true, - adapt_initial_condition_only_refine=true) + interval = 5, + adapt_initial_condition = true, + adapt_initial_condition_only_refine = true) -stepsize_callback = StepsizeCallback(cfl=1.6) +stepsize_callback = StepsizeCallback(cfl = 1.6) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, save_restart, save_solution, amr_callback, stepsize_callback); - ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=stepsize_callback(ode), # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = stepsize_callback(ode), # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/tree_1d_dgsem/elixir_advection_basic.jl b/examples/tree_1d_dgsem/elixir_advection_basic.jl index d61062c772e..cba522f6366 100644 --- a/examples/tree_1d_dgsem/elixir_advection_basic.jl +++ b/examples/tree_1d_dgsem/elixir_advection_basic.jl @@ -9,19 +9,19 @@ advection_velocity = 1.0 equations = LinearScalarAdvectionEquation1D(advection_velocity) # Create DG solver with polynomial degree = 3 and (local) Lax-Friedrichs/Rusanov flux as surface flux -solver = DGSEM(polydeg=3, surface_flux=flux_lax_friedrichs) +solver = DGSEM(polydeg = 3, surface_flux = flux_lax_friedrichs) coordinates_min = -1.0 # minimum coordinate -coordinates_max = 1.0 # maximum coordinate +coordinates_max = 1.0 # maximum coordinate # Create a uniformly refined mesh with periodic boundaries mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=4, - n_cells_max=30_000) # set maximum capacity of tree data structure + initial_refinement_level = 4, + n_cells_max = 30_000) # set maximum capacity of tree data structure # A semidiscretization collects data structures and functions for the spatial discretization -semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition_convergence_test, solver) - +semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition_convergence_test, + solver) ############################################################################### # ODE solvers, callbacks etc. @@ -34,26 +34,26 @@ ode = semidiscretize(semi, (0.0, 1.0)); summary_callback = SummaryCallback() # The AnalysisCallback allows to analyse the solution in regular intervals and prints the results -analysis_callback = AnalysisCallback(semi, interval=100) +analysis_callback = AnalysisCallback(semi, interval = 100) # The SaveSolutionCallback allows to save the solution to a file in regular intervals -save_solution = SaveSolutionCallback(interval=100, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 100, + solution_variables = cons2prim) # The StepsizeCallback handles the re-calculation of the maximum Δt after each time step -stepsize_callback = StepsizeCallback(cfl=1.6) +stepsize_callback = StepsizeCallback(cfl = 1.6) # Create a CallbackSet to collect all callbacks such that they can be passed to the ODE solver -callbacks = CallbackSet(summary_callback, analysis_callback, save_solution, stepsize_callback) - +callbacks = CallbackSet(summary_callback, analysis_callback, save_solution, + stepsize_callback) ############################################################################### # run the simulation # OrdinaryDiffEq's `solve` method evolves the solution in time and executes the passed callbacks -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); # Print the timer summary summary_callback() diff --git a/examples/tree_1d_dgsem/elixir_advection_diffusion.jl b/examples/tree_1d_dgsem/elixir_advection_diffusion.jl index 0472bd25a71..72b8b3f1933 100644 --- a/examples/tree_1d_dgsem/elixir_advection_diffusion.jl +++ b/examples/tree_1d_dgsem/elixir_advection_diffusion.jl @@ -11,49 +11,52 @@ diffusivity() = 0.1 equations_parabolic = LaplaceDiffusion1D(diffusivity(), equations) # Create DG solver with polynomial degree = 3 and (local) Lax-Friedrichs/Rusanov flux as surface flux -solver = DGSEM(polydeg=3, surface_flux=flux_lax_friedrichs) +solver = DGSEM(polydeg = 3, surface_flux = flux_lax_friedrichs) coordinates_min = -pi # minimum coordinate -coordinates_max = pi # maximum coordinate +coordinates_max = pi # maximum coordinate # Create a uniformly refined mesh with periodic boundaries mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=4, - n_cells_max=30_000, # set maximum capacity of tree data structure - periodicity=true) - -function x_trans_periodic(x, domain_length = SVector(2*pi), center = SVector(0.0)) - x_normalized = x .- center - x_shifted = x_normalized .% domain_length - x_offset = ((x_shifted .< -0.5*domain_length) - (x_shifted .> 0.5*domain_length)) .* domain_length - return center + x_shifted + x_offset + initial_refinement_level = 4, + n_cells_max = 30_000, # set maximum capacity of tree data structure + periodicity = true) + +function x_trans_periodic(x, domain_length = SVector(2 * pi), center = SVector(0.0)) + x_normalized = x .- center + x_shifted = x_normalized .% domain_length + x_offset = ((x_shifted .< -0.5 * domain_length) - (x_shifted .> 0.5 * domain_length)) .* + domain_length + return center + x_shifted + x_offset end # Define initial condition -function initial_condition_diffusive_convergence_test(x, t, equation::LinearScalarAdvectionEquation1D) - # Store translated coordinate for easy use of exact solution - x_trans = x_trans_periodic(x - equation.advection_velocity * t) - - nu = diffusivity() - c = 0.0 - A = 1.0 - L = 2 - f = 1/L - omega = 1.0 - scalar = c + A * sin(omega * sum(x_trans)) * exp(-nu * omega^2 * t) - return SVector(scalar) +function initial_condition_diffusive_convergence_test(x, t, + equation::LinearScalarAdvectionEquation1D) + # Store translated coordinate for easy use of exact solution + x_trans = x_trans_periodic(x - equation.advection_velocity * t) + + nu = diffusivity() + c = 0.0 + A = 1.0 + L = 2 + f = 1 / L + omega = 1.0 + scalar = c + A * sin(omega * sum(x_trans)) * exp(-nu * omega^2 * t) + return SVector(scalar) end initial_condition = initial_condition_diffusive_convergence_test - + # define periodic boundary conditions everywhere boundary_conditions = boundary_condition_periodic boundary_conditions_parabolic = boundary_condition_periodic # A semidiscretization collects data structures and functions for the spatial discretization -semi = SemidiscretizationHyperbolicParabolic(mesh, (equations, equations_parabolic), - initial_condition_diffusive_convergence_test, solver; - boundary_conditions=(boundary_conditions, boundary_conditions_parabolic)) - +semi = SemidiscretizationHyperbolicParabolic(mesh, (equations, equations_parabolic), + initial_condition_diffusive_convergence_test, + solver; + boundary_conditions = (boundary_conditions, + boundary_conditions_parabolic)) ############################################################################### # ODE solvers, callbacks etc. @@ -67,23 +70,22 @@ ode = semidiscretize(semi, tspan); summary_callback = SummaryCallback() # The AnalysisCallback allows to analyse the solution in regular intervals and prints the results -analysis_callback = AnalysisCallback(semi, interval=100) +analysis_callback = AnalysisCallback(semi, interval = 100) # The AliveCallback prints short status information in regular intervals -alive_callback = AliveCallback(analysis_interval=100) +alive_callback = AliveCallback(analysis_interval = 100) # Create a CallbackSet to collect all callbacks such that they can be passed to the ODE solver callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback) - ############################################################################### # run the simulation # OrdinaryDiffEq's `solve` method evolves the solution in time and executes the passed callbacks time_int_tol = 1.0e-10 time_abs_tol = 1.0e-10 -sol = solve(ode, KenCarp4(autodiff=false), abstol=time_abs_tol, reltol=time_int_tol, - save_everystep=false, callback=callbacks) +sol = solve(ode, KenCarp4(autodiff = false), abstol = time_abs_tol, reltol = time_int_tol, + save_everystep = false, callback = callbacks) # Print the timer summary summary_callback() diff --git a/examples/tree_1d_dgsem/elixir_advection_extended.jl b/examples/tree_1d_dgsem/elixir_advection_extended.jl index 5c87ac7ef5c..df185834701 100644 --- a/examples/tree_1d_dgsem/elixir_advection_extended.jl +++ b/examples/tree_1d_dgsem/elixir_advection_extended.jl @@ -18,21 +18,20 @@ initial_condition = initial_condition_convergence_test boundary_conditions = boundary_condition_periodic # Create DG solver with polynomial degree = 3 and (local) Lax-Friedrichs/Rusanov flux as surface flux -solver = DGSEM(polydeg=3, surface_flux=flux_lax_friedrichs) +solver = DGSEM(polydeg = 3, surface_flux = flux_lax_friedrichs) coordinates_min = -1.0 # minimum coordinate -coordinates_max = 1.0 # maximum coordinate +coordinates_max = 1.0 # maximum coordinate # Create a uniformly refined mesh with periodic boundaries mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=4, - n_cells_max=30_000, # set maximum capacity of tree data structure - periodicity=true) + initial_refinement_level = 4, + n_cells_max = 30_000, # set maximum capacity of tree data structure + periodicity = true) # A semidiscretization collects data structures and functions for the spatial discretization semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver, - boundary_conditions=boundary_conditions) - + boundary_conditions = boundary_conditions) ############################################################################### # ODE solvers, callbacks etc. @@ -47,24 +46,24 @@ summary_callback = SummaryCallback() # The AnalysisCallback allows to analyse the solution in regular intervals and prints the results analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval, - extra_analysis_integrals=(entropy, energy_total)) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval, + extra_analysis_integrals = (entropy, energy_total)) # The AliveCallback prints short status information in regular intervals -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) # The SaveRestartCallback allows to save a file from which a Trixi.jl simulation can be restarted -save_restart = SaveRestartCallback(interval=100, - save_final_restart=true) +save_restart = SaveRestartCallback(interval = 100, + save_final_restart = true) # The SaveSolutionCallback allows to save the solution to a file in regular intervals -save_solution = SaveSolutionCallback(interval=100, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 100, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) # The StepsizeCallback handles the re-calculation of the maximum Δt after each time step -stepsize_callback = StepsizeCallback(cfl=1.6) +stepsize_callback = StepsizeCallback(cfl = 1.6) # Create a CallbackSet to collect all callbacks such that they can be passed to the ODE solver callbacks = CallbackSet(summary_callback, @@ -72,14 +71,13 @@ callbacks = CallbackSet(summary_callback, save_restart, save_solution, stepsize_callback) - ############################################################################### # run the simulation # OrdinaryDiffEq's `solve` method evolves the solution in time and executes the passed callbacks -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); # Print the timer summary summary_callback() diff --git a/examples/tree_1d_dgsem/elixir_advection_finite_volume.jl b/examples/tree_1d_dgsem/elixir_advection_finite_volume.jl index 28518e7276a..62701f3ecf5 100644 --- a/examples/tree_1d_dgsem/elixir_advection_finite_volume.jl +++ b/examples/tree_1d_dgsem/elixir_advection_finite_volume.jl @@ -10,19 +10,19 @@ equations = LinearScalarAdvectionEquation1D(advection_velocity) # Create DG solver with polynomial degree = 0, i.e., a first order finite volume solver, # with (local) Lax-Friedrichs/Rusanov flux as surface flux -solver = DGSEM(polydeg=0, surface_flux=flux_lax_friedrichs) +solver = DGSEM(polydeg = 0, surface_flux = flux_lax_friedrichs) coordinates_min = -1.0 # minimum coordinate -coordinates_max = 1.0 # maximum coordinate +coordinates_max = 1.0 # maximum coordinate # Create a uniformly refined mesh with periodic boundaries mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=5, - n_cells_max=30_000) # set maximum capacity of tree data structure + initial_refinement_level = 5, + n_cells_max = 30_000) # set maximum capacity of tree data structure # A semidiscretization collects data structures and functions for the spatial discretization -semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition_convergence_test, solver) - +semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition_convergence_test, + solver) ############################################################################### # ODE solvers, callbacks etc. @@ -35,22 +35,21 @@ ode = semidiscretize(semi, (0.0, 1.0)); summary_callback = SummaryCallback() # The AnalysisCallback allows to analyse the solution in regular intervals and prints the results -analysis_callback = AnalysisCallback(semi, interval=100) +analysis_callback = AnalysisCallback(semi, interval = 100) # The StepsizeCallback handles the re-calculation of the maximum Δt after each time step -stepsize_callback = StepsizeCallback(cfl=0.9) +stepsize_callback = StepsizeCallback(cfl = 0.9) # Create a CallbackSet to collect all callbacks such that they can be passed to the ODE solver callbacks = CallbackSet(summary_callback, analysis_callback, stepsize_callback) - ############################################################################### # run the simulation # OrdinaryDiffEq's `solve` method evolves the solution in time and executes the passed callbacks sol = solve(ode, Euler(), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); # Print the timer summary summary_callback() diff --git a/examples/tree_1d_dgsem/elixir_burgers_basic.jl b/examples/tree_1d_dgsem/elixir_burgers_basic.jl index cebd9b11201..f57b8e730fe 100644 --- a/examples/tree_1d_dgsem/elixir_burgers_basic.jl +++ b/examples/tree_1d_dgsem/elixir_burgers_basic.jl @@ -9,18 +9,16 @@ equations = InviscidBurgersEquation1D() initial_condition = initial_condition_convergence_test -solver = DGSEM(polydeg=3, surface_flux=flux_lax_friedrichs) +solver = DGSEM(polydeg = 3, surface_flux = flux_lax_friedrichs) coordinates_min = 0.0 coordinates_max = 1.0 mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=4, - n_cells_max=10_000) - + initial_refinement_level = 4, + n_cells_max = 10_000) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver, - source_terms=source_terms_convergence_test) - + source_terms = source_terms_convergence_test) ############################################################################### # ODE solvers, callbacks etc. @@ -31,29 +29,28 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval, - extra_analysis_errors=(:l2_error_primitive, - :linf_error_primitive)) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval, + extra_analysis_errors = (:l2_error_primitive, + :linf_error_primitive)) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=100, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 100, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) -stepsize_callback = StepsizeCallback(cfl=0.8) +stepsize_callback = StepsizeCallback(cfl = 0.8) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, save_solution, stepsize_callback) - ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/tree_1d_dgsem/elixir_burgers_linear_stability.jl b/examples/tree_1d_dgsem/elixir_burgers_linear_stability.jl index 6a25f94ca05..ae2039edde6 100644 --- a/examples/tree_1d_dgsem/elixir_burgers_linear_stability.jl +++ b/examples/tree_1d_dgsem/elixir_burgers_linear_stability.jl @@ -8,23 +8,22 @@ using Trixi equations = InviscidBurgersEquation1D() function initial_condition_linear_stability(x, t, equation::InviscidBurgersEquation1D) - k = 1 - 2 + sinpi(k * (x[1] - 0.7)) |> SVector + k = 1 + 2 + sinpi(k * (x[1] - 0.7)) |> SVector end volume_flux = flux_ec -solver = DGSEM(polydeg=3, surface_flux=flux_ec, - volume_integral=VolumeIntegralFluxDifferencing(volume_flux)) +solver = DGSEM(polydeg = 3, surface_flux = flux_ec, + volume_integral = VolumeIntegralFluxDifferencing(volume_flux)) coordinates_min = -1.0 -coordinates_max = 1.0 +coordinates_max = 1.0 mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=4, - n_cells_max=10_000) - - -semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition_linear_stability, solver) + initial_refinement_level = 4, + n_cells_max = 10_000) +semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition_linear_stability, + solver) ############################################################################### # ODE solvers, callbacks etc. @@ -35,23 +34,22 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval, - extra_analysis_errors=(:l2_error_primitive, - :linf_error_primitive)) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval, + extra_analysis_errors = (:l2_error_primitive, + :linf_error_primitive)) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -stepsize_callback = StepsizeCallback(cfl=0.8) +stepsize_callback = StepsizeCallback(cfl = 0.8) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, stepsize_callback) - ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/tree_1d_dgsem/elixir_burgers_rarefaction.jl b/examples/tree_1d_dgsem/elixir_burgers_rarefaction.jl index 28ab7b7c768..d32b9d6f1f4 100644 --- a/examples/tree_1d_dgsem/elixir_burgers_rarefaction.jl +++ b/examples/tree_1d_dgsem/elixir_burgers_rarefaction.jl @@ -10,18 +10,18 @@ equations = InviscidBurgersEquation1D() basis = LobattoLegendreBasis(3) # Use shock capturing techniques to suppress oscillations at discontinuities indicator_sc = IndicatorHennemannGassner(equations, basis, - alpha_max=1.0, - alpha_min=0.001, - alpha_smooth=true, - variable=first) + alpha_max = 1.0, + alpha_min = 0.001, + alpha_smooth = true, + variable = first) -volume_flux = flux_ec +volume_flux = flux_ec surface_flux = flux_lax_friedrichs volume_integral = VolumeIntegralShockCapturingHG(indicator_sc; - volume_flux_dg=volume_flux, - volume_flux_fv=surface_flux) - + volume_flux_dg = volume_flux, + volume_flux_fv = surface_flux) + solver = DGSEM(basis, surface_flux, volume_integral) coordinate_min = 0.0 @@ -29,42 +29,41 @@ coordinate_max = 1.0 # Make sure to turn periodicity explicitly off as special boundary conditions are specified mesh = TreeMesh(coordinate_min, coordinate_max, - initial_refinement_level=6, - n_cells_max=10_000, - periodicity=false) + initial_refinement_level = 6, + n_cells_max = 10_000, + periodicity = false) # Discontinuous initial condition (Riemann Problem) leading to a rarefaction fan. function initial_condition_rarefaction(x, t, equation::InviscidBurgersEquation1D) - scalar = x[1] < 0.5 ? 0.5 : 1.5 + scalar = x[1] < 0.5 ? 0.5 : 1.5 - return SVector(scalar) -end + return SVector(scalar) +end ############################################################################### # Specify non-periodic boundary conditions function inflow(x, t, equations::InviscidBurgersEquation1D) - return initial_condition_rarefaction(coordinate_min, t, equations) + return initial_condition_rarefaction(coordinate_min, t, equations) end boundary_condition_inflow = BoundaryConditionDirichlet(inflow) function boundary_condition_outflow(u_inner, orientation, normal_direction, x, t, - surface_flux_function, equations::InviscidBurgersEquation1D) - # Calculate the boundary flux entirely from the internal solution state - flux = Trixi.flux(u_inner, normal_direction, equations) + surface_flux_function, + equations::InviscidBurgersEquation1D) + # Calculate the boundary flux entirely from the internal solution state + flux = Trixi.flux(u_inner, normal_direction, equations) - return flux + return flux end +boundary_conditions = (x_neg = boundary_condition_inflow, + x_pos = boundary_condition_outflow) -boundary_conditions = (x_neg=boundary_condition_inflow, - x_pos=boundary_condition_outflow) - initial_condition = initial_condition_rarefaction semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver, - boundary_conditions=boundary_conditions) - + boundary_conditions = boundary_conditions) ############################################################################### # ODE solvers, callbacks etc. @@ -75,12 +74,11 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) -alive_callback = AliveCallback(analysis_interval=analysis_interval) - -stepsize_callback = StepsizeCallback(cfl=0.9) +alive_callback = AliveCallback(analysis_interval = analysis_interval) +stepsize_callback = StepsizeCallback(cfl = 0.9) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, @@ -89,9 +87,8 @@ callbacks = CallbackSet(summary_callback, ############################################################################### # run the simulation - -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=42, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 42, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/tree_1d_dgsem/elixir_burgers_shock.jl b/examples/tree_1d_dgsem/elixir_burgers_shock.jl index 00b5314e19f..1f0b0e7e042 100644 --- a/examples/tree_1d_dgsem/elixir_burgers_shock.jl +++ b/examples/tree_1d_dgsem/elixir_burgers_shock.jl @@ -10,17 +10,17 @@ equations = InviscidBurgersEquation1D() basis = LobattoLegendreBasis(3) # Use shock capturing techniques to suppress oscillations at discontinuities indicator_sc = IndicatorHennemannGassner(equations, basis, - alpha_max=1.0, - alpha_min=0.001, - alpha_smooth=true, - variable=first) + alpha_max = 1.0, + alpha_min = 0.001, + alpha_smooth = true, + variable = first) -volume_flux = flux_ec +volume_flux = flux_ec surface_flux = flux_lax_friedrichs volume_integral = VolumeIntegralShockCapturingHG(indicator_sc; - volume_flux_dg=surface_flux, - volume_flux_fv=surface_flux) + volume_flux_dg = surface_flux, + volume_flux_fv = surface_flux) solver = DGSEM(basis, surface_flux, volume_integral) @@ -29,42 +29,41 @@ coordinate_max = 1.0 # Make sure to turn periodicity explicitly off as special boundary conditions are specified mesh = TreeMesh(coordinate_min, coordinate_max, - initial_refinement_level=6, - n_cells_max=10_000, - periodicity=false) + initial_refinement_level = 6, + n_cells_max = 10_000, + periodicity = false) # Discontinuous initial condition (Riemann Problem) leading to a shock to test e.g. correct shock speed. function initial_condition_shock(x, t, equation::InviscidBurgersEquation1D) - scalar = x[1] < 0.5 ? 1.5 : 0.5 + scalar = x[1] < 0.5 ? 1.5 : 0.5 - return SVector(scalar) + return SVector(scalar) end ############################################################################### # Specify non-periodic boundary conditions function inflow(x, t, equations::InviscidBurgersEquation1D) - return initial_condition_shock(coordinate_min, t, equations) + return initial_condition_shock(coordinate_min, t, equations) end boundary_condition_inflow = BoundaryConditionDirichlet(inflow) function boundary_condition_outflow(u_inner, orientation, normal_direction, x, t, - surface_flux_function, equations::InviscidBurgersEquation1D) - # Calculate the boundary flux entirely from the internal solution state - flux = Trixi.flux(u_inner, normal_direction, equations) + surface_flux_function, + equations::InviscidBurgersEquation1D) + # Calculate the boundary flux entirely from the internal solution state + flux = Trixi.flux(u_inner, normal_direction, equations) - return flux + return flux end - -boundary_conditions = (x_neg=boundary_condition_inflow, - x_pos=boundary_condition_outflow) +boundary_conditions = (x_neg = boundary_condition_inflow, + x_pos = boundary_condition_outflow) initial_condition = initial_condition_shock semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver, - boundary_conditions=boundary_conditions) - + boundary_conditions = boundary_conditions) ############################################################################### # ODE solvers, callbacks etc. @@ -75,12 +74,11 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) -alive_callback = AliveCallback(analysis_interval=analysis_interval) - -stepsize_callback = StepsizeCallback(cfl=0.85) +alive_callback = AliveCallback(analysis_interval = analysis_interval) +stepsize_callback = StepsizeCallback(cfl = 0.85) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, @@ -89,9 +87,8 @@ callbacks = CallbackSet(summary_callback, ############################################################################### # run the simulation - -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=42, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 42, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/tree_1d_dgsem/elixir_euler_blast_wave.jl b/examples/tree_1d_dgsem/elixir_euler_blast_wave.jl index 2318063c2be..9cba4936d22 100644 --- a/examples/tree_1d_dgsem/elixir_euler_blast_wave.jl +++ b/examples/tree_1d_dgsem/elixir_euler_blast_wave.jl @@ -16,49 +16,47 @@ A medium blast wave taken from [arXiv: 2008.12044](https://arxiv.org/abs/2008.12044) """ function initial_condition_blast_wave(x, t, equations::CompressibleEulerEquations1D) - # Modified From Hennemann & Gassner JCP paper 2020 (Sec. 6.3) -> "medium blast wave" - # Set up polar coordinates - inicenter = SVector(0.0) - x_norm = x[1] - inicenter[1] - r = abs(x_norm) - # The following code is equivalent to - # phi = atan(0.0, x_norm) - # cos_phi = cos(phi) - # in 1D but faster - cos_phi = x_norm > 0 ? one(x_norm) : -one(x_norm) - - # Calculate primitive variables - rho = r > 0.5 ? 1.0 : 1.1691 - v1 = r > 0.5 ? 0.0 : 0.1882 * cos_phi - p = r > 0.5 ? 1.0E-3 : 1.245 - - return prim2cons(SVector(rho, v1, p), equations) + # Modified From Hennemann & Gassner JCP paper 2020 (Sec. 6.3) -> "medium blast wave" + # Set up polar coordinates + inicenter = SVector(0.0) + x_norm = x[1] - inicenter[1] + r = abs(x_norm) + # The following code is equivalent to + # phi = atan(0.0, x_norm) + # cos_phi = cos(phi) + # in 1D but faster + cos_phi = x_norm > 0 ? one(x_norm) : -one(x_norm) + + # Calculate primitive variables + rho = r > 0.5 ? 1.0 : 1.1691 + v1 = r > 0.5 ? 0.0 : 0.1882 * cos_phi + p = r > 0.5 ? 1.0E-3 : 1.245 + + return prim2cons(SVector(rho, v1, p), equations) end initial_condition = initial_condition_blast_wave surface_flux = flux_lax_friedrichs -volume_flux = flux_ranocha +volume_flux = flux_ranocha basis = LobattoLegendreBasis(3) indicator_sc = IndicatorHennemannGassner(equations, basis, - alpha_max=0.5, - alpha_min=0.001, - alpha_smooth=true, - variable=density_pressure) + alpha_max = 0.5, + alpha_min = 0.001, + alpha_smooth = true, + variable = density_pressure) volume_integral = VolumeIntegralShockCapturingHG(indicator_sc; - volume_flux_dg=volume_flux, - volume_flux_fv=surface_flux) + volume_flux_dg = volume_flux, + volume_flux_fv = surface_flux) solver = DGSEM(basis, surface_flux, volume_integral) coordinates_min = (-2.0,) -coordinates_max = ( 2.0,) +coordinates_max = (2.0,) mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=6, - n_cells_max=10_000) - + initial_refinement_level = 6, + n_cells_max = 10_000) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver) - ############################################################################### # ODE solvers, callbacks etc. @@ -69,27 +67,26 @@ summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=100, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 100, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) -stepsize_callback = StepsizeCallback(cfl=0.5) +stepsize_callback = StepsizeCallback(cfl = 0.5) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, save_solution, stepsize_callback) - ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/tree_1d_dgsem/elixir_euler_blast_wave_neuralnetwork_perssonperaire.jl b/examples/tree_1d_dgsem/elixir_euler_blast_wave_neuralnetwork_perssonperaire.jl index d35dec6bc73..05f392624fd 100644 --- a/examples/tree_1d_dgsem/elixir_euler_blast_wave_neuralnetwork_perssonperaire.jl +++ b/examples/tree_1d_dgsem/elixir_euler_blast_wave_neuralnetwork_perssonperaire.jl @@ -2,7 +2,8 @@ using Downloads: download using Flux using BSON: load network = joinpath(@__DIR__, "modelnnpp-0.97-0.0001.bson") -download("https://github.com/trixi-framework/Trixi_IndicatorNeuralNetwork_networks/raw/main/networks/modelnnpp-0.97-0.0001.bson", network) +download("https://github.com/trixi-framework/Trixi_IndicatorNeuralNetwork_networks/raw/main/networks/modelnnpp-0.97-0.0001.bson", + network) model1d = load(network, @__MODULE__)[:model1d] using OrdinaryDiffEq @@ -14,7 +15,6 @@ using Trixi # University of Cologne, advisors: Gregor Gassner, Michael Schlottke-Lakemper # This motivates the particular choice of fluxes, mesh resolution etc. - ############################################################################### # semidiscretization of the compressible Euler equations @@ -29,53 +29,51 @@ A medium blast wave taken from [arXiv: 2008.12044](https://arxiv.org/abs/2008.12044) """ function initial_condition_blast_wave(x, t, equations::CompressibleEulerEquations1D) - # Modified From Hennemann & Gassner JCP paper 2020 (Sec. 6.3) -> "medium blast wave" - # Set up polar coordinates - inicenter = SVector(0.0) - x_norm = x[1] - inicenter[1] - r = abs(x_norm) - # The following code is equivalent to - # phi = atan(0.0, x_norm) - # cos_phi = cos(phi) - # in 1D but faster - cos_phi = x_norm > 0 ? one(x_norm) : -one(x_norm) - - # Calculate primitive variables - rho = r > 0.5 ? 1.0 : 1.1691 - v1 = r > 0.5 ? 0.0 : 0.1882 * cos_phi - p = r > 0.5 ? 1.0E-3 : 1.245 - - return prim2cons(SVector(rho, v1, p), equations) + # Modified From Hennemann & Gassner JCP paper 2020 (Sec. 6.3) -> "medium blast wave" + # Set up polar coordinates + inicenter = SVector(0.0) + x_norm = x[1] - inicenter[1] + r = abs(x_norm) + # The following code is equivalent to + # phi = atan(0.0, x_norm) + # cos_phi = cos(phi) + # in 1D but faster + cos_phi = x_norm > 0 ? one(x_norm) : -one(x_norm) + + # Calculate primitive variables + rho = r > 0.5 ? 1.0 : 1.1691 + v1 = r > 0.5 ? 0.0 : 0.1882 * cos_phi + p = r > 0.5 ? 1.0E-3 : 1.245 + + return prim2cons(SVector(rho, v1, p), equations) end initial_condition = initial_condition_blast_wave surface_flux = flux_lax_friedrichs -volume_flux = flux_chandrashekar +volume_flux = flux_chandrashekar basis = LobattoLegendreBasis(3) indicator_sc = IndicatorNeuralNetwork(equations, basis, - indicator_type=NeuralNetworkPerssonPeraire(), - alpha_max=0.5, - alpha_min=0.001, - alpha_smooth=true, - alpha_continuous=false, - alpha_amr=false, - variable=density_pressure, - network=model1d) + indicator_type = NeuralNetworkPerssonPeraire(), + alpha_max = 0.5, + alpha_min = 0.001, + alpha_smooth = true, + alpha_continuous = false, + alpha_amr = false, + variable = density_pressure, + network = model1d) volume_integral = VolumeIntegralShockCapturingHG(indicator_sc; - volume_flux_dg=volume_flux, - volume_flux_fv=surface_flux) + volume_flux_dg = volume_flux, + volume_flux_fv = surface_flux) solver = DGSEM(basis, surface_flux, volume_integral) coordinates_min = (-2.0,) -coordinates_max = ( 2.0,) +coordinates_max = (2.0,) mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=6, - n_cells_max=10_000) - + initial_refinement_level = 6, + n_cells_max = 10_000) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver) - ############################################################################### # ODE solvers, callbacks etc. @@ -86,27 +84,26 @@ summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=100, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 100, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) -stepsize_callback = StepsizeCallback(cfl=0.5) +stepsize_callback = StepsizeCallback(cfl = 0.5) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, save_solution, stepsize_callback) - ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/tree_1d_dgsem/elixir_euler_blast_wave_neuralnetwork_rayhesthaven.jl b/examples/tree_1d_dgsem/elixir_euler_blast_wave_neuralnetwork_rayhesthaven.jl index fb36f8540f8..de2f5134a49 100644 --- a/examples/tree_1d_dgsem/elixir_euler_blast_wave_neuralnetwork_rayhesthaven.jl +++ b/examples/tree_1d_dgsem/elixir_euler_blast_wave_neuralnetwork_rayhesthaven.jl @@ -2,7 +2,8 @@ using Downloads: download using Flux using BSON: load network = joinpath(@__DIR__, "modelnnrh-0.95-0.009.bson") -download("https://github.com/trixi-framework/Trixi_IndicatorNeuralNetwork_networks/raw/main/networks/modelnnrh-0.95-0.009.bson", network) +download("https://github.com/trixi-framework/Trixi_IndicatorNeuralNetwork_networks/raw/main/networks/modelnnrh-0.95-0.009.bson", + network) model1d = load(network, @__MODULE__)[:model1d] using OrdinaryDiffEq @@ -14,7 +15,6 @@ using Trixi # University of Cologne, advisors: Gregor Gassner, Michael Schlottke-Lakemper # This motivates the particular choice of fluxes, mesh resolution etc. - ############################################################################### # semidiscretization of the compressible Euler equations @@ -29,53 +29,51 @@ A medium blast wave taken from [arXiv: 2008.12044](https://arxiv.org/abs/2008.12044) """ function initial_condition_blast_wave(x, t, equations::CompressibleEulerEquations1D) - # Modified From Hennemann & Gassner JCP paper 2020 (Sec. 6.3) -> "medium blast wave" - # Set up polar coordinates - inicenter = SVector(0.0) - x_norm = x[1] - inicenter[1] - r = abs(x_norm) - # The following code is equivalent to - # phi = atan(0.0, x_norm) - # cos_phi = cos(phi) - # in 1D but faster - cos_phi = x_norm > 0 ? one(x_norm) : -one(x_norm) - - # Calculate primitive variables - rho = r > 0.5 ? 1.0 : 1.1691 - v1 = r > 0.5 ? 0.0 : 0.1882 * cos_phi - p = r > 0.5 ? 1.0E-3 : 1.245 - - return prim2cons(SVector(rho, v1, p), equations) + # Modified From Hennemann & Gassner JCP paper 2020 (Sec. 6.3) -> "medium blast wave" + # Set up polar coordinates + inicenter = SVector(0.0) + x_norm = x[1] - inicenter[1] + r = abs(x_norm) + # The following code is equivalent to + # phi = atan(0.0, x_norm) + # cos_phi = cos(phi) + # in 1D but faster + cos_phi = x_norm > 0 ? one(x_norm) : -one(x_norm) + + # Calculate primitive variables + rho = r > 0.5 ? 1.0 : 1.1691 + v1 = r > 0.5 ? 0.0 : 0.1882 * cos_phi + p = r > 0.5 ? 1.0E-3 : 1.245 + + return prim2cons(SVector(rho, v1, p), equations) end initial_condition = initial_condition_blast_wave surface_flux = flux_lax_friedrichs -volume_flux = flux_chandrashekar +volume_flux = flux_chandrashekar basis = LobattoLegendreBasis(3) indicator_sc = IndicatorNeuralNetwork(equations, basis, - indicator_type=NeuralNetworkRayHesthaven(), - alpha_max=0.5, - alpha_min=0.001, - alpha_smooth=true, - alpha_continuous=false, - alpha_amr=false, - variable=density_pressure, - network=model1d) + indicator_type = NeuralNetworkRayHesthaven(), + alpha_max = 0.5, + alpha_min = 0.001, + alpha_smooth = true, + alpha_continuous = false, + alpha_amr = false, + variable = density_pressure, + network = model1d) volume_integral = VolumeIntegralShockCapturingHG(indicator_sc; - volume_flux_dg=volume_flux, - volume_flux_fv=surface_flux) + volume_flux_dg = volume_flux, + volume_flux_fv = surface_flux) solver = DGSEM(basis, surface_flux, volume_integral) coordinates_min = (-2.0,) -coordinates_max = ( 2.0,) +coordinates_max = (2.0,) mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=6, - n_cells_max=10_000) - + initial_refinement_level = 6, + n_cells_max = 10_000) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver) - ############################################################################### # ODE solvers, callbacks etc. @@ -86,27 +84,26 @@ summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=100, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 100, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) -stepsize_callback = StepsizeCallback(cfl=0.5) +stepsize_callback = StepsizeCallback(cfl = 0.5) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, save_solution, stepsize_callback) - ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/tree_1d_dgsem/elixir_euler_convergence_pure_fv.jl b/examples/tree_1d_dgsem/elixir_euler_convergence_pure_fv.jl index fe221ea5bd7..1fa07d4edda 100644 --- a/examples/tree_1d_dgsem/elixir_euler_convergence_pure_fv.jl +++ b/examples/tree_1d_dgsem/elixir_euler_convergence_pure_fv.jl @@ -9,19 +9,17 @@ equations = CompressibleEulerEquations1D(1.4) initial_condition = initial_condition_convergence_test -solver = DGSEM(polydeg=3, surface_flux=flux_hllc, - volume_integral=VolumeIntegralPureLGLFiniteVolume(flux_hllc)) +solver = DGSEM(polydeg = 3, surface_flux = flux_hllc, + volume_integral = VolumeIntegralPureLGLFiniteVolume(flux_hllc)) coordinates_min = 0.0 coordinates_max = 2.0 mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=4, - n_cells_max=10_000) - + initial_refinement_level = 4, + n_cells_max = 10_000) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver, - source_terms=source_terms_convergence_test) - + source_terms = source_terms_convergence_test) ############################################################################### # ODE solvers, callbacks etc. @@ -32,29 +30,28 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval, - extra_analysis_errors=(:l2_error_primitive, - :linf_error_primitive)) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval, + extra_analysis_errors = (:l2_error_primitive, + :linf_error_primitive)) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=100, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 100, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) -stepsize_callback = StepsizeCallback(cfl=0.8) +stepsize_callback = StepsizeCallback(cfl = 0.8) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, save_solution, stepsize_callback) - ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/tree_1d_dgsem/elixir_euler_density_wave.jl b/examples/tree_1d_dgsem/elixir_euler_density_wave.jl index 746989dfe56..01ccbb2b517 100644 --- a/examples/tree_1d_dgsem/elixir_euler_density_wave.jl +++ b/examples/tree_1d_dgsem/elixir_euler_density_wave.jl @@ -8,18 +8,16 @@ equations = CompressibleEulerEquations1D(1.4) initial_condition = initial_condition_density_wave -solver = DGSEM(polydeg=5, surface_flux=flux_central) +solver = DGSEM(polydeg = 5, surface_flux = flux_central) coordinates_min = -1.0 -coordinates_max = 1.0 +coordinates_max = 1.0 mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=2, - n_cells_max=30_000) - + initial_refinement_level = 2, + n_cells_max = 30_000) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver) - ############################################################################### # ODE solvers, callbacks etc. @@ -29,16 +27,16 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 2000 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=100, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 100, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) -stepsize_callback = StepsizeCallback(cfl=0.8) +stepsize_callback = StepsizeCallback(cfl = 0.8) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, @@ -48,7 +46,7 @@ callbacks = CallbackSet(summary_callback, ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=stepsize_callback(ode), # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = stepsize_callback(ode), # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/tree_1d_dgsem/elixir_euler_ec.jl b/examples/tree_1d_dgsem/elixir_euler_ec.jl index f20bd4fd69e..0be9c8fbf4c 100644 --- a/examples/tree_1d_dgsem/elixir_euler_ec.jl +++ b/examples/tree_1d_dgsem/elixir_euler_ec.jl @@ -9,19 +9,17 @@ equations = CompressibleEulerEquations1D(1.4) initial_condition = initial_condition_weak_blast_wave volume_flux = flux_ranocha -solver = DGSEM(polydeg=3, surface_flux=flux_ranocha, - volume_integral=VolumeIntegralFluxDifferencing(volume_flux)) +solver = DGSEM(polydeg = 3, surface_flux = flux_ranocha, + volume_integral = VolumeIntegralFluxDifferencing(volume_flux)) coordinates_min = (-2.0,) -coordinates_max = ( 2.0,) +coordinates_max = (2.0,) mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=5, - n_cells_max=10_000) - + initial_refinement_level = 5, + n_cells_max = 10_000) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver) - ############################################################################### # ODE solvers, callbacks etc. @@ -31,27 +29,26 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=100, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 100, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) -stepsize_callback = StepsizeCallback(cfl=0.8) +stepsize_callback = StepsizeCallback(cfl = 0.8) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, save_solution, stepsize_callback) - ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/tree_1d_dgsem/elixir_euler_positivity.jl b/examples/tree_1d_dgsem/elixir_euler_positivity.jl index 966661e8894..3fb96fb807b 100644 --- a/examples/tree_1d_dgsem/elixir_euler_positivity.jl +++ b/examples/tree_1d_dgsem/elixir_euler_positivity.jl @@ -14,97 +14,92 @@ The Sedov blast wave setup based on Flash - https://flash.rochester.edu/site/flashcode/user_support/flash_ug_devel/node187.html#SECTION010114000000000000000 """ function initial_condition_sedov_blast_wave(x, t, equations::CompressibleEulerEquations1D) - # Set up polar coordinates - inicenter = SVector(0.0) - x_norm = x[1] - inicenter[1] - r = abs(x_norm) - - # Setup based on https://flash.rochester.edu/site/flashcode/user_support/flash_ug_devel/node187.html#SECTION010114000000000000000 - r0 = 0.21875 # = 3.5 * smallest dx (for domain length=4 and max-ref=6) - # r0 = 0.5 # = more reasonable setup - E = 1.0 - p0_inner = 6 * (equations.gamma - 1) * E / (3 * pi * r0) - p0_outer = 1.0e-5 # = true Sedov setup - # p0_outer = 1.0e-3 # = more reasonable setup - - # Calculate primitive variables - rho = 1.0 - v1 = 0.0 - p = r > r0 ? p0_outer : p0_inner - - return prim2cons(SVector(rho, v1, p), equations) + # Set up polar coordinates + inicenter = SVector(0.0) + x_norm = x[1] - inicenter[1] + r = abs(x_norm) + + # Setup based on https://flash.rochester.edu/site/flashcode/user_support/flash_ug_devel/node187.html#SECTION010114000000000000000 + r0 = 0.21875 # = 3.5 * smallest dx (for domain length=4 and max-ref=6) + # r0 = 0.5 # = more reasonable setup + E = 1.0 + p0_inner = 6 * (equations.gamma - 1) * E / (3 * pi * r0) + p0_outer = 1.0e-5 # = true Sedov setup + # p0_outer = 1.0e-3 # = more reasonable setup + + # Calculate primitive variables + rho = 1.0 + v1 = 0.0 + p = r > r0 ? p0_outer : p0_inner + + return prim2cons(SVector(rho, v1, p), equations) end initial_condition = initial_condition_sedov_blast_wave surface_flux = flux_lax_friedrichs -volume_flux = flux_ranocha +volume_flux = flux_ranocha basis = LobattoLegendreBasis(3) indicator_sc = IndicatorHennemannGassner(equations, basis, - alpha_max=0.5, - alpha_min=0.001, - alpha_smooth=true, - variable=density_pressure) + alpha_max = 0.5, + alpha_min = 0.001, + alpha_smooth = true, + variable = density_pressure) volume_integral = VolumeIntegralShockCapturingHG(indicator_sc; - volume_flux_dg=volume_flux, - volume_flux_fv=surface_flux) + volume_flux_dg = volume_flux, + volume_flux_fv = surface_flux) solver = DGSEM(basis, surface_flux, volume_integral) coordinates_min = (-2.0,) -coordinates_max = ( 2.0,) +coordinates_max = (2.0,) mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=6, - n_cells_max=10_000) - + initial_refinement_level = 6, + n_cells_max = 10_000) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver) - ############################################################################### # ODE solvers, callbacks etc. tspan = (0.0, 4.0) ode = semidiscretize(semi, tspan) - summary_callback = SummaryCallback() analysis_interval = 500 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=100, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 100, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) amr_indicator = IndicatorLöhner(semi, - variable=density_pressure) + variable = density_pressure) amr_controller = ControllerThreeLevel(semi, amr_indicator, - base_level=4, - med_level =0, med_threshold=0.1, # med_level = current level - max_level =6, max_threshold=0.3) + base_level = 4, + med_level = 0, med_threshold = 0.1, # med_level = current level + max_level = 6, max_threshold = 0.3) amr_callback = AMRCallback(semi, amr_controller, - interval=2, - adapt_initial_condition=true, - adapt_initial_condition_only_refine=true) + interval = 2, + adapt_initial_condition = true, + adapt_initial_condition_only_refine = true) -stepsize_callback = StepsizeCallback(cfl=0.5) +stepsize_callback = StepsizeCallback(cfl = 0.5) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, save_solution, amr_callback, stepsize_callback) - -stage_limiter! = PositivityPreservingLimiterZhangShu(thresholds=(5.0e-6, 5.0e-6), - variables=(Trixi.density, pressure)) - +stage_limiter! = PositivityPreservingLimiterZhangShu(thresholds = (5.0e-6, 5.0e-6), + variables = (Trixi.density, pressure)) ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(stage_limiter!, williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(stage_limiter!, williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/tree_1d_dgsem/elixir_euler_sedov_blast_wave.jl b/examples/tree_1d_dgsem/elixir_euler_sedov_blast_wave.jl index 106ccacf4f5..b67b2bc602e 100644 --- a/examples/tree_1d_dgsem/elixir_euler_sedov_blast_wave.jl +++ b/examples/tree_1d_dgsem/elixir_euler_sedov_blast_wave.jl @@ -14,96 +14,92 @@ The Sedov blast wave setup based on Flash - https://flash.rochester.edu/site/flashcode/user_support/flash_ug_devel/node187.html#SECTION010114000000000000000 """ function initial_condition_sedov_blast_wave(x, t, equations::CompressibleEulerEquations1D) - # Set up polar coordinates - inicenter = SVector(0.0) - x_norm = x[1] - inicenter[1] - r = abs(x_norm) - - # Setup based on https://flash.rochester.edu/site/flashcode/user_support/flash_ug_devel/node187.html#SECTION010114000000000000000 - r0 = 0.21875 # = 3.5 * smallest dx (for domain length=4 and max-ref=6) - # r0 = 0.5 # = more reasonable setup - E = 1.0 - p0_inner = 6 * (equations.gamma - 1) * E / (3 * pi * r0) - p0_outer = 1.0e-5 # = true Sedov setup - # p0_outer = 1.0e-3 # = more reasonable setup - - # Calculate primitive variables - rho = 1.0 - v1 = 0.0 - p = r > r0 ? p0_outer : p0_inner - - return prim2cons(SVector(rho, v1, p), equations) + # Set up polar coordinates + inicenter = SVector(0.0) + x_norm = x[1] - inicenter[1] + r = abs(x_norm) + + # Setup based on https://flash.rochester.edu/site/flashcode/user_support/flash_ug_devel/node187.html#SECTION010114000000000000000 + r0 = 0.21875 # = 3.5 * smallest dx (for domain length=4 and max-ref=6) + # r0 = 0.5 # = more reasonable setup + E = 1.0 + p0_inner = 6 * (equations.gamma - 1) * E / (3 * pi * r0) + p0_outer = 1.0e-5 # = true Sedov setup + # p0_outer = 1.0e-3 # = more reasonable setup + + # Calculate primitive variables + rho = 1.0 + v1 = 0.0 + p = r > r0 ? p0_outer : p0_inner + + return prim2cons(SVector(rho, v1, p), equations) end initial_condition = initial_condition_sedov_blast_wave surface_flux = flux_lax_friedrichs -volume_flux = flux_chandrashekar +volume_flux = flux_chandrashekar basis = LobattoLegendreBasis(3) shock_indicator_variable = density_pressure indicator_sc = IndicatorHennemannGassner(equations, basis, - alpha_max=0.5, - alpha_min=0.001, - alpha_smooth=true, - variable=shock_indicator_variable) + alpha_max = 0.5, + alpha_min = 0.001, + alpha_smooth = true, + variable = shock_indicator_variable) volume_integral = VolumeIntegralShockCapturingHG(indicator_sc; - volume_flux_dg=volume_flux, - volume_flux_fv=surface_flux) + volume_flux_dg = volume_flux, + volume_flux_fv = surface_flux) solver = DGSEM(basis, surface_flux, volume_integral) coordinates_min = (-2.0,) -coordinates_max = ( 2.0,) +coordinates_max = (2.0,) mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=6, - n_cells_max=10_000) - + initial_refinement_level = 6, + n_cells_max = 10_000) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver) - ############################################################################### # ODE solvers, callbacks etc. tspan = (0.0, 12.5) ode = semidiscretize(semi, tspan) - summary_callback = SummaryCallback() analysis_interval = 1000 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=100, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 100, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) amr_indicator = IndicatorHennemannGassner(semi, - alpha_max=0.5, - alpha_min=0.001, - alpha_smooth=true, - variable=density_pressure) + alpha_max = 0.5, + alpha_min = 0.001, + alpha_smooth = true, + variable = density_pressure) amr_controller = ControllerThreeLevel(semi, amr_indicator, - base_level=4, - max_level=6, max_threshold=0.01) + base_level = 4, + max_level = 6, max_threshold = 0.01) amr_callback = AMRCallback(semi, amr_controller, - interval=5, - adapt_initial_condition=true, - adapt_initial_condition_only_refine=true) + interval = 5, + adapt_initial_condition = true, + adapt_initial_condition_only_refine = true) -stepsize_callback = StepsizeCallback(cfl=0.5) +stepsize_callback = StepsizeCallback(cfl = 0.5) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, save_solution, amr_callback, stepsize_callback) - ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=stepsize_callback(ode), # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = stepsize_callback(ode), # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/tree_1d_dgsem/elixir_euler_sedov_blast_wave_pure_fv.jl b/examples/tree_1d_dgsem/elixir_euler_sedov_blast_wave_pure_fv.jl index ebe8fa7cebf..8a0241680b9 100644 --- a/examples/tree_1d_dgsem/elixir_euler_sedov_blast_wave_pure_fv.jl +++ b/examples/tree_1d_dgsem/elixir_euler_sedov_blast_wave_pure_fv.jl @@ -14,25 +14,25 @@ The Sedov blast wave setup based on Flash - https://flash.rochester.edu/site/flashcode/user_support/flash_ug_devel/node187.html#SECTION010114000000000000000 """ function initial_condition_sedov_blast_wave(x, t, equations::CompressibleEulerEquations1D) - # Set up polar coordinates - inicenter = SVector(0.0) - x_norm = x[1] - inicenter[1] - r = abs(x_norm) - - # Setup based on https://flash.rochester.edu/site/flashcode/user_support/flash_ug_devel/node187.html#SECTION010114000000000000000 - r0 = 0.21875 # = 3.5 * smallest dx (for domain length=4 and max-ref=6) - # r0 = 0.5 # = more reasonable setup - E = 1.0 - p0_inner = 6 * (equations.gamma - 1) * E / (3 * pi * r0) - p0_outer = 1.0e-5 # = true Sedov setup - # p0_outer = 1.0e-3 # = more reasonable setup - - # Calculate primitive variables - rho = 1.0 - v1 = 0.0 - p = r > r0 ? p0_outer : p0_inner - - return prim2cons(SVector(rho, v1, p), equations) + # Set up polar coordinates + inicenter = SVector(0.0) + x_norm = x[1] - inicenter[1] + r = abs(x_norm) + + # Setup based on https://flash.rochester.edu/site/flashcode/user_support/flash_ug_devel/node187.html#SECTION010114000000000000000 + r0 = 0.21875 # = 3.5 * smallest dx (for domain length=4 and max-ref=6) + # r0 = 0.5 # = more reasonable setup + E = 1.0 + p0_inner = 6 * (equations.gamma - 1) * E / (3 * pi * r0) + p0_outer = 1.0e-5 # = true Sedov setup + # p0_outer = 1.0e-3 # = more reasonable setup + + # Calculate primitive variables + rho = 1.0 + v1 = 0.0 + p = r > r0 ? p0_outer : p0_inner + + return prim2cons(SVector(rho, v1, p), equations) end initial_condition = initial_condition_sedov_blast_wave @@ -42,59 +42,55 @@ volume_integral = VolumeIntegralPureLGLFiniteVolume(flux_hllc) solver = DGSEM(basis, surface_flux, volume_integral) coordinates_min = (-2.0,) -coordinates_max = ( 2.0,) +coordinates_max = (2.0,) mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=7, - n_cells_max=10_000) - + initial_refinement_level = 7, + n_cells_max = 10_000) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver) - ############################################################################### # ODE solvers, callbacks etc. tspan = (0.0, 12.5) ode = semidiscretize(semi, tspan) - summary_callback = SummaryCallback() analysis_interval = 1000 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=100, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 100, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) amr_indicator = IndicatorHennemannGassner(semi, - alpha_max=0.5, - alpha_min=0.001, - alpha_smooth=true, - variable=density_pressure) + alpha_max = 0.5, + alpha_min = 0.001, + alpha_smooth = true, + variable = density_pressure) amr_controller = ControllerThreeLevel(semi, amr_indicator, - base_level=4, - max_level=7, max_threshold=0.01) + base_level = 4, + max_level = 7, max_threshold = 0.01) amr_callback = AMRCallback(semi, amr_controller, - interval=5, - adapt_initial_condition=true, - adapt_initial_condition_only_refine=true) + interval = 5, + adapt_initial_condition = true, + adapt_initial_condition_only_refine = true) -stepsize_callback = StepsizeCallback(cfl=0.25) +stepsize_callback = StepsizeCallback(cfl = 0.25) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, save_solution, amr_callback, stepsize_callback) - ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=stepsize_callback(ode), # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = stepsize_callback(ode), # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/tree_1d_dgsem/elixir_euler_shockcapturing.jl b/examples/tree_1d_dgsem/elixir_euler_shockcapturing.jl index 90547f8ddc1..08367505377 100644 --- a/examples/tree_1d_dgsem/elixir_euler_shockcapturing.jl +++ b/examples/tree_1d_dgsem/elixir_euler_shockcapturing.jl @@ -10,28 +10,26 @@ equations = CompressibleEulerEquations1D(1.4) initial_condition = initial_condition_weak_blast_wave surface_flux = flux_lax_friedrichs -volume_flux = flux_shima_etal +volume_flux = flux_shima_etal basis = LobattoLegendreBasis(3) indicator_sc = IndicatorHennemannGassner(equations, basis, - alpha_max=0.5, - alpha_min=0.001, - alpha_smooth=true, - variable=density_pressure) + alpha_max = 0.5, + alpha_min = 0.001, + alpha_smooth = true, + variable = density_pressure) volume_integral = VolumeIntegralShockCapturingHG(indicator_sc; - volume_flux_dg=volume_flux, - volume_flux_fv=surface_flux) + volume_flux_dg = volume_flux, + volume_flux_fv = surface_flux) solver = DGSEM(basis, surface_flux, volume_integral) coordinates_min = -2.0 -coordinates_max = 2.0 +coordinates_max = 2.0 mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=5, - n_cells_max=10_000) - + initial_refinement_level = 5, + n_cells_max = 10_000) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver) - ############################################################################### # ODE solvers, callbacks etc. @@ -41,27 +39,26 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=100, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 100, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) -stepsize_callback = StepsizeCallback(cfl=0.8) +stepsize_callback = StepsizeCallback(cfl = 0.8) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, save_solution, stepsize_callback) - ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/tree_1d_dgsem/elixir_euler_source_terms.jl b/examples/tree_1d_dgsem/elixir_euler_source_terms.jl index 213206eb9e0..555910f69f0 100644 --- a/examples/tree_1d_dgsem/elixir_euler_source_terms.jl +++ b/examples/tree_1d_dgsem/elixir_euler_source_terms.jl @@ -11,18 +11,16 @@ initial_condition = initial_condition_convergence_test # Note that the expected EOC of 5 is not reached with this flux. # Using flux_hll instead yields the expected EOC. -solver = DGSEM(polydeg=4, surface_flux=flux_lax_friedrichs) +solver = DGSEM(polydeg = 4, surface_flux = flux_lax_friedrichs) coordinates_min = 0.0 coordinates_max = 2.0 mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=4, - n_cells_max=10_000) - + initial_refinement_level = 4, + n_cells_max = 10_000) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver, - source_terms=source_terms_convergence_test) - + source_terms = source_terms_convergence_test) ############################################################################### # ODE solvers, callbacks etc. @@ -33,29 +31,28 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval, - extra_analysis_errors=(:l2_error_primitive, - :linf_error_primitive)) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval, + extra_analysis_errors = (:l2_error_primitive, + :linf_error_primitive)) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=100, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 100, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) -stepsize_callback = StepsizeCallback(cfl=0.8) +stepsize_callback = StepsizeCallback(cfl = 0.8) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, save_solution, stepsize_callback) - ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/tree_1d_dgsem/elixir_euler_source_terms_nonperiodic.jl b/examples/tree_1d_dgsem/elixir_euler_source_terms_nonperiodic.jl index 3794e0c8d54..922ac3dd97d 100644 --- a/examples/tree_1d_dgsem/elixir_euler_source_terms_nonperiodic.jl +++ b/examples/tree_1d_dgsem/elixir_euler_source_terms_nonperiodic.jl @@ -13,23 +13,21 @@ initial_condition = initial_condition_convergence_test # 1*ndims == 2 directions or you can pass a tuple containing BCs for # each direction boundary_condition = BoundaryConditionDirichlet(initial_condition) -boundary_conditions = (x_neg=boundary_condition, - x_pos=boundary_condition) +boundary_conditions = (x_neg = boundary_condition, + x_pos = boundary_condition) -solver = DGSEM(polydeg=3, surface_flux=flux_lax_friedrichs) +solver = DGSEM(polydeg = 3, surface_flux = flux_lax_friedrichs) coordinates_min = (0.0,) coordinates_max = (2.0,) mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=4, - n_cells_max=10_000, - periodicity=false) - + initial_refinement_level = 4, + n_cells_max = 10_000, + periodicity = false) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver, - source_terms=source_terms_convergence_test, - boundary_conditions=boundary_conditions) - + source_terms = source_terms_convergence_test, + boundary_conditions = boundary_conditions) ############################################################################### # ODE solvers, callbacks etc. @@ -40,30 +38,29 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_restart = SaveRestartCallback(interval=100, - save_final_restart=true) +save_restart = SaveRestartCallback(interval = 100, + save_final_restart = true) -save_solution = SaveSolutionCallback(interval=100, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 100, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) -stepsize_callback = StepsizeCallback(cfl=0.8) +stepsize_callback = StepsizeCallback(cfl = 0.8) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, save_restart, save_solution, stepsize_callback) - ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/tree_1d_dgsem/elixir_eulergravity_convergence.jl b/examples/tree_1d_dgsem/elixir_eulergravity_convergence.jl index 42de0e18e51..acde04780ee 100644 --- a/examples/tree_1d_dgsem/elixir_eulergravity_convergence.jl +++ b/examples/tree_1d_dgsem/elixir_eulergravity_convergence.jl @@ -15,11 +15,11 @@ solver_euler = DGSEM(polydeg, flux_hll) coordinates_min = 0.0 coordinates_max = 2.0 mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=2, - n_cells_max=10_000) - -semi_euler = SemidiscretizationHyperbolic(mesh, equations_euler, initial_condition, solver_euler) + initial_refinement_level = 2, + n_cells_max = 10_000) +semi_euler = SemidiscretizationHyperbolic(mesh, equations_euler, initial_condition, + solver_euler) ############################################################################### # semidiscretization of the hyperbolic diffusion equations @@ -27,22 +27,21 @@ equations_gravity = HyperbolicDiffusionEquations1D() solver_gravity = DGSEM(polydeg, flux_lax_friedrichs) -semi_gravity = SemidiscretizationHyperbolic(mesh, equations_gravity, initial_condition, solver_gravity, - source_terms=source_terms_harmonic) - +semi_gravity = SemidiscretizationHyperbolic(mesh, equations_gravity, initial_condition, + solver_gravity, + source_terms = source_terms_harmonic) ############################################################################### # combining both semidiscretizations for Euler + self-gravity -parameters = ParametersEulerGravity(background_density=2.0, # aka rho0 - gravitational_constant=1.0, # aka G - cfl=1.5, - resid_tol=1.0e-10, - n_iterations_max=1000, - timestep_gravity=timestep_gravity_erk52_3Sstar!) +parameters = ParametersEulerGravity(background_density = 2.0, # aka rho0 + gravitational_constant = 1.0, # aka G + cfl = 1.5, + resid_tol = 1.0e-10, + n_iterations_max = 1000, + timestep_gravity = timestep_gravity_erk52_3Sstar!) semi = SemidiscretizationEulerGravity(semi_euler, semi_gravity, parameters) - ############################################################################### # ODE solvers, callbacks etc. tspan = (0.0, 0.5) @@ -51,20 +50,20 @@ ode = semidiscretize(semi, tspan); summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi_euler, interval=analysis_interval, - save_analysis=true) +analysis_callback = AnalysisCallback(semi_euler, interval = analysis_interval, + save_analysis = true) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_restart = SaveRestartCallback(interval=100, - save_final_restart=true) +save_restart = SaveRestartCallback(interval = 100, + save_final_restart = true) -save_solution = SaveSolutionCallback(interval=10, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 10, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) -stepsize_callback = StepsizeCallback(cfl=1.1) +stepsize_callback = StepsizeCallback(cfl = 1.1) callbacks = CallbackSet(summary_callback, analysis_callback, @@ -73,11 +72,10 @@ callbacks = CallbackSet(summary_callback, save_solution, stepsize_callback) - ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary println("Number of gravity subcycles: ", semi.gravity_counter.ncalls_since_readout) diff --git a/examples/tree_1d_dgsem/elixir_eulermulti_convergence_ec.jl b/examples/tree_1d_dgsem/elixir_eulermulti_convergence_ec.jl index 2444fe8611d..6d6316898b7 100644 --- a/examples/tree_1d_dgsem/elixir_eulermulti_convergence_ec.jl +++ b/examples/tree_1d_dgsem/elixir_eulermulti_convergence_ec.jl @@ -4,25 +4,23 @@ using Trixi ############################################################################### # semidiscretization of the compressible Euler multicomponent equations -equations = CompressibleEulerMulticomponentEquations1D(gammas = (1.4, 1.4), +equations = CompressibleEulerMulticomponentEquations1D(gammas = (1.4, 1.4), gas_constants = (0.4, 0.4)) initial_condition = initial_condition_convergence_test volume_flux = flux_ranocha -solver = DGSEM(polydeg=3, surface_flux=flux_ranocha, - volume_integral=VolumeIntegralFluxDifferencing(volume_flux)) +solver = DGSEM(polydeg = 3, surface_flux = flux_ranocha, + volume_integral = VolumeIntegralFluxDifferencing(volume_flux)) coordinates_min = (-1.0,) -coordinates_max = ( 1.0,) +coordinates_max = (1.0,) mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=3, - n_cells_max=30_000) - + initial_refinement_level = 3, + n_cells_max = 30_000) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver, - source_terms=source_terms_convergence_test) - + source_terms = source_terms_convergence_test) ############################################################################### # ODE solvers, callbacks etc. @@ -33,27 +31,26 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=100, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 100, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) -stepsize_callback = StepsizeCallback(cfl=0.5) +stepsize_callback = StepsizeCallback(cfl = 0.5) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, save_solution, stepsize_callback) - ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/tree_1d_dgsem/elixir_eulermulti_convergence_es.jl b/examples/tree_1d_dgsem/elixir_eulermulti_convergence_es.jl index 86f4a4bad04..1b37a8a2279 100644 --- a/examples/tree_1d_dgsem/elixir_eulermulti_convergence_es.jl +++ b/examples/tree_1d_dgsem/elixir_eulermulti_convergence_es.jl @@ -4,25 +4,23 @@ using Trixi ############################################################################### # semidiscretization of the compressible Euler multicomponent equations -equations = CompressibleEulerMulticomponentEquations1D(gammas = (1.4, 1.4, 1.4, 1.4), +equations = CompressibleEulerMulticomponentEquations1D(gammas = (1.4, 1.4, 1.4, 1.4), gas_constants = (0.4, 0.4, 0.4, 0.4)) initial_condition = initial_condition_convergence_test volume_flux = flux_ranocha -solver = DGSEM(polydeg=3, surface_flux=flux_lax_friedrichs, - volume_integral=VolumeIntegralFluxDifferencing(volume_flux)) +solver = DGSEM(polydeg = 3, surface_flux = flux_lax_friedrichs, + volume_integral = VolumeIntegralFluxDifferencing(volume_flux)) coordinates_min = (-1.0,) -coordinates_max = ( 1.0,) +coordinates_max = (1.0,) mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=3, - n_cells_max=30_000) - + initial_refinement_level = 3, + n_cells_max = 30_000) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver, - source_terms=source_terms_convergence_test) - + source_terms = source_terms_convergence_test) ############################################################################### # ODE solvers, callbacks etc. @@ -33,27 +31,26 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=100, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 100, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) -stepsize_callback = StepsizeCallback(cfl=0.5) +stepsize_callback = StepsizeCallback(cfl = 0.5) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, save_solution, stepsize_callback) - ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/tree_1d_dgsem/elixir_eulermulti_ec.jl b/examples/tree_1d_dgsem/elixir_eulermulti_ec.jl index 04d937a9a8f..73f8de15d82 100644 --- a/examples/tree_1d_dgsem/elixir_eulermulti_ec.jl +++ b/examples/tree_1d_dgsem/elixir_eulermulti_ec.jl @@ -4,26 +4,23 @@ using Trixi ############################################################################### # semidiscretization of the compressible Euler multicomponent equations -equations = CompressibleEulerMulticomponentEquations1D(gammas = (1.4, 1.4, 1.4), +equations = CompressibleEulerMulticomponentEquations1D(gammas = (1.4, 1.4, 1.4), gas_constants = (0.4, 0.4, 0.4)) - initial_condition = initial_condition_weak_blast_wave volume_flux = flux_ranocha -solver = DGSEM(polydeg=3, surface_flux=flux_ranocha, - volume_integral=VolumeIntegralFluxDifferencing(volume_flux)) +solver = DGSEM(polydeg = 3, surface_flux = flux_ranocha, + volume_integral = VolumeIntegralFluxDifferencing(volume_flux)) coordinates_min = (-2.0,) -coordinates_max = ( 2.0,) +coordinates_max = (2.0,) mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=5, - n_cells_max=10_000) - + initial_refinement_level = 5, + n_cells_max = 10_000) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver) - ############################################################################### # ODE solvers, callbacks etc. @@ -34,28 +31,27 @@ summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval, - extra_analysis_integrals=(Trixi.density,)) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval, + extra_analysis_integrals = (Trixi.density,)) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=100, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 100, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) -stepsize_callback = StepsizeCallback(cfl=0.8) +stepsize_callback = StepsizeCallback(cfl = 0.8) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, save_solution, stepsize_callback) - ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/tree_1d_dgsem/elixir_eulermulti_es.jl b/examples/tree_1d_dgsem/elixir_eulermulti_es.jl index 7abb3b0d021..7fbec0c0055 100644 --- a/examples/tree_1d_dgsem/elixir_eulermulti_es.jl +++ b/examples/tree_1d_dgsem/elixir_eulermulti_es.jl @@ -4,26 +4,23 @@ using Trixi ############################################################################### # semidiscretization of the compressible Euler multicomponent equations -equations = CompressibleEulerMulticomponentEquations1D(gammas = (1.4, 1.4), +equations = CompressibleEulerMulticomponentEquations1D(gammas = (1.4, 1.4), gas_constants = (0.4, 0.4)) - initial_condition = initial_condition_weak_blast_wave volume_flux = flux_ranocha -solver = DGSEM(polydeg=3, surface_flux=flux_lax_friedrichs, - volume_integral=VolumeIntegralFluxDifferencing(volume_flux)) +solver = DGSEM(polydeg = 3, surface_flux = flux_lax_friedrichs, + volume_integral = VolumeIntegralFluxDifferencing(volume_flux)) coordinates_min = (-2.0,) -coordinates_max = ( 2.0,) +coordinates_max = (2.0,) mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=5, - n_cells_max=10_000) - + initial_refinement_level = 5, + n_cells_max = 10_000) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver) - ############################################################################### # ODE solvers, callbacks etc. @@ -34,31 +31,30 @@ summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval, - extra_analysis_integrals=(Trixi.density,)) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval, + extra_analysis_integrals = (Trixi.density,)) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_restart = SaveRestartCallback(interval=100, - save_final_restart=true) +save_restart = SaveRestartCallback(interval = 100, + save_final_restart = true) -save_solution = SaveSolutionCallback(interval=100, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 100, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) -stepsize_callback = StepsizeCallback(cfl=0.8) +stepsize_callback = StepsizeCallback(cfl = 0.8) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, save_restart, save_solution, stepsize_callback) - ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/tree_1d_dgsem/elixir_eulermulti_two_interacting_blast_waves.jl b/examples/tree_1d_dgsem/elixir_eulermulti_two_interacting_blast_waves.jl index 81966194180..c093420cc7c 100644 --- a/examples/tree_1d_dgsem/elixir_eulermulti_two_interacting_blast_waves.jl +++ b/examples/tree_1d_dgsem/elixir_eulermulti_two_interacting_blast_waves.jl @@ -5,8 +5,8 @@ using Trixi ############################################################################### # semidiscretization of the compressible Euler equations -equations = CompressibleEulerMulticomponentEquations1D(gammas = (1.4, 1.4, 1.4), - gas_constants = (0.4, 0.4, 0.4)) +equations = CompressibleEulerMulticomponentEquations1D(gammas = (1.4, 1.4, 1.4), + gas_constants = (0.4, 0.4, 0.4)) """ initial_condition_two_interacting_blast_waves(x, t, equations::CompressibleEulerMulticomponentEquations1D) @@ -16,69 +16,67 @@ A multicomponent two interacting blast wave test taken from The consistent multi-fluid advection method [arXiv: 9807241](https://arxiv.org/pdf/astro-ph/9807241.pdf) """ -function initial_condition_two_interacting_blast_waves(x, t, equations::CompressibleEulerMulticomponentEquations1D) +function initial_condition_two_interacting_blast_waves(x, t, + equations::CompressibleEulerMulticomponentEquations1D) + rho1 = 0.5 * x[1]^2 + rho2 = 0.5 * (sin(20 * x[1]))^2 + rho3 = 1 - rho1 - rho2 - rho1 = 0.5 * x[1]^2 - rho2 = 0.5 * (sin(20 * x[1]))^2 - rho3 = 1 - rho1 - rho2 + prim_rho = SVector{3, real(equations)}(rho1, rho2, rho3) - prim_rho = SVector{3, real(equations)}(rho1, rho2, rho3) + v1 = 0.0 - v1 = 0.0 + if x[1] <= 0.1 + p = 1000 + elseif x[1] < 0.9 + p = 0.01 + else + p = 100 + end - if x[1] <= 0.1 - p = 1000 - elseif x[1] < 0.9 - p = 0.01 - else - p = 100 - end + prim_other = SVector{2, real(equations)}(v1, p) - prim_other = SVector{2, real(equations)}(v1, p) - - return prim2cons(vcat(prim_other, prim_rho), equations) + return prim2cons(vcat(prim_other, prim_rho), equations) end initial_condition = initial_condition_two_interacting_blast_waves -function boundary_condition_two_interacting_blast_waves(u_inner, orientation, direction, x, t, - surface_flux_function, +function boundary_condition_two_interacting_blast_waves(u_inner, orientation, direction, + x, t, surface_flux_function, equations::CompressibleEulerMulticomponentEquations1D) - - u_inner_reflect = SVector(-u_inner[1], u_inner[2], u_inner[3], u_inner[4], u_inner[5]) - # Calculate boundary flux - if iseven(direction) # u_inner is "left" of boundary, u_boundary is "right" of boundary - flux = surface_flux_function(u_inner, u_inner_reflect, orientation, equations) - else # u_boundary is "left" of boundary, u_inner is "right" of boundary - flux = surface_flux_function(u_inner_reflect, u_inner, orientation, equations) - end - - return flux + u_inner_reflect = SVector(-u_inner[1], u_inner[2], u_inner[3], u_inner[4], u_inner[5]) + # Calculate boundary flux + if iseven(direction) # u_inner is "left" of boundary, u_boundary is "right" of boundary + flux = surface_flux_function(u_inner, u_inner_reflect, orientation, equations) + else # u_boundary is "left" of boundary, u_inner is "right" of boundary + flux = surface_flux_function(u_inner_reflect, u_inner, orientation, equations) + end + + return flux end boundary_conditions = boundary_condition_two_interacting_blast_waves surface_flux = flux_lax_friedrichs -volume_flux = flux_ranocha +volume_flux = flux_ranocha basis = LobattoLegendreBasis(3) indicator_sc = IndicatorHennemannGassner(equations, basis, alpha_max = 0.8, alpha_min = 0.0, alpha_smooth = true, - variable=pressure) + variable = pressure) volume_integral = VolumeIntegralShockCapturingHG(indicator_sc; - volume_flux_dg=volume_flux, - volume_flux_fv=surface_flux) + volume_flux_dg = volume_flux, + volume_flux_fv = surface_flux) solver = DGSEM(basis, surface_flux, volume_integral) coordinates_min = (0.0,) coordinates_max = (1.0,) mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=9, - n_cells_max=10_000, - periodicity=false) - - -semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver, boundary_conditions=boundary_conditions) + initial_refinement_level = 9, + n_cells_max = 10_000, + periodicity = false) +semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver, + boundary_conditions = boundary_conditions) ############################################################################### # ODE solvers, callbacks etc. @@ -90,16 +88,16 @@ summary_callback = SummaryCallback() analysis_interval = 1000 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=100, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 100, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) -stepsize_callback = StepsizeCallback(cfl=0.1) +stepsize_callback = StepsizeCallback(cfl = 0.1) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, @@ -109,7 +107,7 @@ callbacks = CallbackSet(summary_callback, ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/tree_1d_dgsem/elixir_hypdiff_harmonic_nonperiodic.jl b/examples/tree_1d_dgsem/elixir_hypdiff_harmonic_nonperiodic.jl index 9a19807ae29..b9173ec9f49 100644 --- a/examples/tree_1d_dgsem/elixir_hypdiff_harmonic_nonperiodic.jl +++ b/examples/tree_1d_dgsem/elixir_hypdiff_harmonic_nonperiodic.jl @@ -5,7 +5,7 @@ using Trixi ############################################################################### # semidiscretization of the hyperbolic diffusion equations -equations = HyperbolicDiffusionEquations1D(nu=1.25) +equations = HyperbolicDiffusionEquations1D(nu = 1.25) """ initial_condition_poisson_nonperiodic(x, t, equations::HyperbolicDiffusionEquations1D) @@ -16,36 +16,36 @@ A non-priodic harmonic function used in combination with !!! note The only harmonic functions in 1D have the form phi(x) = A + Bx """ -function initial_condition_harmonic_nonperiodic(x, t, equations::HyperbolicDiffusionEquations1D) - # elliptic equation: -νΔϕ = f - if t == 0.0 - phi = 5.0 - q1 = 0.0 - else - A = 3 - B = exp(1) - phi = A + B * x[1] - q1 = B - end - return SVector(phi, q1) +function initial_condition_harmonic_nonperiodic(x, t, + equations::HyperbolicDiffusionEquations1D) + # elliptic equation: -νΔϕ = f + if t == 0.0 + phi = 5.0 + q1 = 0.0 + else + A = 3 + B = exp(1) + phi = A + B * x[1] + q1 = B + end + return SVector(phi, q1) end initial_condition = initial_condition_harmonic_nonperiodic boundary_conditions = BoundaryConditionDirichlet(initial_condition) -solver = DGSEM(polydeg=3, surface_flux=flux_lax_friedrichs) +solver = DGSEM(polydeg = 3, surface_flux = flux_lax_friedrichs) coordinates_min = -1.0 -coordinates_max = 2.0 +coordinates_max = 2.0 mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=2, - n_cells_max=30_000, - periodicity=false) + initial_refinement_level = 2, + n_cells_max = 30_000, + periodicity = false) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver, - boundary_conditions=boundary_conditions, - source_terms=source_terms_harmonic) - + boundary_conditions = boundary_conditions, + source_terms = source_terms_harmonic) ############################################################################### # ODE solvers, callbacks etc. @@ -56,30 +56,29 @@ ode = semidiscretize(semi, tspan); summary_callback = SummaryCallback() resid_tol = 5.0e-12 -steady_state_callback = SteadyStateCallback(abstol=resid_tol, reltol=0.0) +steady_state_callback = SteadyStateCallback(abstol = resid_tol, reltol = 0.0) analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=100, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 100, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) -stepsize_callback = StepsizeCallback(cfl=1.75) +stepsize_callback = StepsizeCallback(cfl = 1.75) callbacks = CallbackSet(summary_callback, steady_state_callback, analysis_callback, alive_callback, save_solution, stepsize_callback) - ############################################################################### # run the simulation sol = Trixi.solve(ode, Trixi.HypDiffN3Erk3Sstar52(), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/tree_1d_dgsem/elixir_hypdiff_nonperiodic.jl b/examples/tree_1d_dgsem/elixir_hypdiff_nonperiodic.jl index 827d8d25ce7..4da3b33a466 100644 --- a/examples/tree_1d_dgsem/elixir_hypdiff_nonperiodic.jl +++ b/examples/tree_1d_dgsem/elixir_hypdiff_nonperiodic.jl @@ -11,19 +11,18 @@ initial_condition = initial_condition_poisson_nonperiodic boundary_conditions = boundary_condition_poisson_nonperiodic -solver = DGSEM(polydeg=4, surface_flux=flux_lax_friedrichs) +solver = DGSEM(polydeg = 4, surface_flux = flux_lax_friedrichs) coordinates_min = 0.0 coordinates_max = 1.0 mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=3, - n_cells_max=30_000, - periodicity=false) + initial_refinement_level = 3, + n_cells_max = 30_000, + periodicity = false) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver, - boundary_conditions=boundary_conditions, - source_terms=source_terms_poisson_nonperiodic) - + boundary_conditions = boundary_conditions, + source_terms = source_terms_poisson_nonperiodic) ############################################################################### # ODE solvers, callbacks etc. @@ -34,31 +33,30 @@ ode = semidiscretize(semi, tspan); summary_callback = SummaryCallback() resid_tol = 5.0e-12 -steady_state_callback = SteadyStateCallback(abstol=resid_tol, reltol=0.0) +steady_state_callback = SteadyStateCallback(abstol = resid_tol, reltol = 0.0) analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval, - extra_analysis_integrals=(entropy, energy_total)) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval, + extra_analysis_integrals = (entropy, energy_total)) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=100, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 100, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) -stepsize_callback = StepsizeCallback(cfl=1.0) +stepsize_callback = StepsizeCallback(cfl = 1.0) callbacks = CallbackSet(summary_callback, steady_state_callback, analysis_callback, alive_callback, save_solution, stepsize_callback) - ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/tree_1d_dgsem/elixir_mhd_alfven_wave.jl b/examples/tree_1d_dgsem/elixir_mhd_alfven_wave.jl index 82bca93c707..1a66ac60b9b 100644 --- a/examples/tree_1d_dgsem/elixir_mhd_alfven_wave.jl +++ b/examples/tree_1d_dgsem/elixir_mhd_alfven_wave.jl @@ -4,25 +4,23 @@ using Trixi ############################################################################### # semidiscretization of the ideal MHD equations -gamma = 5/3 +gamma = 5 / 3 equations = IdealGlmMhdEquations1D(gamma) initial_condition = initial_condition_convergence_test volume_flux = flux_hindenlang_gassner -solver = DGSEM(polydeg=4, surface_flux=flux_lax_friedrichs, - volume_integral=VolumeIntegralFluxDifferencing(volume_flux)) +solver = DGSEM(polydeg = 4, surface_flux = flux_lax_friedrichs, + volume_integral = VolumeIntegralFluxDifferencing(volume_flux)) coordinates_min = 0.0 coordinates_max = 1.0 mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=2, - n_cells_max=10_000) - + initial_refinement_level = 2, + n_cells_max = 10_000) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver) - ############################################################################### # ODE solvers, callbacks etc. @@ -32,32 +30,33 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval, - extra_analysis_errors=(:l2_error_primitive, - :linf_error_primitive), - extra_analysis_integrals=(entropy, energy_total, - energy_kinetic, energy_internal, - energy_magnetic, cross_helicity)) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval, + extra_analysis_errors = (:l2_error_primitive, + :linf_error_primitive), + extra_analysis_integrals = (entropy, energy_total, + energy_kinetic, + energy_internal, + energy_magnetic, + cross_helicity)) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=100, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 100, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) -stepsize_callback = StepsizeCallback(cfl=1.0) +stepsize_callback = StepsizeCallback(cfl = 1.0) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, save_solution, stepsize_callback) - ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/tree_1d_dgsem/elixir_mhd_briowu_shock_tube.jl b/examples/tree_1d_dgsem/elixir_mhd_briowu_shock_tube.jl index c5727109d92..bb294af68cb 100644 --- a/examples/tree_1d_dgsem/elixir_mhd_briowu_shock_tube.jl +++ b/examples/tree_1d_dgsem/elixir_mhd_briowu_shock_tube.jl @@ -17,46 +17,44 @@ MHD extension of the Sod shock tube. Taken from Section V of the article [DOI: 10.1016/0021-9991(88)90120-9](https://doi.org/10.1016/0021-9991(88)90120-9) """ function initial_condition_briowu_shock_tube(x, t, equations::IdealGlmMhdEquations1D) - # domain must be set to [0, 1], γ = 2, final time = 0.12 - rho = x[1] < 0.5 ? 1.0 : 0.125 - v1 = 0.0 - v2 = 0.0 - v3 = 0.0 - p = x[1] < 0.5 ? 1.0 : 0.1 - B1 = 0.75 - B2 = x[1] < 0.5 ? 1.0 : -1.0 - B3 = 0.0 - return prim2cons(SVector(rho, v1, v2, v3, p, B1, B2, B3), equations) + # domain must be set to [0, 1], γ = 2, final time = 0.12 + rho = x[1] < 0.5 ? 1.0 : 0.125 + v1 = 0.0 + v2 = 0.0 + v3 = 0.0 + p = x[1] < 0.5 ? 1.0 : 0.1 + B1 = 0.75 + B2 = x[1] < 0.5 ? 1.0 : -1.0 + B3 = 0.0 + return prim2cons(SVector(rho, v1, v2, v3, p, B1, B2, B3), equations) end initial_condition = initial_condition_briowu_shock_tube boundary_conditions = BoundaryConditionDirichlet(initial_condition) surface_flux = flux_hll -volume_flux = flux_derigs_etal +volume_flux = flux_derigs_etal basis = LobattoLegendreBasis(4) indicator_sc = IndicatorHennemannGassner(equations, basis, - alpha_max=0.5, - alpha_min=0.001, - alpha_smooth=true, - variable=density_pressure) + alpha_max = 0.5, + alpha_min = 0.001, + alpha_smooth = true, + variable = density_pressure) volume_integral = VolumeIntegralShockCapturingHG(indicator_sc; - volume_flux_dg=volume_flux, - volume_flux_fv=surface_flux) + volume_flux_dg = volume_flux, + volume_flux_fv = surface_flux) solver = DGSEM(basis, surface_flux, volume_integral) coordinates_min = 0.0 coordinates_max = 1.0 mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=4, - n_cells_max=10_000, - periodicity=false) - + initial_refinement_level = 4, + n_cells_max = 10_000, + periodicity = false) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver, - boundary_conditions=boundary_conditions) - + boundary_conditions = boundary_conditions) ############################################################################### # ODE solvers, callbacks etc. @@ -67,45 +65,44 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval, - extra_analysis_errors=(:l2_error_primitive, - :linf_error_primitive)) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval, + extra_analysis_errors = (:l2_error_primitive, + :linf_error_primitive)) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_restart = SaveRestartCallback(interval=100, - save_final_restart=true) +save_restart = SaveRestartCallback(interval = 100, + save_final_restart = true) -save_solution = SaveSolutionCallback(interval=100, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 100, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) amr_indicator = IndicatorHennemannGassner(semi, - alpha_max=0.5, - alpha_min=0.001, - alpha_smooth=true, - variable=density_pressure) + alpha_max = 0.5, + alpha_min = 0.001, + alpha_smooth = true, + variable = density_pressure) amr_controller = ControllerThreeLevel(semi, amr_indicator, - base_level=4, - max_level=6, max_threshold=0.01) + base_level = 4, + max_level = 6, max_threshold = 0.01) amr_callback = AMRCallback(semi, amr_controller, - interval=5, - adapt_initial_condition=true, - adapt_initial_condition_only_refine=true) + interval = 5, + adapt_initial_condition = true, + adapt_initial_condition_only_refine = true) -stepsize_callback = StepsizeCallback(cfl=0.65) +stepsize_callback = StepsizeCallback(cfl = 0.65) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, save_restart, save_solution, amr_callback, stepsize_callback) - ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/tree_1d_dgsem/elixir_mhd_ec.jl b/examples/tree_1d_dgsem/elixir_mhd_ec.jl index 1f2e77006b1..e5da808f696 100644 --- a/examples/tree_1d_dgsem/elixir_mhd_ec.jl +++ b/examples/tree_1d_dgsem/elixir_mhd_ec.jl @@ -10,19 +10,17 @@ equations = IdealGlmMhdEquations1D(gamma) initial_condition = initial_condition_weak_blast_wave volume_flux = flux_hindenlang_gassner -solver = DGSEM(polydeg=3, surface_flux=flux_hindenlang_gassner, - volume_integral=VolumeIntegralFluxDifferencing(volume_flux)) +solver = DGSEM(polydeg = 3, surface_flux = flux_hindenlang_gassner, + volume_integral = VolumeIntegralFluxDifferencing(volume_flux)) coordinates_min = 0.0 coordinates_max = 1.0 mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=4, - n_cells_max=10_000) - + initial_refinement_level = 4, + n_cells_max = 10_000) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver) - ############################################################################### # ODE solvers, callbacks etc. @@ -32,29 +30,28 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval, - extra_analysis_errors=(:l2_error_primitive, - :linf_error_primitive)) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval, + extra_analysis_errors = (:l2_error_primitive, + :linf_error_primitive)) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=100, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 100, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) -stepsize_callback = StepsizeCallback(cfl=0.5) +stepsize_callback = StepsizeCallback(cfl = 0.5) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, save_solution, stepsize_callback) - ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/tree_1d_dgsem/elixir_mhd_ryujones_shock_tube.jl b/examples/tree_1d_dgsem/elixir_mhd_ryujones_shock_tube.jl index 010788d48f5..b6f856fbc64 100644 --- a/examples/tree_1d_dgsem/elixir_mhd_ryujones_shock_tube.jl +++ b/examples/tree_1d_dgsem/elixir_mhd_ryujones_shock_tube.jl @@ -4,7 +4,7 @@ using Trixi ############################################################################### # semidiscretization of the ideal MHD equations -gamma = 5/3 +gamma = 5 / 3 equations = IdealGlmMhdEquations1D(gamma) """ @@ -22,48 +22,46 @@ present in the one dimensional MHD equations. It is the second test from Section This paper has a typo in the initial conditions. Their variable `E` should be `p`. """ function initial_condition_ryujones_shock_tube(x, t, equations::IdealGlmMhdEquations1D) - # domain must be set to [0, 1], γ = 5/3, final time = 0.2 - rho = x[1] <= 0.5 ? 1.08 : 1.0 - v1 = x[1] <= 0.5 ? 1.2 : 0.0 - v2 = x[1] <= 0.5 ? 0.01 : 0.0 - v3 = x[1] <= 0.5 ? 0.5 : 0.0 - p = x[1] <= 0.5 ? 0.95 : 1.0 - inv_sqrt4pi = 1.0 / sqrt(4 * pi) - B1 = 2 * inv_sqrt4pi - B2 = x[1] <= 0.5 ? 3.6 * inv_sqrt4pi : 4.0 * inv_sqrt4pi - B3 = B1 - - return prim2cons(SVector(rho, v1, v2, v3, p, B1, B2, B3), equations) + # domain must be set to [0, 1], γ = 5/3, final time = 0.2 + rho = x[1] <= 0.5 ? 1.08 : 1.0 + v1 = x[1] <= 0.5 ? 1.2 : 0.0 + v2 = x[1] <= 0.5 ? 0.01 : 0.0 + v3 = x[1] <= 0.5 ? 0.5 : 0.0 + p = x[1] <= 0.5 ? 0.95 : 1.0 + inv_sqrt4pi = 1.0 / sqrt(4 * pi) + B1 = 2 * inv_sqrt4pi + B2 = x[1] <= 0.5 ? 3.6 * inv_sqrt4pi : 4.0 * inv_sqrt4pi + B3 = B1 + + return prim2cons(SVector(rho, v1, v2, v3, p, B1, B2, B3), equations) end initial_condition = initial_condition_ryujones_shock_tube boundary_conditions = BoundaryConditionDirichlet(initial_condition) surface_flux = flux_hll -volume_flux = flux_hindenlang_gassner +volume_flux = flux_hindenlang_gassner basis = LobattoLegendreBasis(3) indicator_sc = IndicatorHennemannGassner(equations, basis, - alpha_max=0.5, - alpha_min=0.001, - alpha_smooth=true, - variable=Trixi.density) + alpha_max = 0.5, + alpha_min = 0.001, + alpha_smooth = true, + variable = Trixi.density) volume_integral = VolumeIntegralShockCapturingHG(indicator_sc; - volume_flux_dg=volume_flux, - volume_flux_fv=surface_flux) + volume_flux_dg = volume_flux, + volume_flux_fv = surface_flux) solver = DGSEM(basis, surface_flux, volume_integral) coordinates_min = 0.0 coordinates_max = 1.0 mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=7, - n_cells_max=10_000, - periodicity=false) - + initial_refinement_level = 7, + n_cells_max = 10_000, + periodicity = false) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver, - boundary_conditions=boundary_conditions) - + boundary_conditions = boundary_conditions) ############################################################################### # ODE solvers, callbacks etc. @@ -74,27 +72,26 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=100, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 100, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) -stepsize_callback = StepsizeCallback(cfl=0.8) +stepsize_callback = StepsizeCallback(cfl = 0.8) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, save_solution, stepsize_callback) - ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/tree_1d_dgsem/elixir_mhd_shu_osher_shock_tube.jl b/examples/tree_1d_dgsem/elixir_mhd_shu_osher_shock_tube.jl index 8c60b449e90..8c0317277b0 100644 --- a/examples/tree_1d_dgsem/elixir_mhd_shu_osher_shock_tube.jl +++ b/examples/tree_1d_dgsem/elixir_mhd_shu_osher_shock_tube.jl @@ -4,7 +4,7 @@ using Trixi ############################################################################### # semidiscretization of the ideal MHD equations -gamma = 5/3 +gamma = 5 / 3 equations = IdealGlmMhdEquations1D(gamma) """ @@ -17,19 +17,19 @@ Taken from Section 4.1 of [DOI: 10.1016/j.jcp.2016.04.048](https://doi.org/10.1016/j.jcp.2016.04.048) """ function initial_condition_shu_osher_shock_tube(x, t, equations::IdealGlmMhdEquations1D) - # domain must be set to [-5, 5], γ = 5/3, final time = 0.7 - # initial shock location is taken to be at x = -4 - x_0 = -4.0 - rho = x[1] <= x_0 ? 3.5 : 1.0 + 0.2 * sin(5.0 * x[1]) - v1 = x[1] <= x_0 ? 5.8846 : 0.0 - v2 = x[1] <= x_0 ? 1.1198 : 0.0 - v3 = 0.0 - p = x[1] <= x_0 ? 42.0267 : 1.0 - B1 = 1.0 - B2 = x[1] <= x_0 ? 3.6359 : 1.0 - B3 = 0.0 - - return prim2cons(SVector(rho, v1, v2, v3, p, B1, B2, B3), equations) + # domain must be set to [-5, 5], γ = 5/3, final time = 0.7 + # initial shock location is taken to be at x = -4 + x_0 = -4.0 + rho = x[1] <= x_0 ? 3.5 : 1.0 + 0.2 * sin(5.0 * x[1]) + v1 = x[1] <= x_0 ? 5.8846 : 0.0 + v2 = x[1] <= x_0 ? 1.1198 : 0.0 + v3 = 0.0 + p = x[1] <= x_0 ? 42.0267 : 1.0 + B1 = 1.0 + B2 = x[1] <= x_0 ? 3.6359 : 1.0 + B3 = 0.0 + + return prim2cons(SVector(rho, v1, v2, v3, p, B1, B2, B3), equations) end """ @@ -41,50 +41,49 @@ but shock propagates from right to left. !!! note This is useful to exercise some of the components of the HLL flux. """ -function initial_condition_shu_osher_shock_tube_flipped(x, t, equations::IdealGlmMhdEquations1D) - # domain must be set to [-5, 5], γ = 5/3, final time = 0.7 - # initial shock location is taken to be at x = 4 - x_0 = 4.0 - rho = x[1] <= x_0 ? 1.0 + 0.2 * sin(5.0 * x[1]) : 3.5 - v1 = x[1] <= x_0 ? 0.0 : -5.8846 - v2 = x[1] <= x_0 ? 0.0 : -1.1198 - v3 = 0.0 - p = x[1] <= x_0 ? 1.0 : 42.0267 - B1 = 1.0 - B2 = x[1] <= x_0 ? 1.0 : 3.6359 - B3 = 0.0 - - return prim2cons(SVector(rho, v1, v2, v3, p, B1, B2, B3), equations) +function initial_condition_shu_osher_shock_tube_flipped(x, t, + equations::IdealGlmMhdEquations1D) + # domain must be set to [-5, 5], γ = 5/3, final time = 0.7 + # initial shock location is taken to be at x = 4 + x_0 = 4.0 + rho = x[1] <= x_0 ? 1.0 + 0.2 * sin(5.0 * x[1]) : 3.5 + v1 = x[1] <= x_0 ? 0.0 : -5.8846 + v2 = x[1] <= x_0 ? 0.0 : -1.1198 + v3 = 0.0 + p = x[1] <= x_0 ? 1.0 : 42.0267 + B1 = 1.0 + B2 = x[1] <= x_0 ? 1.0 : 3.6359 + B3 = 0.0 + + return prim2cons(SVector(rho, v1, v2, v3, p, B1, B2, B3), equations) end initial_condition = initial_condition_shu_osher_shock_tube boundary_conditions = BoundaryConditionDirichlet(initial_condition) surface_flux = flux_hll -volume_flux = flux_hindenlang_gassner +volume_flux = flux_hindenlang_gassner basis = LobattoLegendreBasis(4) indicator_sc = IndicatorHennemannGassner(equations, basis, - alpha_max=0.5, - alpha_min=0.001, - alpha_smooth=true, - variable=density_pressure) + alpha_max = 0.5, + alpha_min = 0.001, + alpha_smooth = true, + variable = density_pressure) volume_integral = VolumeIntegralShockCapturingHG(indicator_sc; - volume_flux_dg=volume_flux, - volume_flux_fv=surface_flux) + volume_flux_dg = volume_flux, + volume_flux_fv = surface_flux) solver = DGSEM(basis, surface_flux, volume_integral) coordinates_min = -5.0 -coordinates_max = 5.0 +coordinates_max = 5.0 mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=4, - n_cells_max=10_000, - periodicity=false) - + initial_refinement_level = 4, + n_cells_max = 10_000, + periodicity = false) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver, - boundary_conditions=boundary_conditions) - + boundary_conditions = boundary_conditions) ############################################################################### # ODE solvers, callbacks etc. @@ -95,42 +94,43 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval, - extra_analysis_integrals=(energy_kinetic, energy_internal, - energy_magnetic, cross_helicity)) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval, + extra_analysis_integrals = (energy_kinetic, + energy_internal, + energy_magnetic, + cross_helicity)) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=100, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 100, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) amr_indicator = IndicatorHennemannGassner(semi, - alpha_max=0.5, - alpha_min=0.001, - alpha_smooth=true, - variable=density_pressure) + alpha_max = 0.5, + alpha_min = 0.001, + alpha_smooth = true, + variable = density_pressure) amr_controller = ControllerThreeLevel(semi, amr_indicator, - base_level=4, - max_level=7, max_threshold=0.01) + base_level = 4, + max_level = 7, max_threshold = 0.01) amr_callback = AMRCallback(semi, amr_controller, - interval=5, - adapt_initial_condition=true, - adapt_initial_condition_only_refine=true) + interval = 5, + adapt_initial_condition = true, + adapt_initial_condition_only_refine = true) -stepsize_callback = StepsizeCallback(cfl=0.8) +stepsize_callback = StepsizeCallback(cfl = 0.8) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, save_solution, amr_callback, stepsize_callback) - ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/tree_1d_dgsem/elixir_mhd_torrilhon_shock_tube.jl b/examples/tree_1d_dgsem/elixir_mhd_torrilhon_shock_tube.jl index 68556764293..3b366c35e0f 100644 --- a/examples/tree_1d_dgsem/elixir_mhd_torrilhon_shock_tube.jl +++ b/examples/tree_1d_dgsem/elixir_mhd_torrilhon_shock_tube.jl @@ -4,7 +4,7 @@ using Trixi ############################################################################### # semidiscretization of the ideal MHD equations -gamma = 5/3 +gamma = 5 / 3 equations = IdealGlmMhdEquations1D(gamma) """ @@ -16,46 +16,44 @@ Torrilhon's shock tube test case for one dimensional ideal MHD equations. [DOI: 10.1017/S0022377803002186](https://doi.org/10.1017/S0022377803002186) """ function initial_condition_torrilhon_shock_tube(x, t, equations::IdealGlmMhdEquations1D) - # domain must be set to [-1, 1.5], γ = 5/3, final time = 0.4 - rho = x[1] <= 0 ? 3.0 : 1.0 - v1 = 0.0 - v2 = 0.0 - v3 = 0.0 - p = x[1] <= 0 ? 3.0 : 1.0 - B1 = 1.5 - B2 = x[1] <= 0 ? 1.0 : cos(1.5) - B3 = x[1] <= 0 ? 0.0 : sin(1.5) - return prim2cons(SVector(rho, v1, v2, v3, p, B1, B2, B3), equations) + # domain must be set to [-1, 1.5], γ = 5/3, final time = 0.4 + rho = x[1] <= 0 ? 3.0 : 1.0 + v1 = 0.0 + v2 = 0.0 + v3 = 0.0 + p = x[1] <= 0 ? 3.0 : 1.0 + B1 = 1.5 + B2 = x[1] <= 0 ? 1.0 : cos(1.5) + B3 = x[1] <= 0 ? 0.0 : sin(1.5) + return prim2cons(SVector(rho, v1, v2, v3, p, B1, B2, B3), equations) end initial_condition = initial_condition_torrilhon_shock_tube boundary_conditions = BoundaryConditionDirichlet(initial_condition) surface_flux = flux_lax_friedrichs -volume_flux = flux_central +volume_flux = flux_central basis = LobattoLegendreBasis(3) indicator_sc = IndicatorHennemannGassner(equations, basis, - alpha_max=0.5, - alpha_min=0.001, - alpha_smooth=true, - variable=pressure) + alpha_max = 0.5, + alpha_min = 0.001, + alpha_smooth = true, + variable = pressure) volume_integral = VolumeIntegralShockCapturingHG(indicator_sc; - volume_flux_dg=volume_flux, - volume_flux_fv=surface_flux) + volume_flux_dg = volume_flux, + volume_flux_fv = surface_flux) solver = DGSEM(basis, surface_flux, volume_integral) coordinates_min = -1.0 -coordinates_max = 1.5 +coordinates_max = 1.5 mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=7, - n_cells_max=10_000, - periodicity=false) - + initial_refinement_level = 7, + n_cells_max = 10_000, + periodicity = false) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver, - boundary_conditions=boundary_conditions) - + boundary_conditions = boundary_conditions) ############################################################################### # ODE solvers, callbacks etc. @@ -66,29 +64,28 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval, - extra_analysis_errors=(:l2_error_primitive, - :linf_error_primitive)) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval, + extra_analysis_errors = (:l2_error_primitive, + :linf_error_primitive)) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=100, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 100, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) -stepsize_callback = StepsizeCallback(cfl=1.0) +stepsize_callback = StepsizeCallback(cfl = 1.0) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, save_solution, stepsize_callback) - ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/tree_1d_dgsem/elixir_mhdmulti_briowu_shock_tube.jl b/examples/tree_1d_dgsem/elixir_mhdmulti_briowu_shock_tube.jl index 376f11d52a2..831fa7afedb 100644 --- a/examples/tree_1d_dgsem/elixir_mhdmulti_briowu_shock_tube.jl +++ b/examples/tree_1d_dgsem/elixir_mhdmulti_briowu_shock_tube.jl @@ -4,8 +4,8 @@ using Trixi ############################################################################### # semidiscretization of the ideal MHD equations -equations = IdealGlmMhdMulticomponentEquations1D(gammas = (2.0, 2.0), - gas_constants = (2.0, 2.0)) +equations = IdealGlmMhdMulticomponentEquations1D(gammas = (2.0, 2.0), + gas_constants = (2.0, 2.0)) """ initial_condition_briowu_shock_tube(x, t, equations::IdealGlmMhdMulticomponentEquations1D) @@ -16,55 +16,62 @@ MHD extension of the Sod shock tube. Taken from Section V of the article An Upwind Differencing Scheme for the Equations of Ideal Magnetohydrodynamics [DOI: 10.1016/0021-9991(88)90120-9](https://doi.org/10.1016/0021-9991(88)90120-9) """ -function initial_condition_briowu_shock_tube(x, t, equations::IdealGlmMhdMulticomponentEquations1D) - # domain must be set to [0, 1], γ = 2, final time = 0.12 - if x[1] < 0.5 - rho = 1.0 - prim_rho = SVector{ncomponents(equations), real(equations)}(2^(i-1) * (1-2)/(1-2^ncomponents(equations)) * rho for i in eachcomponent(equations)) - else - rho = 0.125 - prim_rho = SVector{ncomponents(equations), real(equations)}(2^(i-1) * (1-2)/(1-2^ncomponents(equations)) * rho for i in eachcomponent(equations)) - end - v1 = 0.0 - v2 = 0.0 - v3 = 0.0 - p = x[1] < 0.5 ? 1.0 : 0.1 - B1 = 0.75 - B2 = x[1] < 0.5 ? 1.0 : -1.0 - B3 = 0.0 - - prim_other = SVector(v1, v2, v3, p, B1, B2, B3) - return prim2cons(vcat(prim_other, prim_rho), equations) +function initial_condition_briowu_shock_tube(x, t, + equations::IdealGlmMhdMulticomponentEquations1D) + # domain must be set to [0, 1], γ = 2, final time = 0.12 + if x[1] < 0.5 + rho = 1.0 + prim_rho = SVector{ncomponents(equations), real(equations)}(2^(i - 1) * (1 - 2) / + (1 - + 2^ncomponents(equations)) * + rho + for i in eachcomponent(equations)) + else + rho = 0.125 + prim_rho = SVector{ncomponents(equations), real(equations)}(2^(i - 1) * (1 - 2) / + (1 - + 2^ncomponents(equations)) * + rho + for i in eachcomponent(equations)) + end + v1 = 0.0 + v2 = 0.0 + v3 = 0.0 + p = x[1] < 0.5 ? 1.0 : 0.1 + B1 = 0.75 + B2 = x[1] < 0.5 ? 1.0 : -1.0 + B3 = 0.0 + + prim_other = SVector(v1, v2, v3, p, B1, B2, B3) + return prim2cons(vcat(prim_other, prim_rho), equations) end initial_condition = initial_condition_briowu_shock_tube boundary_conditions = BoundaryConditionDirichlet(initial_condition) surface_flux = flux_lax_friedrichs -volume_flux = flux_hindenlang_gassner +volume_flux = flux_hindenlang_gassner basis = LobattoLegendreBasis(3) indicator_sc = IndicatorHennemannGassner(equations, basis, - alpha_max=0.8, - alpha_min=0.001, - alpha_smooth=true, - variable=density_pressure) + alpha_max = 0.8, + alpha_min = 0.001, + alpha_smooth = true, + variable = density_pressure) volume_integral = VolumeIntegralShockCapturingHG(indicator_sc; - volume_flux_dg=volume_flux, - volume_flux_fv=surface_flux) + volume_flux_dg = volume_flux, + volume_flux_fv = surface_flux) solver = DGSEM(basis, surface_flux, volume_integral) coordinates_min = 0.0 coordinates_max = 1.0 mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=4, - n_cells_max=10_000, - periodicity=false) - + initial_refinement_level = 4, + n_cells_max = 10_000, + periodicity = false) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver, - boundary_conditions=boundary_conditions) - + boundary_conditions = boundary_conditions) ############################################################################### # ODE solvers, callbacks etc. @@ -75,45 +82,44 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval, - extra_analysis_errors=(:l2_error_primitive, - :linf_error_primitive)) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval, + extra_analysis_errors = (:l2_error_primitive, + :linf_error_primitive)) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_restart = SaveRestartCallback(interval=100, - save_final_restart=true) +save_restart = SaveRestartCallback(interval = 100, + save_final_restart = true) -save_solution = SaveSolutionCallback(interval=100, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 100, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) amr_indicator = IndicatorHennemannGassner(semi, - alpha_max=0.5, - alpha_min=0.001, - alpha_smooth=true, - variable=density_pressure) + alpha_max = 0.5, + alpha_min = 0.001, + alpha_smooth = true, + variable = density_pressure) amr_controller = ControllerThreeLevel(semi, amr_indicator, - base_level=4, - max_level=6, max_threshold=0.01) + base_level = 4, + max_level = 6, max_threshold = 0.01) amr_callback = AMRCallback(semi, amr_controller, - interval=5, - adapt_initial_condition=true, - adapt_initial_condition_only_refine=true) + interval = 5, + adapt_initial_condition = true, + adapt_initial_condition_only_refine = true) -stepsize_callback = StepsizeCallback(cfl=0.5) +stepsize_callback = StepsizeCallback(cfl = 0.5) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, save_restart, save_solution, amr_callback, stepsize_callback) - ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/tree_1d_dgsem/elixir_mhdmulti_convergence.jl b/examples/tree_1d_dgsem/elixir_mhdmulti_convergence.jl index 573bf6bc3e9..a1636c08478 100644 --- a/examples/tree_1d_dgsem/elixir_mhdmulti_convergence.jl +++ b/examples/tree_1d_dgsem/elixir_mhdmulti_convergence.jl @@ -5,25 +5,23 @@ using Trixi ############################################################################### # semidiscretization of the compressible ideal GLM-MHD equations -equations = IdealGlmMhdMulticomponentEquations1D(gammas = (5/3, 5/3, 5/3), - gas_constants = (2.08, 2.08, 2.08)) +equations = IdealGlmMhdMulticomponentEquations1D(gammas = (5 / 3, 5 / 3, 5 / 3), + gas_constants = (2.08, 2.08, 2.08)) initial_condition = initial_condition_convergence_test volume_flux = flux_hindenlang_gassner -solver = DGSEM(polydeg=3, surface_flux=flux_lax_friedrichs, - volume_integral=VolumeIntegralFluxDifferencing(volume_flux)) +solver = DGSEM(polydeg = 3, surface_flux = flux_lax_friedrichs, + volume_integral = VolumeIntegralFluxDifferencing(volume_flux)) coordinates_min = 0.0 coordinates_max = 1.0 mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=2, - n_cells_max=10_000) - + initial_refinement_level = 2, + n_cells_max = 10_000) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver) - ############################################################################### # ODE solvers, callbacks etc. @@ -33,17 +31,18 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval, save_analysis=true) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval, + save_analysis = true) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=10, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 10, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) cfl = 0.5 -stepsize_callback = StepsizeCallback(cfl=cfl) +stepsize_callback = StepsizeCallback(cfl = cfl) callbacks = CallbackSet(summary_callback, analysis_callback, @@ -51,11 +50,10 @@ callbacks = CallbackSet(summary_callback, save_solution, stepsize_callback) - ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/tree_1d_dgsem/elixir_mhdmulti_ec.jl b/examples/tree_1d_dgsem/elixir_mhdmulti_ec.jl index 69ea0551bed..71466f3138a 100644 --- a/examples/tree_1d_dgsem/elixir_mhdmulti_ec.jl +++ b/examples/tree_1d_dgsem/elixir_mhdmulti_ec.jl @@ -4,25 +4,23 @@ using Trixi ############################################################################### # semidiscretization of the ideal MHD equations -equations = IdealGlmMhdMulticomponentEquations1D(gammas = (2.0, 2.0, 2.0), +equations = IdealGlmMhdMulticomponentEquations1D(gammas = (2.0, 2.0, 2.0), gas_constants = (2.0, 2.0, 2.0)) initial_condition = initial_condition_weak_blast_wave volume_flux = flux_hindenlang_gassner -solver = DGSEM(polydeg=3, surface_flux=flux_hindenlang_gassner, - volume_integral=VolumeIntegralFluxDifferencing(volume_flux)) +solver = DGSEM(polydeg = 3, surface_flux = flux_hindenlang_gassner, + volume_integral = VolumeIntegralFluxDifferencing(volume_flux)) coordinates_min = 0.0 coordinates_max = 1.0 mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=4, - n_cells_max=10_000) - + initial_refinement_level = 4, + n_cells_max = 10_000) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver) - ############################################################################### # ODE solvers, callbacks etc. @@ -32,26 +30,25 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=100, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 100, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) -stepsize_callback = StepsizeCallback(cfl=0.5) +stepsize_callback = StepsizeCallback(cfl = 0.5) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, save_solution, stepsize_callback) - ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/tree_1d_dgsem/elixir_mhdmulti_es.jl b/examples/tree_1d_dgsem/elixir_mhdmulti_es.jl index 93cf3e0fdb2..37623e048ed 100644 --- a/examples/tree_1d_dgsem/elixir_mhdmulti_es.jl +++ b/examples/tree_1d_dgsem/elixir_mhdmulti_es.jl @@ -4,25 +4,23 @@ using Trixi ############################################################################### # semidiscretization of the ideal MHD equations -equations = IdealGlmMhdMulticomponentEquations1D(gammas = (2.0, 2.0, 2.0), +equations = IdealGlmMhdMulticomponentEquations1D(gammas = (2.0, 2.0, 2.0), gas_constants = (2.0, 2.0, 2.0)) initial_condition = initial_condition_weak_blast_wave volume_flux = flux_hindenlang_gassner -solver = DGSEM(polydeg=3, surface_flux=flux_lax_friedrichs, - volume_integral=VolumeIntegralFluxDifferencing(volume_flux)) +solver = DGSEM(polydeg = 3, surface_flux = flux_lax_friedrichs, + volume_integral = VolumeIntegralFluxDifferencing(volume_flux)) coordinates_min = 0.0 coordinates_max = 1.0 mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=4, - n_cells_max=10_000) - + initial_refinement_level = 4, + n_cells_max = 10_000) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver) - ############################################################################### # ODE solvers, callbacks etc. @@ -32,29 +30,28 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval, - extra_analysis_errors=(:l2_error_primitive, - :linf_error_primitive)) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval, + extra_analysis_errors = (:l2_error_primitive, + :linf_error_primitive)) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=100, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 100, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) -stepsize_callback = StepsizeCallback(cfl=0.5) +stepsize_callback = StepsizeCallback(cfl = 0.5) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, save_solution, stepsize_callback) - ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/tree_1d_dgsem/elixir_navierstokes_convergence_periodic.jl b/examples/tree_1d_dgsem/elixir_navierstokes_convergence_periodic.jl index 3f72d319b0b..33ad0d5271c 100644 --- a/examples/tree_1d_dgsem/elixir_navierstokes_convergence_periodic.jl +++ b/examples/tree_1d_dgsem/elixir_navierstokes_convergence_periodic.jl @@ -10,101 +10,101 @@ prandtl_number() = 0.72 mu() = 6.25e-4 # equivalent to Re = 1600 equations = CompressibleEulerEquations1D(1.4) -equations_parabolic = CompressibleNavierStokesDiffusion1D(equations, mu=mu(), - Prandtl=prandtl_number()) +equations_parabolic = CompressibleNavierStokesDiffusion1D(equations, mu = mu(), + Prandtl = prandtl_number()) # This convergence test setup was originally derived by Andrew Winters (@andrewwinters5000) # (Simplified version of the 2D) function initial_condition_navier_stokes_convergence_test(x, t, equations) - # Amplitude and shift - A = 0.5 - c = 2.0 + # Amplitude and shift + A = 0.5 + c = 2.0 - # convenience values for trig. functions - pi_x = pi * x[1] - pi_t = pi * t + # convenience values for trig. functions + pi_x = pi * x[1] + pi_t = pi * t - rho = c + A * sin(pi_x) * cos(pi_t) - v1 = sin(pi_x) * cos(pi_t) - p = rho^2 + rho = c + A * sin(pi_x) * cos(pi_t) + v1 = sin(pi_x) * cos(pi_t) + p = rho^2 - return prim2cons(SVector(rho, v1, p), equations) + return prim2cons(SVector(rho, v1, p), equations) end initial_condition = initial_condition_navier_stokes_convergence_test @inline function source_terms_navier_stokes_convergence_test(u, x, t, equations) - # we currently need to hardcode these parameters until we fix the "combined equation" issue - # see also https://github.com/trixi-framework/Trixi.jl/pull/1160 - inv_gamma_minus_one = inv(equations.gamma - 1) - Pr = prandtl_number() - mu_ = mu() - - # Same settings as in `initial_condition` - # Amplitude and shift - A = 0.5 - c = 2.0 - - # convenience values for trig. functions - pi_x = pi * x[1] - pi_t = pi * t - - # compute the manufactured solution and all necessary derivatives - rho = c + A * sin(pi_x) * cos(pi_t) - rho_t = -pi * A * sin(pi_x) * sin(pi_t) - rho_x = pi * A * cos(pi_x) * cos(pi_t) - rho_xx = -pi * pi * A * sin(pi_x) * cos(pi_t) - - v1 = sin(pi_x) * cos(pi_t) - v1_t = -pi * sin(pi_x) * sin(pi_t) - v1_x = pi * cos(pi_x) * cos(pi_t) - v1_xx = -pi * pi * sin(pi_x) * cos(pi_t) - - p = rho * rho - p_t = 2.0 * rho * rho_t - p_x = 2.0 * rho * rho_x - p_xx = 2.0 * rho * rho_xx + 2.0 * rho_x * rho_x - - E = p * inv_gamma_minus_one + 0.5 * rho * v1^2 - E_t = p_t * inv_gamma_minus_one + 0.5 * rho_t * v1^2 + rho * v1 * v1_t - E_x = p_x * inv_gamma_minus_one + 0.5 * rho_x * v1^2 + rho * v1 * v1_x - - # Some convenience constants - T_const = equations.gamma * inv_gamma_minus_one / Pr - inv_rho_cubed = 1.0 / (rho^3) - - # compute the source terms - # density equation - du1 = rho_t + rho_x * v1 + rho * v1_x - - # x-momentum equation - du2 = ( rho_t * v1 + rho * v1_t - + p_x + rho_x * v1^2 + 2.0 * rho * v1 * v1_x - # stress tensor from x-direction - - v1_xx * mu_) - - # total energy equation - du3 = ( E_t + v1_x * (E + p) + v1 * (E_x + p_x) - # stress tensor and temperature gradient terms from x-direction - - v1_xx * v1 * mu_ - - v1_x * v1_x * mu_ - - T_const * inv_rho_cubed * ( p_xx * rho * rho - - 2.0 * p_x * rho * rho_x - + 2.0 * p * rho_x * rho_x - - p * rho * rho_xx ) * mu_) - - return SVector(du1, du2, du3) + # we currently need to hardcode these parameters until we fix the "combined equation" issue + # see also https://github.com/trixi-framework/Trixi.jl/pull/1160 + inv_gamma_minus_one = inv(equations.gamma - 1) + Pr = prandtl_number() + mu_ = mu() + + # Same settings as in `initial_condition` + # Amplitude and shift + A = 0.5 + c = 2.0 + + # convenience values for trig. functions + pi_x = pi * x[1] + pi_t = pi * t + + # compute the manufactured solution and all necessary derivatives + rho = c + A * sin(pi_x) * cos(pi_t) + rho_t = -pi * A * sin(pi_x) * sin(pi_t) + rho_x = pi * A * cos(pi_x) * cos(pi_t) + rho_xx = -pi * pi * A * sin(pi_x) * cos(pi_t) + + v1 = sin(pi_x) * cos(pi_t) + v1_t = -pi * sin(pi_x) * sin(pi_t) + v1_x = pi * cos(pi_x) * cos(pi_t) + v1_xx = -pi * pi * sin(pi_x) * cos(pi_t) + + p = rho * rho + p_t = 2.0 * rho * rho_t + p_x = 2.0 * rho * rho_x + p_xx = 2.0 * rho * rho_xx + 2.0 * rho_x * rho_x + + E = p * inv_gamma_minus_one + 0.5 * rho * v1^2 + E_t = p_t * inv_gamma_minus_one + 0.5 * rho_t * v1^2 + rho * v1 * v1_t + E_x = p_x * inv_gamma_minus_one + 0.5 * rho_x * v1^2 + rho * v1 * v1_x + + # Some convenience constants + T_const = equations.gamma * inv_gamma_minus_one / Pr + inv_rho_cubed = 1.0 / (rho^3) + + # compute the source terms + # density equation + du1 = rho_t + rho_x * v1 + rho * v1_x + + # x-momentum equation + du2 = (rho_t * v1 + rho * v1_t + + p_x + rho_x * v1^2 + 2.0 * rho * v1 * v1_x - + # stress tensor from x-direction + v1_xx * mu_) + + # total energy equation + du3 = (E_t + v1_x * (E + p) + v1 * (E_x + p_x) - + # stress tensor and temperature gradient terms from x-direction + v1_xx * v1 * mu_ - + v1_x * v1_x * mu_ - + T_const * inv_rho_cubed * + (p_xx * rho * rho - + 2.0 * p_x * rho * rho_x + + 2.0 * p * rho_x * rho_x - + p * rho * rho_xx) * mu_) + + return SVector(du1, du2, du3) end volume_flux = flux_ranocha -solver = DGSEM(polydeg=3, surface_flux=flux_hllc, - volume_integral=VolumeIntegralFluxDifferencing(volume_flux)) +solver = DGSEM(polydeg = 3, surface_flux = flux_hllc, + volume_integral = VolumeIntegralFluxDifferencing(volume_flux)) coordinates_min = -1.0 -coordinates_max = 1.0 +coordinates_max = 1.0 mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=4, - n_cells_max=100_000) - + initial_refinement_level = 4, + n_cells_max = 100_000) semi = SemidiscretizationHyperbolicParabolic(mesh, (equations, equations_parabolic), initial_condition, solver, @@ -119,9 +119,9 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 1000 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) -alive_callback = AliveCallback(analysis_interval=analysis_interval,) +alive_callback = AliveCallback(analysis_interval = analysis_interval) callbacks = CallbackSet(summary_callback, analysis_callback, @@ -131,6 +131,6 @@ callbacks = CallbackSet(summary_callback, # run the simulation time_int_tol = 1e-9 -sol = solve(ode, RDPK3SpFSAL49(); abstol=time_int_tol, reltol=time_int_tol, - ode_default_options()..., callback=callbacks) -summary_callback() # print the timer summary \ No newline at end of file +sol = solve(ode, RDPK3SpFSAL49(); abstol = time_int_tol, reltol = time_int_tol, + ode_default_options()..., callback = callbacks) +summary_callback() # print the timer summary diff --git a/examples/tree_1d_dgsem/elixir_navierstokes_convergence_walls.jl b/examples/tree_1d_dgsem/elixir_navierstokes_convergence_walls.jl index 181a2cb209f..40030d53345 100644 --- a/examples/tree_1d_dgsem/elixir_navierstokes_convergence_walls.jl +++ b/examples/tree_1d_dgsem/elixir_navierstokes_convergence_walls.jl @@ -8,135 +8,145 @@ prandtl_number() = 0.72 mu() = 0.01 equations = CompressibleEulerEquations1D(1.4) -equations_parabolic = CompressibleNavierStokesDiffusion1D(equations, mu=mu(), Prandtl=prandtl_number(), - gradient_variables=GradientVariablesPrimitive()) +equations_parabolic = CompressibleNavierStokesDiffusion1D(equations, mu = mu(), + Prandtl = prandtl_number(), + gradient_variables = GradientVariablesPrimitive()) # Create DG solver with polynomial degree = 3 and (local) Lax-Friedrichs/Rusanov flux as surface flux -solver = DGSEM(polydeg=3, surface_flux=flux_lax_friedrichs, - volume_integral=VolumeIntegralWeakForm()) +solver = DGSEM(polydeg = 3, surface_flux = flux_lax_friedrichs, + volume_integral = VolumeIntegralWeakForm()) coordinates_min = -1.0 -coordinates_max = 1.0 +coordinates_max = 1.0 # Create a uniformly refined mesh with periodic boundaries mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=3, - periodicity=false, - n_cells_max=30_000) # set maximum capacity of tree data structure + initial_refinement_level = 3, + periodicity = false, + n_cells_max = 30_000) # set maximum capacity of tree data structure # Note: the initial condition cannot be specialized to `CompressibleNavierStokesDiffusion1D` # since it is called by both the parabolic solver (which passes in `CompressibleNavierStokesDiffusion1D`) # and by the initial condition (which passes in `CompressibleEulerEquations1D`). # This convergence test setup was originally derived by Andrew Winters (@andrewwinters5000) function initial_condition_navier_stokes_convergence_test(x, t, equations) - # Amplitude and shift - A = 0.5 - c = 2.0 + # Amplitude and shift + A = 0.5 + c = 2.0 - # convenience values for trig. functions - pi_x = pi * x[1] - pi_t = pi * t + # convenience values for trig. functions + pi_x = pi * x[1] + pi_t = pi * t - rho = c + A * cos(pi_x) * cos(pi_t) - v1 = log(x[1] + 2.0) * (1.0 - exp(-A * (x[1] - 1.0)) ) * cos(pi_t) - p = rho^2 + rho = c + A * cos(pi_x) * cos(pi_t) + v1 = log(x[1] + 2.0) * (1.0 - exp(-A * (x[1] - 1.0))) * cos(pi_t) + p = rho^2 - return prim2cons(SVector(rho, v1, p), equations) + return prim2cons(SVector(rho, v1, p), equations) end @inline function source_terms_navier_stokes_convergence_test(u, x, t, equations) - x = x[1] - - # TODO: parabolic - # we currently need to hardcode these parameters until we fix the "combined equation" issue - # see also https://github.com/trixi-framework/Trixi.jl/pull/1160 - inv_gamma_minus_one = inv(equations.gamma - 1) - Pr = prandtl_number() - mu_ = mu() - - # Same settings as in `initial_condition` - # Amplitude and shift - A = 0.5 - c = 2.0 - - # convenience values for trig. functions - pi_x = pi * x - pi_t = pi * t - - # compute the manufactured solution and all necessary derivatives - rho = c + A * cos(pi_x) * cos(pi_t) - rho_t = -pi * A * cos(pi_x) * sin(pi_t) - rho_x = -pi * A * sin(pi_x) * cos(pi_t) - rho_xx = -pi * pi * A * cos(pi_x) * cos(pi_t) - - v1 = log(x + 2.0) * (1.0 - exp(-A * (x - 1.0))) * cos(pi_t) - v1_t = -pi * log(x + 2.0) * (1.0 - exp(-A * (x - 1.0))) * sin(pi_t) - v1_x = (A * log(x + 2.0) * exp(-A * (x - 1.0)) + (1.0 - exp(-A * (x - 1.0))) / (x + 2.0)) * cos(pi_t) - v1_xx = (( 2.0 * A * exp(-A * (x - 1.0)) / (x + 2.0) - - A * A * log(x + 2.0) * exp(-A * (x - 1.0)) - - (1.0 - exp(-A * (x - 1.0))) / ((x + 2.0) * (x + 2.0))) * cos(pi_t)) - - p = rho * rho - p_t = 2.0 * rho * rho_t - p_x = 2.0 * rho * rho_x - p_xx = 2.0 * rho * rho_xx + 2.0 * rho_x * rho_x - - # Note this simplifies slightly because the ansatz assumes that v1 = v2 - E = p * inv_gamma_minus_one + 0.5 * rho * v1^2 - E_t = p_t * inv_gamma_minus_one + 0.5 * rho_t * v1^2 + rho * v1 * v1_t - E_x = p_x * inv_gamma_minus_one + 0.5 * rho_x * v1^2 + rho * v1 * v1_x - - # Some convenience constants - T_const = equations.gamma * inv_gamma_minus_one / Pr - inv_rho_cubed = 1.0 / (rho^3) - - # compute the source terms - # density equation - du1 = rho_t + rho_x * v1 + rho * v1_x - - # y-momentum equation - du2 = ( rho_t * v1 + rho * v1_t - + p_x + rho_x * v1^2 + 2.0 * rho * v1 * v1_x - # stress tensor from y-direction - - v1_xx * mu_) - - # total energy equation - du3 = ( E_t + v1_x * (E + p) + v1 * (E_x + p_x) - # stress tensor and temperature gradient terms from x-direction - - v1_xx * v1 * mu_ - - v1_x * v1_x * mu_ - - T_const * inv_rho_cubed * ( p_xx * rho * rho - - 2.0 * p_x * rho * rho_x - + 2.0 * p * rho_x * rho_x - - p * rho * rho_xx ) * mu_ ) - - return SVector(du1, du2, du3) + x = x[1] + + # TODO: parabolic + # we currently need to hardcode these parameters until we fix the "combined equation" issue + # see also https://github.com/trixi-framework/Trixi.jl/pull/1160 + inv_gamma_minus_one = inv(equations.gamma - 1) + Pr = prandtl_number() + mu_ = mu() + + # Same settings as in `initial_condition` + # Amplitude and shift + A = 0.5 + c = 2.0 + + # convenience values for trig. functions + pi_x = pi * x + pi_t = pi * t + + # compute the manufactured solution and all necessary derivatives + rho = c + A * cos(pi_x) * cos(pi_t) + rho_t = -pi * A * cos(pi_x) * sin(pi_t) + rho_x = -pi * A * sin(pi_x) * cos(pi_t) + rho_xx = -pi * pi * A * cos(pi_x) * cos(pi_t) + + v1 = log(x + 2.0) * (1.0 - exp(-A * (x - 1.0))) * cos(pi_t) + v1_t = -pi * log(x + 2.0) * (1.0 - exp(-A * (x - 1.0))) * sin(pi_t) + v1_x = (A * log(x + 2.0) * exp(-A * (x - 1.0)) + + (1.0 - exp(-A * (x - 1.0))) / (x + 2.0)) * cos(pi_t) + v1_xx = ((2.0 * A * exp(-A * (x - 1.0)) / (x + 2.0) - + A * A * log(x + 2.0) * exp(-A * (x - 1.0)) - + (1.0 - exp(-A * (x - 1.0))) / ((x + 2.0) * (x + 2.0))) * cos(pi_t)) + + p = rho * rho + p_t = 2.0 * rho * rho_t + p_x = 2.0 * rho * rho_x + p_xx = 2.0 * rho * rho_xx + 2.0 * rho_x * rho_x + + # Note this simplifies slightly because the ansatz assumes that v1 = v2 + E = p * inv_gamma_minus_one + 0.5 * rho * v1^2 + E_t = p_t * inv_gamma_minus_one + 0.5 * rho_t * v1^2 + rho * v1 * v1_t + E_x = p_x * inv_gamma_minus_one + 0.5 * rho_x * v1^2 + rho * v1 * v1_x + + # Some convenience constants + T_const = equations.gamma * inv_gamma_minus_one / Pr + inv_rho_cubed = 1.0 / (rho^3) + + # compute the source terms + # density equation + du1 = rho_t + rho_x * v1 + rho * v1_x + + # y-momentum equation + du2 = (rho_t * v1 + rho * v1_t + + p_x + rho_x * v1^2 + 2.0 * rho * v1 * v1_x - + # stress tensor from y-direction + v1_xx * mu_) + + # total energy equation + du3 = (E_t + v1_x * (E + p) + v1 * (E_x + p_x) - + # stress tensor and temperature gradient terms from x-direction + v1_xx * v1 * mu_ - + v1_x * v1_x * mu_ - + T_const * inv_rho_cubed * + (p_xx * rho * rho - + 2.0 * p_x * rho * rho_x + + 2.0 * p * rho_x * rho_x - + p * rho * rho_xx) * mu_) + + return SVector(du1, du2, du3) end initial_condition = initial_condition_navier_stokes_convergence_test # BC types -velocity_bc_left_right = NoSlip((x, t, equations) -> initial_condition_navier_stokes_convergence_test(x, t, equations)[2]) - -heat_bc_left = Isothermal((x, t, equations) -> - Trixi.temperature(initial_condition_navier_stokes_convergence_test(x, t, equations), - equations_parabolic)) +velocity_bc_left_right = NoSlip((x, t, equations) -> initial_condition_navier_stokes_convergence_test(x, + t, + equations)[2]) + +heat_bc_left = Isothermal((x, t, equations) -> Trixi.temperature(initial_condition_navier_stokes_convergence_test(x, + t, + equations), + equations_parabolic)) heat_bc_right = Adiabatic((x, t, equations) -> 0.0) -boundary_condition_left = BoundaryConditionNavierStokesWall(velocity_bc_left_right, heat_bc_left) -boundary_condition_right = BoundaryConditionNavierStokesWall(velocity_bc_left_right, heat_bc_right) +boundary_condition_left = BoundaryConditionNavierStokesWall(velocity_bc_left_right, + heat_bc_left) +boundary_condition_right = BoundaryConditionNavierStokesWall(velocity_bc_left_right, + heat_bc_right) # define inviscid boundary conditions boundary_conditions = (; x_neg = boundary_condition_slip_wall, - x_pos = boundary_condition_slip_wall) + x_pos = boundary_condition_slip_wall) # define viscous boundary conditions boundary_conditions_parabolic = (; x_neg = boundary_condition_left, - x_pos = boundary_condition_right) + x_pos = boundary_condition_right) -semi = SemidiscretizationHyperbolicParabolic(mesh, (equations, equations_parabolic), initial_condition, solver; - boundary_conditions=(boundary_conditions, boundary_conditions_parabolic), - source_terms=source_terms_navier_stokes_convergence_test) +semi = SemidiscretizationHyperbolicParabolic(mesh, (equations, equations_parabolic), + initial_condition, solver; + boundary_conditions = (boundary_conditions, + boundary_conditions_parabolic), + source_terms = source_terms_navier_stokes_convergence_test) ############################################################################### # ODE solvers, callbacks etc. @@ -146,15 +156,15 @@ tspan = (0.0, 1.0) ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() -alive_callback = AliveCallback(alive_interval=10) +alive_callback = AliveCallback(alive_interval = 10) analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) callbacks = CallbackSet(summary_callback, alive_callback, analysis_callback) ############################################################################### # run the simulation time_int_tol = 1e-8 -sol = solve(ode, RDPK3SpFSAL49(); abstol=time_int_tol, reltol=time_int_tol, dt = 1e-5, - ode_default_options()..., callback=callbacks) -summary_callback() # print the timer summary \ No newline at end of file +sol = solve(ode, RDPK3SpFSAL49(); abstol = time_int_tol, reltol = time_int_tol, dt = 1e-5, + ode_default_options()..., callback = callbacks) +summary_callback() # print the timer summary diff --git a/examples/tree_1d_dgsem/elixir_navierstokes_convergence_walls_amr.jl b/examples/tree_1d_dgsem/elixir_navierstokes_convergence_walls_amr.jl index 1daeab04a71..e833155a68e 100644 --- a/examples/tree_1d_dgsem/elixir_navierstokes_convergence_walls_amr.jl +++ b/examples/tree_1d_dgsem/elixir_navierstokes_convergence_walls_amr.jl @@ -8,135 +8,145 @@ prandtl_number() = 0.72 mu() = 0.01 equations = CompressibleEulerEquations1D(1.4) -equations_parabolic = CompressibleNavierStokesDiffusion1D(equations, mu=mu(), Prandtl=prandtl_number(), - gradient_variables=GradientVariablesEntropy()) +equations_parabolic = CompressibleNavierStokesDiffusion1D(equations, mu = mu(), + Prandtl = prandtl_number(), + gradient_variables = GradientVariablesEntropy()) # Create DG solver with polynomial degree = 3 and (local) Lax-Friedrichs/Rusanov flux as surface flux -solver = DGSEM(polydeg=3, surface_flux=flux_lax_friedrichs, - volume_integral=VolumeIntegralWeakForm()) +solver = DGSEM(polydeg = 3, surface_flux = flux_lax_friedrichs, + volume_integral = VolumeIntegralWeakForm()) coordinates_min = -1.0 -coordinates_max = 1.0 +coordinates_max = 1.0 # Create a uniformly refined mesh with periodic boundaries mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=3, - periodicity=false, - n_cells_max=30_000) # set maximum capacity of tree data structure + initial_refinement_level = 3, + periodicity = false, + n_cells_max = 30_000) # set maximum capacity of tree data structure # Note: the initial condition cannot be specialized to `CompressibleNavierStokesDiffusion1D` # since it is called by both the parabolic solver (which passes in `CompressibleNavierStokesDiffusion1D`) # and by the initial condition (which passes in `CompressibleEulerEquations1D`). # This convergence test setup was originally derived by Andrew Winters (@andrewwinters5000) function initial_condition_navier_stokes_convergence_test(x, t, equations) - # Amplitude and shift - A = 0.5 - c = 2.0 + # Amplitude and shift + A = 0.5 + c = 2.0 - # convenience values for trig. functions - pi_x = pi * x[1] - pi_t = pi * t + # convenience values for trig. functions + pi_x = pi * x[1] + pi_t = pi * t - rho = c + A * cos(pi_x) * cos(pi_t) - v1 = log(x[1] + 2.0) * (1.0 - exp(-A * (x[1] - 1.0)) ) * cos(pi_t) - p = rho^2 + rho = c + A * cos(pi_x) * cos(pi_t) + v1 = log(x[1] + 2.0) * (1.0 - exp(-A * (x[1] - 1.0))) * cos(pi_t) + p = rho^2 - return prim2cons(SVector(rho, v1, p), equations) + return prim2cons(SVector(rho, v1, p), equations) end @inline function source_terms_navier_stokes_convergence_test(u, x, t, equations) - x = x[1] - - # TODO: parabolic - # we currently need to hardcode these parameters until we fix the "combined equation" issue - # see also https://github.com/trixi-framework/Trixi.jl/pull/1160 - inv_gamma_minus_one = inv(equations.gamma - 1) - Pr = prandtl_number() - mu_ = mu() - - # Same settings as in `initial_condition` - # Amplitude and shift - A = 0.5 - c = 2.0 - - # convenience values for trig. functions - pi_x = pi * x - pi_t = pi * t - - # compute the manufactured solution and all necessary derivatives - rho = c + A * cos(pi_x) * cos(pi_t) - rho_t = -pi * A * cos(pi_x) * sin(pi_t) - rho_x = -pi * A * sin(pi_x) * cos(pi_t) - rho_xx = -pi * pi * A * cos(pi_x) * cos(pi_t) - - v1 = log(x + 2.0) * (1.0 - exp(-A * (x - 1.0))) * cos(pi_t) - v1_t = -pi * log(x + 2.0) * (1.0 - exp(-A * (x - 1.0))) * sin(pi_t) - v1_x = (A * log(x + 2.0) * exp(-A * (x - 1.0)) + (1.0 - exp(-A * (x - 1.0))) / (x + 2.0)) * cos(pi_t) - v1_xx = (( 2.0 * A * exp(-A * (x - 1.0)) / (x + 2.0) - - A * A * log(x + 2.0) * exp(-A * (x - 1.0)) - - (1.0 - exp(-A * (x - 1.0))) / ((x + 2.0) * (x + 2.0))) * cos(pi_t)) - - p = rho * rho - p_t = 2.0 * rho * rho_t - p_x = 2.0 * rho * rho_x - p_xx = 2.0 * rho * rho_xx + 2.0 * rho_x * rho_x - - # Note this simplifies slightly because the ansatz assumes that v1 = v2 - E = p * inv_gamma_minus_one + 0.5 * rho * v1^2 - E_t = p_t * inv_gamma_minus_one + 0.5 * rho_t * v1^2 + rho * v1 * v1_t - E_x = p_x * inv_gamma_minus_one + 0.5 * rho_x * v1^2 + rho * v1 * v1_x - - # Some convenience constants - T_const = equations.gamma * inv_gamma_minus_one / Pr - inv_rho_cubed = 1.0 / (rho^3) - - # compute the source terms - # density equation - du1 = rho_t + rho_x * v1 + rho * v1_x - - # y-momentum equation - du2 = ( rho_t * v1 + rho * v1_t - + p_x + rho_x * v1^2 + 2.0 * rho * v1 * v1_x - # stress tensor from y-direction - - v1_xx * mu_) - - # total energy equation - du3 = ( E_t + v1_x * (E + p) + v1 * (E_x + p_x) - # stress tensor and temperature gradient terms from x-direction - - v1_xx * v1 * mu_ - - v1_x * v1_x * mu_ - - T_const * inv_rho_cubed * ( p_xx * rho * rho - - 2.0 * p_x * rho * rho_x - + 2.0 * p * rho_x * rho_x - - p * rho * rho_xx ) * mu_ ) - - return SVector(du1, du2, du3) + x = x[1] + + # TODO: parabolic + # we currently need to hardcode these parameters until we fix the "combined equation" issue + # see also https://github.com/trixi-framework/Trixi.jl/pull/1160 + inv_gamma_minus_one = inv(equations.gamma - 1) + Pr = prandtl_number() + mu_ = mu() + + # Same settings as in `initial_condition` + # Amplitude and shift + A = 0.5 + c = 2.0 + + # convenience values for trig. functions + pi_x = pi * x + pi_t = pi * t + + # compute the manufactured solution and all necessary derivatives + rho = c + A * cos(pi_x) * cos(pi_t) + rho_t = -pi * A * cos(pi_x) * sin(pi_t) + rho_x = -pi * A * sin(pi_x) * cos(pi_t) + rho_xx = -pi * pi * A * cos(pi_x) * cos(pi_t) + + v1 = log(x + 2.0) * (1.0 - exp(-A * (x - 1.0))) * cos(pi_t) + v1_t = -pi * log(x + 2.0) * (1.0 - exp(-A * (x - 1.0))) * sin(pi_t) + v1_x = (A * log(x + 2.0) * exp(-A * (x - 1.0)) + + (1.0 - exp(-A * (x - 1.0))) / (x + 2.0)) * cos(pi_t) + v1_xx = ((2.0 * A * exp(-A * (x - 1.0)) / (x + 2.0) - + A * A * log(x + 2.0) * exp(-A * (x - 1.0)) - + (1.0 - exp(-A * (x - 1.0))) / ((x + 2.0) * (x + 2.0))) * cos(pi_t)) + + p = rho * rho + p_t = 2.0 * rho * rho_t + p_x = 2.0 * rho * rho_x + p_xx = 2.0 * rho * rho_xx + 2.0 * rho_x * rho_x + + # Note this simplifies slightly because the ansatz assumes that v1 = v2 + E = p * inv_gamma_minus_one + 0.5 * rho * v1^2 + E_t = p_t * inv_gamma_minus_one + 0.5 * rho_t * v1^2 + rho * v1 * v1_t + E_x = p_x * inv_gamma_minus_one + 0.5 * rho_x * v1^2 + rho * v1 * v1_x + + # Some convenience constants + T_const = equations.gamma * inv_gamma_minus_one / Pr + inv_rho_cubed = 1.0 / (rho^3) + + # compute the source terms + # density equation + du1 = rho_t + rho_x * v1 + rho * v1_x + + # y-momentum equation + du2 = (rho_t * v1 + rho * v1_t + + p_x + rho_x * v1^2 + 2.0 * rho * v1 * v1_x - + # stress tensor from y-direction + v1_xx * mu_) + + # total energy equation + du3 = (E_t + v1_x * (E + p) + v1 * (E_x + p_x) - + # stress tensor and temperature gradient terms from x-direction + v1_xx * v1 * mu_ - + v1_x * v1_x * mu_ - + T_const * inv_rho_cubed * + (p_xx * rho * rho - + 2.0 * p_x * rho * rho_x + + 2.0 * p * rho_x * rho_x - + p * rho * rho_xx) * mu_) + + return SVector(du1, du2, du3) end initial_condition = initial_condition_navier_stokes_convergence_test # BC types -velocity_bc_left_right = NoSlip((x, t, equations) -> initial_condition_navier_stokes_convergence_test(x, t, equations)[2]) - -heat_bc_left = Isothermal((x, t, equations) -> - Trixi.temperature(initial_condition_navier_stokes_convergence_test(x, t, equations), - equations_parabolic)) +velocity_bc_left_right = NoSlip((x, t, equations) -> initial_condition_navier_stokes_convergence_test(x, + t, + equations)[2]) + +heat_bc_left = Isothermal((x, t, equations) -> Trixi.temperature(initial_condition_navier_stokes_convergence_test(x, + t, + equations), + equations_parabolic)) heat_bc_right = Adiabatic((x, t, equations) -> 0.0) -boundary_condition_left = BoundaryConditionNavierStokesWall(velocity_bc_left_right, heat_bc_left) -boundary_condition_right = BoundaryConditionNavierStokesWall(velocity_bc_left_right, heat_bc_right) +boundary_condition_left = BoundaryConditionNavierStokesWall(velocity_bc_left_right, + heat_bc_left) +boundary_condition_right = BoundaryConditionNavierStokesWall(velocity_bc_left_right, + heat_bc_right) # define inviscid boundary conditions boundary_conditions = (; x_neg = boundary_condition_slip_wall, - x_pos = boundary_condition_slip_wall) + x_pos = boundary_condition_slip_wall) # define viscous boundary conditions boundary_conditions_parabolic = (; x_neg = boundary_condition_left, - x_pos = boundary_condition_right) + x_pos = boundary_condition_right) -semi = SemidiscretizationHyperbolicParabolic(mesh, (equations, equations_parabolic), initial_condition, solver; - boundary_conditions=(boundary_conditions, boundary_conditions_parabolic), - source_terms=source_terms_navier_stokes_convergence_test) +semi = SemidiscretizationHyperbolicParabolic(mesh, (equations, equations_parabolic), + initial_condition, solver; + boundary_conditions = (boundary_conditions, + boundary_conditions_parabolic), + source_terms = source_terms_navier_stokes_convergence_test) ############################################################################### # ODE solvers, callbacks etc. @@ -146,19 +156,19 @@ tspan = (0.0, 1.0) ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() -alive_callback = AliveCallback(alive_interval=10) +alive_callback = AliveCallback(alive_interval = 10) analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) -amr_controller = ControllerThreeLevel(semi, - IndicatorLöhner(semi, variable=Trixi.density), - base_level=3, - med_level=4, med_threshold=0.005, - max_level=5, max_threshold=0.01) +amr_controller = ControllerThreeLevel(semi, + IndicatorLöhner(semi, variable = Trixi.density), + base_level = 3, + med_level = 4, med_threshold = 0.005, + max_level = 5, max_threshold = 0.01) amr_callback = AMRCallback(semi, amr_controller, - interval=5, - adapt_initial_condition=true) + interval = 5, + adapt_initial_condition = true) # Create a CallbackSet to collect all callbacks such that they can be passed to the ODE solver callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, amr_callback) @@ -167,6 +177,6 @@ callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, amr # run the simulation time_int_tol = 1e-8 -sol = solve(ode, RDPK3SpFSAL49(); abstol=time_int_tol, reltol=time_int_tol, dt = 1e-5, - ode_default_options()..., callback=callbacks) -summary_callback() # print the timer summary \ No newline at end of file +sol = solve(ode, RDPK3SpFSAL49(); abstol = time_int_tol, reltol = time_int_tol, dt = 1e-5, + ode_default_options()..., callback = callbacks) +summary_callback() # print the timer summary diff --git a/examples/tree_1d_dgsem/elixir_shallowwater_beach.jl b/examples/tree_1d_dgsem/elixir_shallowwater_beach.jl index 1288bc5e66a..378079ca334 100644 --- a/examples/tree_1d_dgsem/elixir_shallowwater_beach.jl +++ b/examples/tree_1d_dgsem/elixir_shallowwater_beach.jl @@ -7,7 +7,7 @@ using Trixi # # TODO: TrixiShallowWater: wet/dry example elixir -equations = ShallowWaterEquations1D(gravity_constant=9.812) +equations = ShallowWaterEquations1D(gravity_constant = 9.812) """ initial_condition_beach(x, t, equations:: ShallowWaterEquations1D) @@ -22,33 +22,33 @@ found in section 5.2 of the paper: Finite volume evolution Galerkin methods for the shallow water equations with dry beds\n [DOI: 10.4208/cicp.220210.020710a](https://dx.doi.org/10.4208/cicp.220210.020710a) """ -function initial_condition_beach(x, t, equations:: ShallowWaterEquations1D) - D = 1 - delta = 0.02 - gamma = sqrt((3 * delta) / (4 * D)) - x_a = sqrt((4 * D) / (3 * delta)) * acosh(sqrt(20)) - - f = D + 40 * delta * sech(gamma * (8 * x[1] - x_a))^2 - - # steep curved beach - b = 0.01 + 99 / 409600 * 4^x[1] - - if x[1] >= 6 - H = b - v = 0.0 - else - H = f - v = sqrt(equations.gravity / D) * H - end - - # It is mandatory to shift the water level at dry areas to make sure the water height h - # stays positive. The system would not be stable for h set to a hard 0 due to division by h in - # the computation of velocity, e.g., (h v) / h. Therefore, a small dry state threshold - # with a default value of 500*eps() ≈ 1e-13 in double precision, is set in the constructor above - # for the ShallowWaterEquations and added to the initial condition if h = 0. - # This default value can be changed within the constructor call depending on the simulation setup. - H = max(H, b + equations.threshold_limiter) - return prim2cons(SVector(H, v, b), equations) +function initial_condition_beach(x, t, equations::ShallowWaterEquations1D) + D = 1 + delta = 0.02 + gamma = sqrt((3 * delta) / (4 * D)) + x_a = sqrt((4 * D) / (3 * delta)) * acosh(sqrt(20)) + + f = D + 40 * delta * sech(gamma * (8 * x[1] - x_a))^2 + + # steep curved beach + b = 0.01 + 99 / 409600 * 4^x[1] + + if x[1] >= 6 + H = b + v = 0.0 + else + H = f + v = sqrt(equations.gravity / D) * H + end + + # It is mandatory to shift the water level at dry areas to make sure the water height h + # stays positive. The system would not be stable for h set to a hard 0 due to division by h in + # the computation of velocity, e.g., (h v) / h. Therefore, a small dry state threshold + # with a default value of 500*eps() ≈ 1e-13 in double precision, is set in the constructor above + # for the ShallowWaterEquations and added to the initial condition if h = 0. + # This default value can be changed within the constructor call depending on the simulation setup. + H = max(H, b + equations.threshold_limiter) + return prim2cons(SVector(H, v, b), equations) end initial_condition = initial_condition_beach @@ -58,19 +58,20 @@ boundary_condition = boundary_condition_slip_wall # Get the DG approximation space volume_flux = (flux_wintermeyer_etal, flux_nonconservative_wintermeyer_etal) -surface_flux = (FluxHydrostaticReconstruction(flux_hll_chen_noelle, hydrostatic_reconstruction_chen_noelle), +surface_flux = (FluxHydrostaticReconstruction(flux_hll_chen_noelle, + hydrostatic_reconstruction_chen_noelle), flux_nonconservative_chen_noelle) basis = LobattoLegendreBasis(3) indicator_sc = IndicatorHennemannGassnerShallowWater(equations, basis, - alpha_max=0.5, - alpha_min=0.001, - alpha_smooth=true, - variable=waterheight_pressure) + alpha_max = 0.5, + alpha_min = 0.001, + alpha_smooth = true, + variable = waterheight_pressure) volume_integral = VolumeIntegralShockCapturingHG(indicator_sc; - volume_flux_dg=volume_flux, - volume_flux_fv=surface_flux) + volume_flux_dg = volume_flux, + volume_flux_fv = surface_flux) solver = DGSEM(basis, surface_flux, volume_integral) @@ -81,13 +82,13 @@ coordinates_min = 0.0 coordinates_max = 8.0 mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=7, - n_cells_max=10_000, - periodicity=false) + initial_refinement_level = 7, + n_cells_max = 10_000, + periodicity = false) # create the semi discretization object semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver, - boundary_conditions=boundary_condition) + boundary_conditions = boundary_condition) ############################################################################### # ODE solvers, callbacks etc. @@ -98,24 +99,25 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 1000 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval, save_analysis=false, - extra_analysis_integrals=(energy_kinetic, - energy_internal)) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval, + save_analysis = false, + extra_analysis_integrals = (energy_kinetic, + energy_internal)) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(dt=0.5, - save_initial_solution=true, - save_final_solution=true) +save_solution = SaveSolutionCallback(dt = 0.5, + save_initial_solution = true, + save_final_solution = true) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, save_solution) -stage_limiter! = PositivityPreservingLimiterShallowWater(variables=(Trixi.waterheight,)) +stage_limiter! = PositivityPreservingLimiterShallowWater(variables = (Trixi.waterheight,)) ############################################################################### # run the simulation sol = solve(ode, SSPRK43(stage_limiter!); - ode_default_options()..., callback=callbacks); + ode_default_options()..., callback = callbacks); -summary_callback() # print the timer summary \ No newline at end of file +summary_callback() # print the timer summary diff --git a/examples/tree_1d_dgsem/elixir_shallowwater_ec.jl b/examples/tree_1d_dgsem/elixir_shallowwater_ec.jl index 1469afec1ca..a3df37fb966 100644 --- a/examples/tree_1d_dgsem/elixir_shallowwater_ec.jl +++ b/examples/tree_1d_dgsem/elixir_shallowwater_ec.jl @@ -6,7 +6,7 @@ using Trixi # Semidiscretization of the shallow water equations with a discontinuous # bottom topography function -equations = ShallowWaterEquations1D(gravity_constant=9.81) +equations = ShallowWaterEquations1D(gravity_constant = 9.81) # Initial condition with a truly discontinuous water height, velocity, and bottom # topography function as an academic testcase for entropy conservation. @@ -16,23 +16,23 @@ equations = ShallowWaterEquations1D(gravity_constant=9.81) # refinement level is changed the initial condition below may need changed as well to # ensure that the discontinuities lie on an element interface. function initial_condition_ec_discontinuous_bottom(x, t, equations::ShallowWaterEquations1D) - # Set the background values - H = 4.25 - v = 0.0 - b = sin(x[1]) # arbitrary continuous function - - # Setup the discontinuous water height and velocity - if x[1] >= 0.125 && x[1] <= 0.25 - H = 5.0 - v = 0.1882 - end - - # Setup a discontinuous bottom topography - if x[1] >= -0.25 && x[1] <= -0.125 - b = 2.0 + 0.5 * sin(2.0 * pi * x[1]) - end - - return prim2cons(SVector(H, v, b), equations) + # Set the background values + H = 4.25 + v = 0.0 + b = sin(x[1]) # arbitrary continuous function + + # Setup the discontinuous water height and velocity + if x[1] >= 0.125 && x[1] <= 0.25 + H = 5.0 + v = 0.1882 + end + + # Setup a discontinuous bottom topography + if x[1] >= -0.25 && x[1] <= -0.125 + b = 2.0 + 0.5 * sin(2.0 * pi * x[1]) + end + + return prim2cons(SVector(H, v, b), equations) end initial_condition = initial_condition_ec_discontinuous_bottom @@ -41,8 +41,9 @@ initial_condition = initial_condition_ec_discontinuous_bottom # Get the DG approximation space volume_flux = (flux_wintermeyer_etal, flux_nonconservative_wintermeyer_etal) -solver = DGSEM(polydeg=4, surface_flux=(flux_fjordholm_etal, flux_nonconservative_fjordholm_etal), - volume_integral=VolumeIntegralFluxDifferencing(volume_flux)) +solver = DGSEM(polydeg = 4, + surface_flux = (flux_fjordholm_etal, flux_nonconservative_fjordholm_etal), + volume_integral = VolumeIntegralFluxDifferencing(volume_flux)) ############################################################################### # Get the TreeMesh and setup a periodic mesh @@ -50,8 +51,8 @@ solver = DGSEM(polydeg=4, surface_flux=(flux_fjordholm_etal, flux_nonconservativ coordinates_min = -1.0 coordinates_max = 1.0 mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=4, - n_cells_max=10_000) + initial_refinement_level = 4, + n_cells_max = 10_000) # Create the semi discretization object semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver) @@ -68,15 +69,15 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=100, - save_initial_solution=true, - save_final_solution=true) +save_solution = SaveSolutionCallback(interval = 100, + save_initial_solution = true, + save_final_solution = true) -stepsize_callback = StepsizeCallback(cfl=3.0) +stepsize_callback = StepsizeCallback(cfl = 3.0) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, save_solution, stepsize_callback) @@ -84,7 +85,7 @@ callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, sav ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/tree_1d_dgsem/elixir_shallowwater_parabolic_bowl.jl b/examples/tree_1d_dgsem/elixir_shallowwater_parabolic_bowl.jl index 916bba76ece..a586562af7e 100644 --- a/examples/tree_1d_dgsem/elixir_shallowwater_parabolic_bowl.jl +++ b/examples/tree_1d_dgsem/elixir_shallowwater_parabolic_bowl.jl @@ -7,7 +7,7 @@ using Trixi # # TODO: TrixiShallowWater: wet/dry example elixir -equations = ShallowWaterEquations1D(gravity_constant=9.81) +equations = ShallowWaterEquations1D(gravity_constant = 9.81) """ initial_condition_parabolic_bowl(x, t, equations:: ShallowWaterEquations1D) @@ -28,26 +28,26 @@ The particular setup below is taken from Section 6.2 of curvilinear meshes with wet/dry fronts accelerated by GPUs [DOI: 10.1016/j.jcp.2018.08.038](https://doi.org/10.1016/j.jcp.2018.08.038). """ -function initial_condition_parabolic_bowl(x, t, equations:: ShallowWaterEquations1D) - a = 1 - h_0 = 0.1 - sigma = 0.5 - ω = sqrt(2 * equations.gravity * h_0) / a - - v = -sigma * ω * sin(ω * t) - - b = h_0 * x[1]^2 / a^2 - - H = sigma * h_0 / a^2 * (2 * x[1] * cos(ω * t) - sigma) + h_0 - - # It is mandatory to shift the water level at dry areas to make sure the water height h - # stays positive. The system would not be stable for h set to a hard 0 due to division by h in - # the computation of velocity, e.g., (h v) / h. Therefore, a small dry state threshold - # with a default value of 500*eps() ≈ 1e-13 in double precision, is set in the constructor above - # for the ShallowWaterEquations and added to the initial condition if h = 0. - # This default value can be changed within the constructor call depending on the simulation setup. - H = max(H, b + equations.threshold_limiter) - return prim2cons(SVector(H, v, b), equations) +function initial_condition_parabolic_bowl(x, t, equations::ShallowWaterEquations1D) + a = 1 + h_0 = 0.1 + sigma = 0.5 + ω = sqrt(2 * equations.gravity * h_0) / a + + v = -sigma * ω * sin(ω * t) + + b = h_0 * x[1]^2 / a^2 + + H = sigma * h_0 / a^2 * (2 * x[1] * cos(ω * t) - sigma) + h_0 + + # It is mandatory to shift the water level at dry areas to make sure the water height h + # stays positive. The system would not be stable for h set to a hard 0 due to division by h in + # the computation of velocity, e.g., (h v) / h. Therefore, a small dry state threshold + # with a default value of 500*eps() ≈ 1e-13 in double precision, is set in the constructor above + # for the ShallowWaterEquations and added to the initial condition if h = 0. + # This default value can be changed within the constructor call depending on the simulation setup. + H = max(H, b + equations.threshold_limiter) + return prim2cons(SVector(H, v, b), equations) end initial_condition = initial_condition_parabolic_bowl @@ -56,19 +56,20 @@ initial_condition = initial_condition_parabolic_bowl # Get the DG approximation space volume_flux = (flux_wintermeyer_etal, flux_nonconservative_wintermeyer_etal) -surface_flux = (FluxHydrostaticReconstruction(flux_hll_chen_noelle, hydrostatic_reconstruction_chen_noelle), +surface_flux = (FluxHydrostaticReconstruction(flux_hll_chen_noelle, + hydrostatic_reconstruction_chen_noelle), flux_nonconservative_chen_noelle) basis = LobattoLegendreBasis(5) indicator_sc = IndicatorHennemannGassnerShallowWater(equations, basis, - alpha_max=0.5, - alpha_min=0.001, - alpha_smooth=true, - variable=waterheight_pressure) + alpha_max = 0.5, + alpha_min = 0.001, + alpha_smooth = true, + variable = waterheight_pressure) volume_integral = VolumeIntegralShockCapturingHG(indicator_sc; - volume_flux_dg=volume_flux, - volume_flux_fv=surface_flux) + volume_flux_dg = volume_flux, + volume_flux_fv = surface_flux) solver = DGSEM(basis, surface_flux, volume_integral) @@ -79,8 +80,8 @@ coordinates_min = -2.0 coordinates_max = 2.0 mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=6, - n_cells_max=10_000) + initial_refinement_level = 6, + n_cells_max = 10_000) # create the semi discretization object semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver) @@ -94,24 +95,25 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 1000 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval, save_analysis=false, - extra_analysis_integrals=(energy_kinetic, - energy_internal)) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval, + save_analysis = false, + extra_analysis_integrals = (energy_kinetic, + energy_internal)) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=1000, - save_initial_solution=true, - save_final_solution=true) +save_solution = SaveSolutionCallback(interval = 1000, + save_initial_solution = true, + save_final_solution = true) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, save_solution) -stage_limiter! = PositivityPreservingLimiterShallowWater(variables=(Trixi.waterheight,)) +stage_limiter! = PositivityPreservingLimiterShallowWater(variables = (Trixi.waterheight,)) ############################################################################### # run the simulation sol = solve(ode, SSPRK43(stage_limiter!); - ode_default_options()..., callback=callbacks); + ode_default_options()..., callback = callbacks); -summary_callback() # print the timer summary \ No newline at end of file +summary_callback() # print the timer summary diff --git a/examples/tree_1d_dgsem/elixir_shallowwater_shock_capturing.jl b/examples/tree_1d_dgsem/elixir_shallowwater_shock_capturing.jl index 62346d7b5ab..511f33d1101 100644 --- a/examples/tree_1d_dgsem/elixir_shallowwater_shock_capturing.jl +++ b/examples/tree_1d_dgsem/elixir_shallowwater_shock_capturing.jl @@ -5,36 +5,37 @@ using Trixi ############################################################################### # Semidiscretization of the shallow water equations -equations = ShallowWaterEquations1D(gravity_constant=9.812, H0=1.75) +equations = ShallowWaterEquations1D(gravity_constant = 9.812, H0 = 1.75) # Initial condition with a truly discontinuous velocity and bottom topography. # Works as intended for TreeMesh1D with `initial_refinement_level=3`. If the mesh # refinement level is changed the initial condition below may need changed as well to # ensure that the discontinuities lie on an element interface. -function initial_condition_stone_throw_discontinuous_bottom(x, t, equations::ShallowWaterEquations1D) +function initial_condition_stone_throw_discontinuous_bottom(x, t, + equations::ShallowWaterEquations1D) - # Calculate primitive variables + # Calculate primitive variables - # flat lake - H = equations.H0 + # flat lake + H = equations.H0 - # Discontinuous velocity - v = 0.0 - if x[1] >= -0.75 && x[1] <= 0.0 - v = -1.0 - elseif x[1] >= 0.0 && x[1] <= 0.75 - v = 1.0 - end + # Discontinuous velocity + v = 0.0 + if x[1] >= -0.75 && x[1] <= 0.0 + v = -1.0 + elseif x[1] >= 0.0 && x[1] <= 0.75 + v = 1.0 + end - b = ( 1.5 / exp( 0.5 * ((x[1] - 1.0)^2 ) ) - + 0.75 / exp( 0.5 * ((x[1] + 1.0)^2 ) ) ) + b = (1.5 / exp(0.5 * ((x[1] - 1.0)^2)) + + 0.75 / exp(0.5 * ((x[1] + 1.0)^2))) - # Force a discontinuous bottom topography - if x[1] >= -1.5 && x[1] <= 0.0 - b = 0.5 - end + # Force a discontinuous bottom topography + if x[1] >= -1.5 && x[1] <= 0.0 + b = 0.5 + end - return prim2cons(SVector(H, v, b), equations) + return prim2cons(SVector(H, v, b), equations) end initial_condition = initial_condition_stone_throw_discontinuous_bottom @@ -45,18 +46,19 @@ boundary_condition = boundary_condition_slip_wall # Get the DG approximation space volume_flux = (flux_wintermeyer_etal, flux_nonconservative_wintermeyer_etal) -surface_flux = (FluxHydrostaticReconstruction(flux_lax_friedrichs, hydrostatic_reconstruction_audusse_etal), +surface_flux = (FluxHydrostaticReconstruction(flux_lax_friedrichs, + hydrostatic_reconstruction_audusse_etal), flux_nonconservative_audusse_etal) basis = LobattoLegendreBasis(4) indicator_sc = IndicatorHennemannGassner(equations, basis, - alpha_max=0.5, - alpha_min=0.001, - alpha_smooth=true, - variable=waterheight_pressure) + alpha_max = 0.5, + alpha_min = 0.001, + alpha_smooth = true, + variable = waterheight_pressure) volume_integral = VolumeIntegralShockCapturingHG(indicator_sc; - volume_flux_dg=volume_flux, - volume_flux_fv=surface_flux) + volume_flux_dg = volume_flux, + volume_flux_fv = surface_flux) solver = DGSEM(basis, surface_flux, volume_integral) @@ -66,9 +68,9 @@ solver = DGSEM(basis, surface_flux, volume_integral) coordinates_min = -3.0 coordinates_max = 3.0 mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=3, - n_cells_max=10_000, - periodicity=false) + initial_refinement_level = 3, + n_cells_max = 10_000, + periodicity = false) # create the semi discretization object semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver, @@ -86,28 +88,29 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval, save_analysis=false, - extra_analysis_integrals=(energy_kinetic, - energy_internal, - lake_at_rest_error)) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval, + save_analysis = false, + extra_analysis_integrals = (energy_kinetic, + energy_internal, + lake_at_rest_error)) # Enable in-situ visualization with a new plot generated every 50 time steps # and we explicitly pass that the plot data will be one-dimensional # visualization = VisualizationCallback(interval=50, plot_data_creator=PlotData1D) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=100, - save_initial_solution=true, - save_final_solution=true) +save_solution = SaveSolutionCallback(interval = 100, + save_initial_solution = true, + save_final_solution = true) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, save_solution)#, - # visualization) +# visualization) ############################################################################### # run the simulation # use a Runge-Kutta method with automatic (error based) time step size control -sol = solve(ode, RDPK3SpFSAL49(); abstol=1.0e-7, reltol=1.0e-7, - ode_default_options()..., callback=callbacks); +sol = solve(ode, RDPK3SpFSAL49(); abstol = 1.0e-7, reltol = 1.0e-7, + ode_default_options()..., callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/tree_1d_dgsem/elixir_shallowwater_source_terms.jl b/examples/tree_1d_dgsem/elixir_shallowwater_source_terms.jl index 2f9f93f4335..af596a377f8 100644 --- a/examples/tree_1d_dgsem/elixir_shallowwater_source_terms.jl +++ b/examples/tree_1d_dgsem/elixir_shallowwater_source_terms.jl @@ -5,17 +5,17 @@ using Trixi ############################################################################### # Semidiscretization of the shallow water equations -equations = ShallowWaterEquations1D(gravity_constant=9.81) +equations = ShallowWaterEquations1D(gravity_constant = 9.81) initial_condition = initial_condition_convergence_test - ############################################################################### # Get the DG approximation space volume_flux = (flux_wintermeyer_etal, flux_nonconservative_wintermeyer_etal) -solver = DGSEM(polydeg=3, surface_flux=(flux_lax_friedrichs, flux_nonconservative_fjordholm_etal), - volume_integral=VolumeIntegralFluxDifferencing(volume_flux)) +solver = DGSEM(polydeg = 3, + surface_flux = (flux_lax_friedrichs, flux_nonconservative_fjordholm_etal), + volume_integral = VolumeIntegralFluxDifferencing(volume_flux)) ############################################################################### # Get the TreeMesh and setup a periodic mesh @@ -23,13 +23,13 @@ solver = DGSEM(polydeg=3, surface_flux=(flux_lax_friedrichs, flux_nonconservativ coordinates_min = 0.0 coordinates_max = sqrt(2.0) mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=3, - n_cells_max=10_000, - periodicity=true) + initial_refinement_level = 3, + n_cells_max = 10_000, + periodicity = true) # create the semi discretization object semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver, - source_terms=source_terms_convergence_test) + source_terms = source_terms_convergence_test) ############################################################################### # ODE solvers, callbacks etc. @@ -40,13 +40,13 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 500 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=200, - save_initial_solution=true, - save_final_solution=true) +save_solution = SaveSolutionCallback(interval = 200, + save_initial_solution = true, + save_final_solution = true) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, save_solution) @@ -54,6 +54,6 @@ callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, sav # run the simulation # use a Runge-Kutta method with automatic (error based) time step size control -sol = solve(ode, RDPK3SpFSAL49(); abstol=1.0e-8, reltol=1.0e-8, - ode_default_options()..., callback=callbacks); +sol = solve(ode, RDPK3SpFSAL49(); abstol = 1.0e-8, reltol = 1.0e-8, + ode_default_options()..., callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/tree_1d_dgsem/elixir_shallowwater_source_terms_dirichlet.jl b/examples/tree_1d_dgsem/elixir_shallowwater_source_terms_dirichlet.jl index c8ef1c1b70b..cbc98a30f9f 100644 --- a/examples/tree_1d_dgsem/elixir_shallowwater_source_terms_dirichlet.jl +++ b/examples/tree_1d_dgsem/elixir_shallowwater_source_terms_dirichlet.jl @@ -5,7 +5,7 @@ using Trixi ############################################################################### # Semidiscretization of the shallow water equations -equations = ShallowWaterEquations1D(gravity_constant=9.81) +equations = ShallowWaterEquations1D(gravity_constant = 9.81) initial_condition = initial_condition_convergence_test @@ -16,8 +16,8 @@ boundary_condition = BoundaryConditionDirichlet(initial_condition) volume_flux = (flux_wintermeyer_etal, flux_nonconservative_wintermeyer_etal) surface_flux = (flux_lax_friedrichs, flux_nonconservative_fjordholm_etal) -solver = DGSEM(polydeg=3, surface_flux=surface_flux, - volume_integral=VolumeIntegralFluxDifferencing(volume_flux)) +solver = DGSEM(polydeg = 3, surface_flux = surface_flux, + volume_integral = VolumeIntegralFluxDifferencing(volume_flux)) ############################################################################### # Get the TreeMesh and setup a periodic mesh @@ -25,14 +25,14 @@ solver = DGSEM(polydeg=3, surface_flux=surface_flux, coordinates_min = 0.0 coordinates_max = sqrt(2.0) mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=3, - n_cells_max=10_000, - periodicity=false) + initial_refinement_level = 3, + n_cells_max = 10_000, + periodicity = false) # create the semi discretization object semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver, boundary_conditions = boundary_condition, - source_terms=source_terms_convergence_test) + source_terms = source_terms_convergence_test) ############################################################################### # ODE solvers, callbacks etc. @@ -43,13 +43,13 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 500 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=200, - save_initial_solution=true, - save_final_solution=true) +save_solution = SaveSolutionCallback(interval = 200, + save_initial_solution = true, + save_final_solution = true) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, save_solution) @@ -57,6 +57,6 @@ callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, sav # run the simulation # use a Runge-Kutta method with automatic (error based) time step size control -sol = solve(ode, RDPK3SpFSAL49(); abstol=1.0e-8, reltol=1.0e-8, - ode_default_options()..., callback=callbacks); +sol = solve(ode, RDPK3SpFSAL49(); abstol = 1.0e-8, reltol = 1.0e-8, + ode_default_options()..., callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/tree_1d_dgsem/elixir_shallowwater_twolayer_convergence.jl b/examples/tree_1d_dgsem/elixir_shallowwater_twolayer_convergence.jl index e9f444aed27..fc76b4f034b 100644 --- a/examples/tree_1d_dgsem/elixir_shallowwater_twolayer_convergence.jl +++ b/examples/tree_1d_dgsem/elixir_shallowwater_twolayer_convergence.jl @@ -5,18 +5,18 @@ using Trixi ############################################################################### # Semidiscretization of the two-layer shallow water equations -equations = ShallowWaterTwoLayerEquations1D(gravity_constant=10.0, rho_upper=0.9, rho_lower=1.0) +equations = ShallowWaterTwoLayerEquations1D(gravity_constant = 10.0, rho_upper = 0.9, + rho_lower = 1.0) initial_condition = initial_condition_convergence_test - ############################################################################### # Get the DG approximation space volume_flux = (flux_wintermeyer_etal, flux_nonconservative_wintermeyer_etal) -solver = DGSEM(polydeg=3, surface_flux=(flux_fjordholm_etal, flux_nonconservative_fjordholm_etal), - volume_integral=VolumeIntegralFluxDifferencing(volume_flux)) - +solver = DGSEM(polydeg = 3, + surface_flux = (flux_fjordholm_etal, flux_nonconservative_fjordholm_etal), + volume_integral = VolumeIntegralFluxDifferencing(volume_flux)) ############################################################################### # Get the TreeMesh and setup a periodic mesh @@ -24,13 +24,13 @@ solver = DGSEM(polydeg=3, surface_flux=(flux_fjordholm_etal, flux_nonconservativ coordinates_min = 0.0 coordinates_max = sqrt(2.0) mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=3, - n_cells_max=10_000, - periodicity=true) + initial_refinement_level = 3, + n_cells_max = 10_000, + periodicity = true) # create the semi discretization object semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver, - source_terms=source_terms_convergence_test) + source_terms = source_terms_convergence_test) ############################################################################### # ODE solvers, callbacks etc. @@ -41,13 +41,13 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 500 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=500, - save_initial_solution=true, - save_final_solution=true) +save_solution = SaveSolutionCallback(interval = 500, + save_initial_solution = true, + save_final_solution = true) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, save_solution) @@ -55,6 +55,6 @@ callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, sav # run the simulation # use a Runge-Kutta method with automatic (error based) time step size control - sol = solve(ode, RDPK3SpFSAL49(), abstol=1.0e-8, reltol=1.0e-8, - save_everystep=false, callback=callbacks); +sol = solve(ode, RDPK3SpFSAL49(), abstol = 1.0e-8, reltol = 1.0e-8, + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/tree_1d_dgsem/elixir_shallowwater_twolayer_dam_break.jl b/examples/tree_1d_dgsem/elixir_shallowwater_twolayer_dam_break.jl index 60770d158fa..b2e6a81401b 100644 --- a/examples/tree_1d_dgsem/elixir_shallowwater_twolayer_dam_break.jl +++ b/examples/tree_1d_dgsem/elixir_shallowwater_twolayer_dam_break.jl @@ -6,28 +6,29 @@ using Trixi # Semidiscretization of the two-layer shallow water equations for a dam break # test with a discontinuous bottom topography function to test entropy conservation -equations = ShallowWaterTwoLayerEquations1D(gravity_constant=9.81, H0=2.0, rho_upper=0.9, rho_lower=1.0) +equations = ShallowWaterTwoLayerEquations1D(gravity_constant = 9.81, H0 = 2.0, + rho_upper = 0.9, rho_lower = 1.0) # Initial condition of a dam break with a discontinuous water heights and bottom topography. # Works as intended for TreeMesh1D with `initial_refinement_level=5`. If the mesh # refinement level is changed the initial condition below may need changed as well to # ensure that the discontinuities lie on an element interface. function initial_condition_dam_break(x, t, equations::ShallowWaterTwoLayerEquations1D) - v1_upper = 0.0 - v1_lower = 0.0 - - # Set the discontinuity - if x[1] <= 10.0 - H_lower = 2.0 - H_upper = 4.0 - b = 0.0 - else - H_lower = 1.5 - H_upper = 3.0 - b = 0.5 - end - - return prim2cons(SVector(H_upper, v1_upper, H_lower, v1_lower, b), equations) + v1_upper = 0.0 + v1_lower = 0.0 + + # Set the discontinuity + if x[1] <= 10.0 + H_lower = 2.0 + H_upper = 4.0 + b = 0.0 + else + H_lower = 1.5 + H_upper = 3.0 + b = 0.5 + end + + return prim2cons(SVector(H_upper, v1_upper, H_lower, v1_lower, b), equations) end initial_condition = initial_condition_dam_break @@ -36,8 +37,9 @@ initial_condition = initial_condition_dam_break # Get the DG approximation space volume_flux = (flux_wintermeyer_etal, flux_nonconservative_wintermeyer_etal) -solver = DGSEM(polydeg=3, surface_flux=(flux_fjordholm_etal, flux_nonconservative_fjordholm_etal), - volume_integral=VolumeIntegralFluxDifferencing(volume_flux)) +solver = DGSEM(polydeg = 3, + surface_flux = (flux_fjordholm_etal, flux_nonconservative_fjordholm_etal), + volume_integral = VolumeIntegralFluxDifferencing(volume_flux)) ############################################################################### # Get the TreeMesh and setup a non-periodic mesh @@ -45,20 +47,20 @@ solver = DGSEM(polydeg=3, surface_flux=(flux_fjordholm_etal, flux_nonconservativ coordinates_min = 0.0 coordinates_max = 20.0 mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=5, - n_cells_max=10000, - periodicity=false) + initial_refinement_level = 5, + n_cells_max = 10000, + periodicity = false) boundary_condition = boundary_condition_slip_wall # create the semidiscretization object semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver, - boundary_conditions=boundary_condition) + boundary_conditions = boundary_condition) ############################################################################### # ODE solvers -tspan = (0.0,0.4) +tspan = (0.0, 0.4) ode = semidiscretize(semi, tspan) ############################################################################### @@ -67,16 +69,19 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 500 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval, save_analysis=false, - extra_analysis_integrals=(energy_total, energy_kinetic, energy_internal,)) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval, + save_analysis = false, + extra_analysis_integrals = (energy_total, + energy_kinetic, + energy_internal)) -stepsize_callback = StepsizeCallback(cfl=1.0) +stepsize_callback = StepsizeCallback(cfl = 1.0) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=500, - save_initial_solution=true, - save_final_solution=true) +save_solution = SaveSolutionCallback(interval = 500, + save_initial_solution = true, + save_final_solution = true) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, save_solution) @@ -84,6 +89,6 @@ callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, sav # run the simulation # use a Runge-Kutta method with automatic (error based) time step size control -sol = solve(ode, RDPK3SpFSAL49(), abstol=1.0e-8, reltol=1.0e-8, - save_everystep=false, callback=callbacks); -summary_callback() # print the timer summary \ No newline at end of file +sol = solve(ode, RDPK3SpFSAL49(), abstol = 1.0e-8, reltol = 1.0e-8, + save_everystep = false, callback = callbacks); +summary_callback() # print the timer summary diff --git a/examples/tree_1d_dgsem/elixir_shallowwater_twolayer_well_balanced.jl b/examples/tree_1d_dgsem/elixir_shallowwater_twolayer_well_balanced.jl index bec0b8ab69c..7236f1697d0 100644 --- a/examples/tree_1d_dgsem/elixir_shallowwater_twolayer_well_balanced.jl +++ b/examples/tree_1d_dgsem/elixir_shallowwater_twolayer_well_balanced.jl @@ -5,7 +5,8 @@ using Trixi ############################################################################### # Semidiscretization of the two-layer shallow water equations to test well-balancedness -equations = ShallowWaterTwoLayerEquations1D(gravity_constant=1.0, H0=0.6, rho_upper=0.9, rho_lower=1.0) +equations = ShallowWaterTwoLayerEquations1D(gravity_constant = 1.0, H0 = 0.6, + rho_upper = 0.9, rho_lower = 1.0) """ initial_condition_fjordholm_well_balanced(x, t, equations::ShallowWaterTwoLayerEquations1D) @@ -15,7 +16,8 @@ Initial condition to test well balanced with a bottom topography from Fjordholm Energy conservative and stable schemes for the two-layer shallow water equations. [DOI: 10.1142/9789814417099_0039](https://doi.org/10.1142/9789814417099_0039) """ -function initial_condition_fjordholm_well_balanced(x, t, equations::ShallowWaterTwoLayerEquations1D) +function initial_condition_fjordholm_well_balanced(x, t, + equations::ShallowWaterTwoLayerEquations1D) inicenter = 0.5 x_norm = x[1] - inicenter r = abs(x_norm) @@ -24,9 +26,9 @@ function initial_condition_fjordholm_well_balanced(x, t, equations::ShallowWater H_upper = 0.6 v1_upper = 0.0 v1_lower = 0.0 - b = r <= 0.1 ? 0.2 * (cos(10 * pi * (x[1] - 0.5)) + 1) : 0.0 + b = r <= 0.1 ? 0.2 * (cos(10 * pi * (x[1] - 0.5)) + 1) : 0.0 return prim2cons(SVector(H_upper, v1_upper, H_lower, v1_lower, b), equations) - end +end initial_condition = initial_condition_fjordholm_well_balanced @@ -34,8 +36,9 @@ initial_condition = initial_condition_fjordholm_well_balanced # Get the DG approximation space volume_flux = (flux_wintermeyer_etal, flux_nonconservative_wintermeyer_etal) -solver = DGSEM(polydeg=3, surface_flux=(flux_es_fjordholm_etal, flux_nonconservative_fjordholm_etal), - volume_integral=VolumeIntegralFluxDifferencing(volume_flux)) +solver = DGSEM(polydeg = 3, + surface_flux = (flux_es_fjordholm_etal, flux_nonconservative_fjordholm_etal), + volume_integral = VolumeIntegralFluxDifferencing(volume_flux)) ############################################################################### # Get the TreeMesh and setup a periodic mesh @@ -43,9 +46,9 @@ solver = DGSEM(polydeg=3, surface_flux=(flux_es_fjordholm_etal, flux_nonconserva coordinates_min = 0.0 coordinates_max = 1.0 mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=4, - n_cells_max=10_000, - periodicity=true) + initial_refinement_level = 4, + n_cells_max = 10_000, + periodicity = true) # create the semi discretization object semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver) @@ -59,16 +62,17 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 1000 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval, save_analysis=false, - extra_analysis_integrals=(lake_at_rest_error,)) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval, + save_analysis = false, + extra_analysis_integrals = (lake_at_rest_error,)) -stepsize_callback = StepsizeCallback(cfl=1.0) +stepsize_callback = StepsizeCallback(cfl = 1.0) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=1000, - save_initial_solution=true, - save_final_solution=true) +save_solution = SaveSolutionCallback(interval = 1000, + save_initial_solution = true, + save_final_solution = true) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, save_solution, stepsize_callback) @@ -76,7 +80,7 @@ callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, sav ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/tree_1d_dgsem/elixir_shallowwater_well_balanced.jl b/examples/tree_1d_dgsem/elixir_shallowwater_well_balanced.jl index e07bc04d76a..649e5023f6d 100644 --- a/examples/tree_1d_dgsem/elixir_shallowwater_well_balanced.jl +++ b/examples/tree_1d_dgsem/elixir_shallowwater_well_balanced.jl @@ -6,7 +6,7 @@ using Trixi # semidiscretization of the shallow water equations with a discontinuous # bottom topography function -equations = ShallowWaterEquations1D(gravity_constant=9.81, H0=3.25) +equations = ShallowWaterEquations1D(gravity_constant = 9.81, H0 = 3.25) # Setup a truly discontinuous bottom topography function for this academic # testcase of well-balancedness. The errors from the analysis callback are @@ -15,18 +15,19 @@ equations = ShallowWaterEquations1D(gravity_constant=9.81, H0=3.25) # Works as intended for TreeMesh1D with `initial_refinement_level=3`. If the mesh # refinement level is changed the initial condition below may need changed as well to # ensure that the discontinuities lie on an element interface. -function initial_condition_discontinuous_well_balancedness(x, t, equations::ShallowWaterEquations1D) - # Set the background values - H = equations.H0 - v = 0.0 - b = 0.0 - - # Setup a discontinuous bottom topography - if x[1] >= 0.5 && x[1] <= 0.75 - b = 2.0 + 0.5 * sin(2.0 * pi * x[1]) - end - - return prim2cons(SVector(H, v, b), equations) +function initial_condition_discontinuous_well_balancedness(x, t, + equations::ShallowWaterEquations1D) + # Set the background values + H = equations.H0 + v = 0.0 + b = 0.0 + + # Setup a discontinuous bottom topography + if x[1] >= 0.5 && x[1] <= 0.75 + b = 2.0 + 0.5 * sin(2.0 * pi * x[1]) + end + + return prim2cons(SVector(H, v, b), equations) end initial_condition = initial_condition_discontinuous_well_balancedness @@ -36,17 +37,17 @@ initial_condition = initial_condition_discontinuous_well_balancedness volume_flux = (flux_wintermeyer_etal, flux_nonconservative_wintermeyer_etal) surface_flux = (flux_fjordholm_etal, flux_nonconservative_fjordholm_etal) -solver = DGSEM(polydeg=4, surface_flux=surface_flux, - volume_integral=VolumeIntegralFluxDifferencing(volume_flux)) +solver = DGSEM(polydeg = 4, surface_flux = surface_flux, + volume_integral = VolumeIntegralFluxDifferencing(volume_flux)) ############################################################################### # Get the TreeMesh and setup a periodic mesh coordinates_min = -1.0 -coordinates_max = 1.0 +coordinates_max = 1.0 mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=3, - n_cells_max=10_000) + initial_refinement_level = 3, + n_cells_max = 10_000) # Create the semi discretization object semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver) @@ -63,16 +64,16 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 1000 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval, - extra_analysis_integrals=(lake_at_rest_error,)) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval, + extra_analysis_integrals = (lake_at_rest_error,)) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=1000, - save_initial_solution=true, - save_final_solution=true) +save_solution = SaveSolutionCallback(interval = 1000, + save_initial_solution = true, + save_final_solution = true) -stepsize_callback = StepsizeCallback(cfl=3.0) +stepsize_callback = StepsizeCallback(cfl = 3.0) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, save_solution, stepsize_callback) @@ -80,7 +81,7 @@ callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, sav ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/tree_1d_dgsem/elixir_shallowwater_well_balanced_nonperiodic.jl b/examples/tree_1d_dgsem/elixir_shallowwater_well_balanced_nonperiodic.jl index ef707b803e9..e55fffc101e 100644 --- a/examples/tree_1d_dgsem/elixir_shallowwater_well_balanced_nonperiodic.jl +++ b/examples/tree_1d_dgsem/elixir_shallowwater_well_balanced_nonperiodic.jl @@ -5,19 +5,19 @@ using Trixi ############################################################################### # Semidiscretization of the shallow water equations -equations = ShallowWaterEquations1D(gravity_constant=1.0, H0=3.0) +equations = ShallowWaterEquations1D(gravity_constant = 1.0, H0 = 3.0) # An initial condition with constant total water height and zero velocities to test well-balancedness. function initial_condition_well_balancedness(x, t, equations::ShallowWaterEquations1D) - # Set the background values - H = equations.H0 - v = 0.0 + # Set the background values + H = equations.H0 + v = 0.0 - b = (1.5 / exp( 0.5 * ((x[1] - 1.0)^2))+ 0.75 / exp(0.5 * ((x[1] + 1.0)^2))) + b = (1.5 / exp(0.5 * ((x[1] - 1.0)^2)) + 0.75 / exp(0.5 * ((x[1] + 1.0)^2))) - return prim2cons(SVector(H, v, b), equations) + return prim2cons(SVector(H, v, b), equations) end - + initial_condition = initial_condition_well_balancedness boundary_condition = BoundaryConditionDirichlet(initial_condition) @@ -26,8 +26,8 @@ boundary_condition = BoundaryConditionDirichlet(initial_condition) # Get the DG approximation space volume_flux = (flux_wintermeyer_etal, flux_nonconservative_wintermeyer_etal) -solver = DGSEM(polydeg=4, surface_flux=(flux_hll, flux_nonconservative_fjordholm_etal), - volume_integral=VolumeIntegralFluxDifferencing(volume_flux)) +solver = DGSEM(polydeg = 4, surface_flux = (flux_hll, flux_nonconservative_fjordholm_etal), + volume_integral = VolumeIntegralFluxDifferencing(volume_flux)) ############################################################################### # Get the TreeMesh and setup a periodic mesh @@ -35,9 +35,9 @@ solver = DGSEM(polydeg=4, surface_flux=(flux_hll, flux_nonconservative_fjordholm coordinates_min = 0.0 coordinates_max = sqrt(2.0) mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=3, - n_cells_max=10_000, - periodicity=false) + initial_refinement_level = 3, + n_cells_max = 10_000, + periodicity = false) # create the semi discretization object semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver, @@ -52,25 +52,25 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 1000 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval, - save_analysis=true, - extra_analysis_integrals=(lake_at_rest_error,)) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval, + save_analysis = true, + extra_analysis_integrals = (lake_at_rest_error,)) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=1000, - save_initial_solution=true, - save_final_solution=true) +save_solution = SaveSolutionCallback(interval = 1000, + save_initial_solution = true, + save_final_solution = true) -stepsize_callback = StepsizeCallback(cfl=1.0) +stepsize_callback = StepsizeCallback(cfl = 1.0) -callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, save_solution, +callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, save_solution, stepsize_callback) ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/tree_1d_dgsem/elixir_shallowwater_well_balanced_wet_dry.jl b/examples/tree_1d_dgsem/elixir_shallowwater_well_balanced_wet_dry.jl index 8de46c61794..26a8960ab46 100644 --- a/examples/tree_1d_dgsem/elixir_shallowwater_well_balanced_wet_dry.jl +++ b/examples/tree_1d_dgsem/elixir_shallowwater_well_balanced_wet_dry.jl @@ -8,7 +8,7 @@ using Printf: @printf, @sprintf # # TODO: TrixiShallowWater: wet/dry example elixir -equations = ShallowWaterEquations1D(gravity_constant=9.812) +equations = ShallowWaterEquations1D(gravity_constant = 9.812) """ initial_condition_complex_bottom_well_balanced(x, t, equations:: ShallowWaterEquations1D) @@ -23,28 +23,29 @@ The initial condition is taken from Section 5.2 of the paper: A new hydrostatic reconstruction scheme based on subcell reconstructions [DOI:10.1137/15M1053074](https://dx.doi.org/10.1137/15M1053074) """ -function initial_condition_complex_bottom_well_balanced(x, t, equations:: ShallowWaterEquations1D) - v = 0.0 - b = sin(4 * pi * x[1]) + 3 - - if x[1] >= 0.5 - b = sin(4 * pi * x[1]) + 1 - end - - H = max(b, 2.5) - - if x[1] >= 0.5 - H = max(b, 1.5) - end - - # It is mandatory to shift the water level at dry areas to make sure the water height h - # stays positive. The system would not be stable for h set to a hard 0 due to division by h in - # the computation of velocity, e.g., (h v) / h. Therefore, a small dry state threshold - # with a default value of 500*eps() ≈ 1e-13 in double precision, is set in the constructor above - # for the ShallowWaterEquations and added to the initial condition if h = 0. - # This default value can be changed within the constructor call depending on the simulation setup. - H = max(H, b + equations.threshold_limiter) - return prim2cons(SVector(H, v, b), equations) +function initial_condition_complex_bottom_well_balanced(x, t, + equations::ShallowWaterEquations1D) + v = 0.0 + b = sin(4 * pi * x[1]) + 3 + + if x[1] >= 0.5 + b = sin(4 * pi * x[1]) + 1 + end + + H = max(b, 2.5) + + if x[1] >= 0.5 + H = max(b, 1.5) + end + + # It is mandatory to shift the water level at dry areas to make sure the water height h + # stays positive. The system would not be stable for h set to a hard 0 due to division by h in + # the computation of velocity, e.g., (h v) / h. Therefore, a small dry state threshold + # with a default value of 500*eps() ≈ 1e-13 in double precision, is set in the constructor above + # for the ShallowWaterEquations and added to the initial condition if h = 0. + # This default value can be changed within the constructor call depending on the simulation setup. + H = max(H, b + equations.threshold_limiter) + return prim2cons(SVector(H, v, b), equations) end initial_condition = initial_condition_complex_bottom_well_balanced @@ -53,19 +54,20 @@ initial_condition = initial_condition_complex_bottom_well_balanced # Get the DG approximation space volume_flux = (flux_wintermeyer_etal, flux_nonconservative_wintermeyer_etal) -surface_flux = (FluxHydrostaticReconstruction(flux_hll_chen_noelle, hydrostatic_reconstruction_chen_noelle), +surface_flux = (FluxHydrostaticReconstruction(flux_hll_chen_noelle, + hydrostatic_reconstruction_chen_noelle), flux_nonconservative_chen_noelle) basis = LobattoLegendreBasis(3) indicator_sc = IndicatorHennemannGassnerShallowWater(equations, basis, - alpha_max=0.5, - alpha_min=0.001, - alpha_smooth=true, - variable=waterheight_pressure) + alpha_max = 0.5, + alpha_min = 0.001, + alpha_smooth = true, + variable = waterheight_pressure) volume_integral = VolumeIntegralShockCapturingHG(indicator_sc; - volume_flux_dg=volume_flux, - volume_flux_fv=surface_flux) + volume_flux_dg = volume_flux, + volume_flux_fv = surface_flux) solver = DGSEM(basis, surface_flux, volume_integral) @@ -76,8 +78,8 @@ coordinates_min = 0.0 coordinates_max = 1.0 mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=6, - n_cells_max=10_000) + initial_refinement_level = 6, + n_cells_max = 10_000) # create the semi discretization object semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver) @@ -91,26 +93,27 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 5000 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval, save_analysis=false) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval, + save_analysis = false) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=5000, - save_initial_solution=true, - save_final_solution=true) +save_solution = SaveSolutionCallback(interval = 5000, + save_initial_solution = true, + save_final_solution = true) -stepsize_callback = StepsizeCallback(cfl=1.5) +stepsize_callback = StepsizeCallback(cfl = 1.5) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, save_solution, stepsize_callback) -stage_limiter! = PositivityPreservingLimiterShallowWater(variables=(Trixi.waterheight,)) +stage_limiter! = PositivityPreservingLimiterShallowWater(variables = (Trixi.waterheight,)) ############################################################################### # run the simulation -sol = solve(ode, SSPRK43(stage_limiter!); dt=1.0, - ode_default_options()..., callback=callbacks, adaptive=false); +sol = solve(ode, SSPRK43(stage_limiter!); dt = 1.0, + ode_default_options()..., callback = callbacks, adaptive = false); summary_callback() # print the timer summary @@ -123,35 +126,39 @@ summary_callback() # print the timer summary # Declare a special version of the function to compute the lake-at-rest error # OBS! The reference water height values are hardcoded for convenience. function lake_at_rest_error_two_level(u, x, equations::ShallowWaterEquations1D) - h, _, b = u - - # For well-balancedness testing with possible wet/dry regions the reference - # water height `H0` accounts for the possibility that the bottom topography - # can emerge out of the water as well as for the threshold offset to avoid - # division by a "hard" zero water heights as well. - if x[1] < 0.5 - H0_wet_dry = max( 2.5 , b + equations.threshold_limiter ) - else - H0_wet_dry = max( 1.5 , b + equations.threshold_limiter ) - end - - return abs(H0_wet_dry - (h + b)) - end + h, _, b = u + + # For well-balancedness testing with possible wet/dry regions the reference + # water height `H0` accounts for the possibility that the bottom topography + # can emerge out of the water as well as for the threshold offset to avoid + # division by a "hard" zero water heights as well. + if x[1] < 0.5 + H0_wet_dry = max(2.5, b + equations.threshold_limiter) + else + H0_wet_dry = max(1.5, b + equations.threshold_limiter) + end + + return abs(H0_wet_dry - (h + b)) +end # point to the data we want to analyze u = Trixi.wrap_array(sol[end], semi) # Perform the actual integration of the well-balancedness error over the domain -l1_well_balance_error = Trixi.integrate_via_indices(u, mesh, equations, semi.solver, semi.cache; normalize=true) do u, i, element, equations, solver - x_node = Trixi.get_node_coords(semi.cache.elements.node_coordinates, equations, solver, i, element) - # We know that the discontinuity is a vertical line. Slightly augment the x value by a factor - # of unit roundoff to avoid the repeted value from the LGL nodes at at interface. - if i == 1 - x_node = SVector(nextfloat(x_node[1])) - elseif i == nnodes(semi.solver) - x_node = SVector(prevfloat(x_node[1])) - end - u_local = Trixi.get_node_vars(u, equations, solver, i, element) - return lake_at_rest_error_two_level(u_local, x_node, equations) +l1_well_balance_error = Trixi.integrate_via_indices(u, mesh, equations, semi.solver, + semi.cache; + normalize = true) do u, i, element, + equations, solver + x_node = Trixi.get_node_coords(semi.cache.elements.node_coordinates, equations, solver, + i, element) + # We know that the discontinuity is a vertical line. Slightly augment the x value by a factor + # of unit roundoff to avoid the repeted value from the LGL nodes at at interface. + if i == 1 + x_node = SVector(nextfloat(x_node[1])) + elseif i == nnodes(semi.solver) + x_node = SVector(prevfloat(x_node[1])) + end + u_local = Trixi.get_node_vars(u, equations, solver, i, element) + return lake_at_rest_error_two_level(u_local, x_node, equations) end # report the well-balancedness lake-at-rest error to the screen @@ -162,4 +169,4 @@ println(" Lake-at-rest error for '", Trixi.get_name(equations), "' with ", summa @printf(" %-12s:", Trixi.pretty_form_utf(lake_at_rest_error)) @printf(" % 10.8e", l1_well_balance_error) println() -println("─"^100) \ No newline at end of file +println("─"^100) diff --git a/examples/tree_1d_fdsbp/elixir_advection_upwind.jl b/examples/tree_1d_fdsbp/elixir_advection_upwind.jl index 1f2498e0866..389a8566c97 100644 --- a/examples/tree_1d_fdsbp/elixir_advection_upwind.jl +++ b/examples/tree_1d_fdsbp/elixir_advection_upwind.jl @@ -24,7 +24,7 @@ solver = FDSBP(D_upw, volume_integral = VolumeIntegralUpwind(flux_splitting)) coordinates_min = -1.0 -coordinates_max = 1.0 +coordinates_max = 1.0 mesh = TreeMesh(coordinates_min, coordinates_max, initial_refinement_level = 4, n_cells_max = 10_000, @@ -32,7 +32,6 @@ mesh = TreeMesh(coordinates_min, coordinates_max, semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition_sin, solver) - ############################################################################### # ODE solvers, callbacks etc. @@ -42,17 +41,16 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 1000 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback) - ############################################################################### # run the simulation -sol = solve(ode, RDPK3SpFSAL49(); abstol=1.0e-6, reltol=1.0e-6, - ode_default_options()..., callback=callbacks); +sol = solve(ode, RDPK3SpFSAL49(); abstol = 1.0e-6, reltol = 1.0e-6, + ode_default_options()..., callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/tree_1d_fdsbp/elixir_advection_upwind_periodic.jl b/examples/tree_1d_fdsbp/elixir_advection_upwind_periodic.jl index 035d3568a80..2d7c13d7e57 100644 --- a/examples/tree_1d_fdsbp/elixir_advection_upwind_periodic.jl +++ b/examples/tree_1d_fdsbp/elixir_advection_upwind_periodic.jl @@ -23,7 +23,7 @@ solver = FDSBP(D_upw, volume_integral = VolumeIntegralUpwind(flux_splitting)) coordinates_min = -1.0 -coordinates_max = 1.0 +coordinates_max = 1.0 mesh = TreeMesh(coordinates_min, coordinates_max, initial_refinement_level = 0, n_cells_max = 10_000, @@ -31,7 +31,6 @@ mesh = TreeMesh(coordinates_min, coordinates_max, semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition_sin, solver) - ############################################################################### # ODE solvers, callbacks etc. @@ -41,17 +40,16 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 1000 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback) - ############################################################################### # run the simulation -sol = solve(ode, RDPK3SpFSAL49(); abstol=1.0e-6, reltol=1.0e-6, - ode_default_options()..., callback=callbacks); +sol = solve(ode, RDPK3SpFSAL49(); abstol = 1.0e-6, reltol = 1.0e-6, + ode_default_options()..., callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/tree_1d_fdsbp/elixir_burgers_basic.jl b/examples/tree_1d_fdsbp/elixir_burgers_basic.jl index c7b0176dfdc..c58fc497e14 100644 --- a/examples/tree_1d_fdsbp/elixir_burgers_basic.jl +++ b/examples/tree_1d_fdsbp/elixir_burgers_basic.jl @@ -12,24 +12,23 @@ equations = InviscidBurgersEquation1D() initial_condition = initial_condition_convergence_test D_upw = upwind_operators(SummationByPartsOperators.Mattsson2017, - derivative_order=1, - accuracy_order=4, - xmin=-1.0, xmax=1.0, - N=32) + derivative_order = 1, + accuracy_order = 4, + xmin = -1.0, xmax = 1.0, + N = 32) flux_splitting = splitting_lax_friedrichs solver = FDSBP(D_upw, - surface_integral=SurfaceIntegralUpwind(flux_splitting), - volume_integral=VolumeIntegralUpwind(flux_splitting)) + surface_integral = SurfaceIntegralUpwind(flux_splitting), + volume_integral = VolumeIntegralUpwind(flux_splitting)) coordinates_min = 0.0 coordinates_max = 1.0 mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=3, - n_cells_max=10_000) + initial_refinement_level = 3, + n_cells_max = 10_000) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver, - source_terms=source_terms_convergence_test) - + source_terms = source_terms_convergence_test) ############################################################################### # ODE solvers, callbacks etc. @@ -40,25 +39,24 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 200 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval, - extra_analysis_errors=(:l2_error_primitive, - :linf_error_primitive)) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval, + extra_analysis_errors = (:l2_error_primitive, + :linf_error_primitive)) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=100, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 100, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, save_solution) - ############################################################################### # run the simulation -sol = solve(ode, SSPRK43(); abstol=1.0e-9, reltol=1.0e-9, - ode_default_options()..., callback=callbacks); +sol = solve(ode, SSPRK43(); abstol = 1.0e-9, reltol = 1.0e-9, + ode_default_options()..., callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/tree_1d_fdsbp/elixir_burgers_linear_stability.jl b/examples/tree_1d_fdsbp/elixir_burgers_linear_stability.jl index 20508feba22..eeaae7a7843 100644 --- a/examples/tree_1d_fdsbp/elixir_burgers_linear_stability.jl +++ b/examples/tree_1d_fdsbp/elixir_burgers_linear_stability.jl @@ -10,28 +10,28 @@ using Trixi equations = InviscidBurgersEquation1D() function initial_condition_linear_stability(x, t, equation::InviscidBurgersEquation1D) - k = 1 - 2 + sinpi(k * (x[1] - 0.7)) |> SVector + k = 1 + 2 + sinpi(k * (x[1] - 0.7)) |> SVector end D_upw = upwind_operators(SummationByPartsOperators.Mattsson2017, - derivative_order=1, - accuracy_order=4, - xmin=-1.0, xmax=1.0, - N=16) + derivative_order = 1, + accuracy_order = 4, + xmin = -1.0, xmax = 1.0, + N = 16) flux_splitting = splitting_lax_friedrichs solver = FDSBP(D_upw, - surface_integral=SurfaceIntegralUpwind(flux_splitting), - volume_integral=VolumeIntegralUpwind(flux_splitting)) + surface_integral = SurfaceIntegralUpwind(flux_splitting), + volume_integral = VolumeIntegralUpwind(flux_splitting)) coordinates_min = -1.0 -coordinates_max = 1.0 +coordinates_max = 1.0 mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=4, - n_cells_max=10_000) - -semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition_linear_stability, solver) + initial_refinement_level = 4, + n_cells_max = 10_000) +semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition_linear_stability, + solver) ############################################################################### # ODE solvers, callbacks etc. @@ -42,19 +42,18 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 1000 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval, - extra_analysis_errors=(:l2_error_primitive, - :linf_error_primitive)) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval, + extra_analysis_errors = (:l2_error_primitive, + :linf_error_primitive)) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback) - ############################################################################### # run the simulation -sol = solve(ode, SSPRK43(); abstol=1.0e-6, reltol=1.0e-6, - ode_default_options()..., callback=callbacks); +sol = solve(ode, SSPRK43(); abstol = 1.0e-6, reltol = 1.0e-6, + ode_default_options()..., callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/tree_1d_fdsbp/elixir_euler_convergence.jl b/examples/tree_1d_fdsbp/elixir_euler_convergence.jl index f9f9297f7c8..7b6bfee946e 100644 --- a/examples/tree_1d_fdsbp/elixir_euler_convergence.jl +++ b/examples/tree_1d_fdsbp/elixir_euler_convergence.jl @@ -12,24 +12,23 @@ equations = CompressibleEulerEquations1D(1.4) initial_condition = initial_condition_convergence_test D_upw = upwind_operators(SummationByPartsOperators.Mattsson2017, - derivative_order=1, - accuracy_order=4, - xmin=-1.0, xmax=1.0, - N=32) + derivative_order = 1, + accuracy_order = 4, + xmin = -1.0, xmax = 1.0, + N = 32) flux_splitting = splitting_steger_warming solver = FDSBP(D_upw, - surface_integral=SurfaceIntegralUpwind(flux_splitting), - volume_integral=VolumeIntegralUpwind(flux_splitting)) + surface_integral = SurfaceIntegralUpwind(flux_splitting), + volume_integral = VolumeIntegralUpwind(flux_splitting)) coordinates_min = 0.0 coordinates_max = 2.0 mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=1, - n_cells_max=10_000) + initial_refinement_level = 1, + n_cells_max = 10_000) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver, - source_terms=source_terms_convergence_test) - + source_terms = source_terms_convergence_test) ############################################################################### # ODE solvers, callbacks etc. @@ -40,25 +39,24 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval, - extra_analysis_errors=(:l2_error_primitive, - :linf_error_primitive)) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval, + extra_analysis_errors = (:l2_error_primitive, + :linf_error_primitive)) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=100, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 100, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, save_solution) - ############################################################################### # run the simulation -sol = solve(ode, SSPRK43(); abstol=1.0e-6, reltol=1.0e-6, - ode_default_options()..., callback=callbacks) +sol = solve(ode, SSPRK43(); abstol = 1.0e-6, reltol = 1.0e-6, + ode_default_options()..., callback = callbacks) summary_callback() # print the timer summary diff --git a/examples/tree_1d_fdsbp/elixir_euler_density_wave.jl b/examples/tree_1d_fdsbp/elixir_euler_density_wave.jl index 5c5192a3fbe..a28cd01120b 100644 --- a/examples/tree_1d_fdsbp/elixir_euler_density_wave.jl +++ b/examples/tree_1d_fdsbp/elixir_euler_density_wave.jl @@ -11,24 +11,23 @@ equations = CompressibleEulerEquations1D(1.4) initial_condition = initial_condition_density_wave D_upw = upwind_operators(SummationByPartsOperators.Mattsson2017, - derivative_order=1, - accuracy_order=4, - xmin=-1.0, xmax=1.0, - N=16) + derivative_order = 1, + accuracy_order = 4, + xmin = -1.0, xmax = 1.0, + N = 16) flux_splitting = splitting_coirier_vanleer solver = FDSBP(D_upw, - surface_integral=SurfaceIntegralUpwind(flux_splitting), - volume_integral=VolumeIntegralUpwind(flux_splitting)) + surface_integral = SurfaceIntegralUpwind(flux_splitting), + volume_integral = VolumeIntegralUpwind(flux_splitting)) coordinates_min = -1.0 -coordinates_max = 1.0 +coordinates_max = 1.0 mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=2, - n_cells_max=30_000) + initial_refinement_level = 2, + n_cells_max = 30_000) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver) - ############################################################################### # ODE solvers, callbacks etc. @@ -38,23 +37,22 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 10000 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=100, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 100, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, save_solution) - ############################################################################### # run the simulation -sol = solve(ode, SSPRK43(); abstol=1.0e-6, reltol=1.0e-6, - ode_default_options()..., callback=callbacks) +sol = solve(ode, SSPRK43(); abstol = 1.0e-6, reltol = 1.0e-6, + ode_default_options()..., callback = callbacks) summary_callback() # print the timer summary diff --git a/examples/tree_2d_dgsem/elixir_acoustics_convergence.jl b/examples/tree_2d_dgsem/elixir_acoustics_convergence.jl index d34399a5576..615da951871 100644 --- a/examples/tree_2d_dgsem/elixir_acoustics_convergence.jl +++ b/examples/tree_2d_dgsem/elixir_acoustics_convergence.jl @@ -4,26 +4,25 @@ using Trixi ############################################################################### # semidiscretization of the acoustic perturbation equations -equations = AcousticPerturbationEquations2D(v_mean_global=(0.5, 0.3), c_mean_global=2.0, - rho_mean_global=0.9) +equations = AcousticPerturbationEquations2D(v_mean_global = (0.5, 0.3), c_mean_global = 2.0, + rho_mean_global = 0.9) initial_condition = initial_condition_convergence_test # Create DG solver with polynomial degree = 3 and (local) Lax-Friedrichs/Rusanov flux as surface flux -solver = DGSEM(polydeg=3, surface_flux=flux_lax_friedrichs) +solver = DGSEM(polydeg = 3, surface_flux = flux_lax_friedrichs) coordinates_min = (0.0, 0.0) # minimum coordinates (min(x), min(y)) coordinates_max = (2.0, 2.0) # maximum coordinates (max(x), max(y)) # Create a uniformly refined mesh with periodic boundaries mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=3, - n_cells_max=30_000) # set maximum capacity of tree data structure + initial_refinement_level = 3, + n_cells_max = 30_000) # set maximum capacity of tree data structure # A semidiscretization collects data structures and functions for the spatial discretization semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver, - source_terms=source_terms_convergence_test) - + source_terms = source_terms_convergence_test) ############################################################################### # ODE solvers, callbacks etc. @@ -37,26 +36,26 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() # The AnalysisCallback allows to analyse the solution in regular intervals and prints the results -analysis_callback = AnalysisCallback(semi, interval=100) +analysis_callback = AnalysisCallback(semi, interval = 100) # The SaveSolutionCallback allows to save the solution to a file in regular intervals -save_solution = SaveSolutionCallback(interval=100, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 100, + solution_variables = cons2prim) # The StepsizeCallback handles the re-calculation of the maximum Δt after each time step -stepsize_callback = StepsizeCallback(cfl=0.5) +stepsize_callback = StepsizeCallback(cfl = 0.5) # Create a CallbackSet to collect all callbacks such that they can be passed to the ODE solver -callbacks = CallbackSet(summary_callback, analysis_callback, save_solution, stepsize_callback) - +callbacks = CallbackSet(summary_callback, analysis_callback, save_solution, + stepsize_callback) ############################################################################### # run the simulation # OrdinaryDiffEq's `solve` method evolves the solution in time and executes the passed callbacks -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); # Print the timer summary summary_callback() diff --git a/examples/tree_2d_dgsem/elixir_acoustics_gauss.jl b/examples/tree_2d_dgsem/elixir_acoustics_gauss.jl index fa608e78693..b3fe55dccea 100644 --- a/examples/tree_2d_dgsem/elixir_acoustics_gauss.jl +++ b/examples/tree_2d_dgsem/elixir_acoustics_gauss.jl @@ -10,20 +10,19 @@ rho_mean_global = 1.0 equations = AcousticPerturbationEquations2D(v_mean_global, c_mean_global, rho_mean_global) # Create DG solver with polynomial degree = 3 and (local) Lax-Friedrichs/Rusanov flux as surface flux -solver = DGSEM(polydeg=3, surface_flux=flux_lax_friedrichs) +solver = DGSEM(polydeg = 3, surface_flux = flux_lax_friedrichs) coordinates_min = (-1.0, -1.0) # minimum coordinates (min(x), min(y)) -coordinates_max = ( 1.0, 1.0) # maximum coordinates (max(x), max(y)) +coordinates_max = (1.0, 1.0) # maximum coordinates (max(x), max(y)) # Create a uniformly refined mesh with periodic boundaries mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=4, - n_cells_max=30_000) # set maximum capacity of tree data structure + initial_refinement_level = 4, + n_cells_max = 30_000) # set maximum capacity of tree data structure # A semidiscretization collects data structures and functions for the spatial discretization semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition_gauss, solver) - ############################################################################### # ODE solvers, callbacks etc. @@ -36,26 +35,26 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() # The AnalysisCallback allows to analyse the solution in regular intervals and prints the results -analysis_callback = AnalysisCallback(semi, interval=100) +analysis_callback = AnalysisCallback(semi, interval = 100) # The SaveSolutionCallback allows to save the solution to a file in regular intervals -save_solution = SaveSolutionCallback(interval=100, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 100, + solution_variables = cons2prim) # The StepsizeCallback handles the re-calculation of the maximum Δt after each time step -stepsize_callback = StepsizeCallback(cfl=0.5) +stepsize_callback = StepsizeCallback(cfl = 0.5) # Create a CallbackSet to collect all callbacks such that they can be passed to the ODE solver -callbacks = CallbackSet(summary_callback, analysis_callback, save_solution, stepsize_callback) - +callbacks = CallbackSet(summary_callback, analysis_callback, save_solution, + stepsize_callback) ############################################################################### # run the simulation # OrdinaryDiffEq's `solve` method evolves the solution in time and executes the passed callbacks -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); # Print the timer summary summary_callback() diff --git a/examples/tree_2d_dgsem/elixir_acoustics_gauss_wall.jl b/examples/tree_2d_dgsem/elixir_acoustics_gauss_wall.jl index 78102eaf874..918c0831fcd 100644 --- a/examples/tree_2d_dgsem/elixir_acoustics_gauss_wall.jl +++ b/examples/tree_2d_dgsem/elixir_acoustics_gauss_wall.jl @@ -4,20 +4,20 @@ using Trixi ############################################################################### # semidiscretization of the acoustic perturbation equations -equations = AcousticPerturbationEquations2D(v_mean_global=(0.5, 0.0), c_mean_global=1.0, - rho_mean_global=1.0) +equations = AcousticPerturbationEquations2D(v_mean_global = (0.5, 0.0), c_mean_global = 1.0, + rho_mean_global = 1.0) # Create DG solver with polynomial degree = 5 and (local) Lax-Friedrichs/Rusanov flux as surface flux -solver = DGSEM(polydeg=5, surface_flux=flux_lax_friedrichs) +solver = DGSEM(polydeg = 5, surface_flux = flux_lax_friedrichs) coordinates_min = (-100.0, 0.0) # minimum coordinates (min(x), min(y)) coordinates_max = (100.0, 200.0) # maximum coordinates (max(x), max(y)) # Create a uniformly refined mesh with periodic boundaries mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=4, - n_cells_max=100_000, - periodicity=false) + initial_refinement_level = 4, + n_cells_max = 100_000, + periodicity = false) """ initial_condition_gauss_wall(x, t, equations::AcousticPerturbationEquations2D) @@ -26,20 +26,19 @@ A Gaussian pulse, used in the `gauss_wall` example elixir in combination with [`boundary_condition_wall`](@ref). Uses the global mean values from `equations`. """ function initial_condition_gauss_wall(x, t, equations::AcousticPerturbationEquations2D) - v1_prime = 0.0 - v2_prime = 0.0 - p_prime = exp(-log(2) * (x[1]^2 + (x[2] - 25)^2) / 25) + v1_prime = 0.0 + v2_prime = 0.0 + p_prime = exp(-log(2) * (x[1]^2 + (x[2] - 25)^2) / 25) - prim = SVector(v1_prime, v2_prime, p_prime, global_mean_vars(equations)...) + prim = SVector(v1_prime, v2_prime, p_prime, global_mean_vars(equations)...) - return prim2cons(prim, equations) + return prim2cons(prim, equations) end initial_condition = initial_condition_gauss_wall # A semidiscretization collects data structures and functions for the spatial discretization semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver, - boundary_conditions=boundary_condition_wall) - + boundary_conditions = boundary_condition_wall) ############################################################################### # ODE solvers, callbacks etc. @@ -53,24 +52,25 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() # The AnalysisCallback allows to analyse the solution in regular intervals and prints the results -analysis_callback = AnalysisCallback(semi, interval=100) +analysis_callback = AnalysisCallback(semi, interval = 100) # The SaveSolutionCallback allows to save the solution to a file in regular intervals -save_solution = SaveSolutionCallback(interval=100, solution_variables=cons2state) +save_solution = SaveSolutionCallback(interval = 100, solution_variables = cons2state) # The StepsizeCallback handles the re-calculation of the maximum Δt after each time step -stepsize_callback = StepsizeCallback(cfl=0.7) +stepsize_callback = StepsizeCallback(cfl = 0.7) # Create a CallbackSet to collect all callbacks such that they can be passed to the ODE solver -callbacks = CallbackSet(summary_callback, analysis_callback, save_solution, stepsize_callback) +callbacks = CallbackSet(summary_callback, analysis_callback, save_solution, + stepsize_callback) ############################################################################### # run the simulation # OrdinaryDiffEq's `solve` method evolves the solution in time and executes the passed callbacks -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks) +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks) # Print the timer summary summary_callback() diff --git a/examples/tree_2d_dgsem/elixir_acoustics_gaussian_source.jl b/examples/tree_2d_dgsem/elixir_acoustics_gaussian_source.jl index 0a0e2520581..71d4f1a9f68 100644 --- a/examples/tree_2d_dgsem/elixir_acoustics_gaussian_source.jl +++ b/examples/tree_2d_dgsem/elixir_acoustics_gaussian_source.jl @@ -3,45 +3,45 @@ using Trixi # Oscillating Gaussian-shaped source terms function source_terms_gauss(u, x, t, equations::AcousticPerturbationEquations2D) - r = 0.1 - A = 1.0 - f = 2.0 + r = 0.1 + A = 1.0 + f = 2.0 - # Velocity sources - s1 = 0.0 - s2 = 0.0 - # Pressure source - s3 = exp(-(x[1]^2 + x[2]^2) / (2 * r^2)) * A * sin(2 * pi * f * t) + # Velocity sources + s1 = 0.0 + s2 = 0.0 + # Pressure source + s3 = exp(-(x[1]^2 + x[2]^2) / (2 * r^2)) * A * sin(2 * pi * f * t) - # Mean sources - s4 = s5 = s6 = s7 = 0.0 + # Mean sources + s4 = s5 = s6 = s7 = 0.0 - return SVector(s1, s2, s3, s4, s5, s6, s7) + return SVector(s1, s2, s3, s4, s5, s6, s7) end ############################################################################### # semidiscretization of the acoustic perturbation equations -equations = AcousticPerturbationEquations2D(v_mean_global=(-0.5, 0.25), c_mean_global=1.0, - rho_mean_global=1.0) +equations = AcousticPerturbationEquations2D(v_mean_global = (-0.5, 0.25), + c_mean_global = 1.0, + rho_mean_global = 1.0) initial_condition = initial_condition_constant # Create DG solver with polynomial degree = 3 and (local) Lax-Friedrichs/Rusanov flux as surface flux -solver = DGSEM(polydeg=3, surface_flux=flux_lax_friedrichs) +solver = DGSEM(polydeg = 3, surface_flux = flux_lax_friedrichs) coordinates_min = (-3.0, -3.0) # minimum coordinates (min(x), min(y)) -coordinates_max = ( 3.0, 3.0) # maximum coordinates (max(x), max(y)) +coordinates_max = (3.0, 3.0) # maximum coordinates (max(x), max(y)) # Create a uniformly refined mesh with periodic boundaries mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=4, - n_cells_max=30_000) # set maximum capacity of tree data structure + initial_refinement_level = 4, + n_cells_max = 30_000) # set maximum capacity of tree data structure # A semidiscretization collects data structures and functions for the spatial discretization semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver, - source_terms=source_terms_gauss) - + source_terms = source_terms_gauss) ############################################################################### # ODE solvers, callbacks etc. @@ -55,30 +55,29 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() # The AnalysisCallback allows to analyse the solution in regular intervals and prints the results -analysis_callback = AnalysisCallback(semi, interval=100) +analysis_callback = AnalysisCallback(semi, interval = 100) # The SaveSolutionCallback allows to save the solution to a file in regular intervals -save_solution = SaveSolutionCallback(interval=100, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 100, + solution_variables = cons2prim) # The TimeSeriesCallback records the solution at the given points over time time_series = TimeSeriesCallback(semi, [(0.0, 0.0), (-1.0, 0.5)]) # The StepsizeCallback handles the re-calculation of the maximum Δt after each time step -stepsize_callback = StepsizeCallback(cfl=0.5) +stepsize_callback = StepsizeCallback(cfl = 0.5) # Create a CallbackSet to collect all callbacks such that they can be passed to the ODE solver callbacks = CallbackSet(summary_callback, analysis_callback, save_solution, time_series, stepsize_callback) - ############################################################################### # run the simulation # OrdinaryDiffEq's `solve` method evolves the solution in time and executes the passed callbacks -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); # Print the timer summary summary_callback() diff --git a/examples/tree_2d_dgsem/elixir_acoustics_monopole.jl b/examples/tree_2d_dgsem/elixir_acoustics_monopole.jl index 0fdcbd22c44..d7265775114 100644 --- a/examples/tree_2d_dgsem/elixir_acoustics_monopole.jl +++ b/examples/tree_2d_dgsem/elixir_acoustics_monopole.jl @@ -4,11 +4,11 @@ using Trixi ############################################################################### # semidiscretization of the acoustic perturbation equations -equations = AcousticPerturbationEquations2D(v_mean_global=(0.0, 0.0), c_mean_global=0.0, - rho_mean_global=0.0) +equations = AcousticPerturbationEquations2D(v_mean_global = (0.0, 0.0), c_mean_global = 0.0, + rho_mean_global = 0.0) # Create DG solver with polynomial degree = 3 and (local) Lax-Friedrichs/Rusanov flux as surface flux -solver = DGSEM(polydeg=3, surface_flux=flux_lax_friedrichs) +solver = DGSEM(polydeg = 3, surface_flux = flux_lax_friedrichs) coordinates_min = (-20.6, 0.0) # minimum coordinates (min(x), min(y)) coordinates_max = (30.6, 51.2) # maximum coordinates (max(x), max(y)) @@ -20,20 +20,20 @@ Initial condition for the monopole in a boundary layer setup, used in combinatio [`boundary_condition_monopole`](@ref). """ function initial_condition_monopole(x, t, equations::AcousticPerturbationEquations2D) - m = 0.3 # Mach number + m = 0.3 # Mach number - v1_prime = 0.0 - v2_prime = 0.0 - p_prime = 0.0 + v1_prime = 0.0 + v2_prime = 0.0 + p_prime = 0.0 - v1_mean = x[2] > 1 ? m : m * (2*x[2] - 2*x[2]^2 + x[2]^4) - v2_mean = 0.0 - c_mean = 1.0 - rho_mean = 1.0 + v1_mean = x[2] > 1 ? m : m * (2 * x[2] - 2 * x[2]^2 + x[2]^4) + v2_mean = 0.0 + c_mean = 1.0 + rho_mean = 1.0 - prim = SVector(v1_prime, v2_prime, p_prime, v1_mean, v2_mean, c_mean, rho_mean) + prim = SVector(v1_prime, v2_prime, p_prime, v1_mean, v2_mean, c_mean, rho_mean) - return prim2cons(prim, equations) + return prim2cons(prim, equations) end initial_condition = initial_condition_monopole # does not use the global mean values given above @@ -45,32 +45,35 @@ Boundary condition for a monopole in a boundary layer at the -y boundary, i.e. ` This will return an error for any other direction. This boundary condition is used in combination with [`initial_condition_monopole`](@ref). """ -function boundary_condition_monopole(u_inner, orientation, direction, x, t, surface_flux_function, +function boundary_condition_monopole(u_inner, orientation, direction, x, t, + surface_flux_function, equations::AcousticPerturbationEquations2D) - if direction != 3 - error("expected direction = 3, got $direction instead") - end - - # Wall at the boundary in -y direction with a monopole at -0.05 <= x <= 0.05. In the monopole area - # we use a sinusoidal boundary state for the perturbed variables. For the rest of the -y boundary - # we set the boundary state to the inner state and multiply the perturbed velocity in the - # y-direction by -1. - if -0.05 <= x[1] <= 0.05 # Monopole - v1_prime = 0.0 - v2_prime = p_prime = sin(2 * pi * t) - - prim_boundary = SVector(v1_prime, v2_prime, p_prime, u_inner[4], u_inner[5], u_inner[6], u_inner[7]) - - u_boundary = prim2cons(prim_boundary, equations) - else # Wall - u_boundary = SVector(u_inner[1], -u_inner[2], u_inner[3], u_inner[4], u_inner[5], u_inner[6], - u_inner[7]) - end - - # Calculate boundary flux - flux = surface_flux_function(u_boundary, u_inner, orientation, equations) + if direction != 3 + error("expected direction = 3, got $direction instead") + end + + # Wall at the boundary in -y direction with a monopole at -0.05 <= x <= 0.05. In the monopole area + # we use a sinusoidal boundary state for the perturbed variables. For the rest of the -y boundary + # we set the boundary state to the inner state and multiply the perturbed velocity in the + # y-direction by -1. + if -0.05 <= x[1] <= 0.05 # Monopole + v1_prime = 0.0 + v2_prime = p_prime = sin(2 * pi * t) + + prim_boundary = SVector(v1_prime, v2_prime, p_prime, u_inner[4], u_inner[5], + u_inner[6], u_inner[7]) + + u_boundary = prim2cons(prim_boundary, equations) + else # Wall + u_boundary = SVector(u_inner[1], -u_inner[2], u_inner[3], u_inner[4], u_inner[5], + u_inner[6], + u_inner[7]) + end + + # Calculate boundary flux + flux = surface_flux_function(u_boundary, u_inner, orientation, equations) - return flux + return flux end """ @@ -80,42 +83,42 @@ end Boundary condition that uses a boundary state where the state variables are zero and the mean variables are the same as in `u_inner`. """ -function boundary_condition_zero(u_inner, orientation, direction, x, t, surface_flux_function, +function boundary_condition_zero(u_inner, orientation, direction, x, t, + surface_flux_function, equations::AcousticPerturbationEquations2D) - value = zero(eltype(u_inner)) - u_boundary = SVector(value, value, value, cons2mean(u_inner, equations)...) + value = zero(eltype(u_inner)) + u_boundary = SVector(value, value, value, cons2mean(u_inner, equations)...) - # Calculate boundary flux - if iseven(direction) # u_inner is "left" of boundary, u_boundary is "right" of boundary - flux = surface_flux_function(u_inner, u_boundary, orientation, equations) - else # u_boundary is "left" of boundary, u_inner is "right" of boundary - flux = surface_flux_function(u_boundary, u_inner, orientation, equations) - end + # Calculate boundary flux + if iseven(direction) # u_inner is "left" of boundary, u_boundary is "right" of boundary + flux = surface_flux_function(u_inner, u_boundary, orientation, equations) + else # u_boundary is "left" of boundary, u_inner is "right" of boundary + flux = surface_flux_function(u_boundary, u_inner, orientation, equations) + end - return flux + return flux end -boundary_conditions = (x_neg=boundary_condition_zero, - x_pos=boundary_condition_zero, - y_neg=boundary_condition_monopole, - y_pos=boundary_condition_zero) +boundary_conditions = (x_neg = boundary_condition_zero, + x_pos = boundary_condition_zero, + y_neg = boundary_condition_monopole, + y_pos = boundary_condition_zero) # Create a uniformly refined mesh with periodic boundaries mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=6, - n_cells_max=100_000, - periodicity=false) + initial_refinement_level = 6, + n_cells_max = 100_000, + periodicity = false) # A semidiscretization collects data structures and functions for the spatial discretization semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver, - boundary_conditions=boundary_conditions) - + boundary_conditions = boundary_conditions) ############################################################################### # ODE solvers, callbacks etc. # Create ODE problem with time span from 0.0 to 24.0 -tspan = (0.0, 24.0) +tspan = (0.0, 24.0) ode = semidiscretize(semi, tspan) # At the beginning of the main loop, the SummaryCallback prints a summary of the simulation setup @@ -123,24 +126,25 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() # The AnalysisCallback allows to analyse the solution in regular intervals and prints the results -analysis_callback = AnalysisCallback(semi, interval=100) +analysis_callback = AnalysisCallback(semi, interval = 100) # The SaveSolutionCallback allows to save the solution to a file in regular intervals -save_solution = SaveSolutionCallback(interval=100, solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 100, solution_variables = cons2prim) # The StepsizeCallback handles the re-calculation of the maximum Δt after each time step -stepsize_callback = StepsizeCallback(cfl=0.8) +stepsize_callback = StepsizeCallback(cfl = 0.8) # Create a CallbackSet to collect all callbacks such that they can be passed to the ODE solver -callbacks = CallbackSet(summary_callback, analysis_callback, save_solution, stepsize_callback) +callbacks = CallbackSet(summary_callback, analysis_callback, save_solution, + stepsize_callback) ############################################################################### # run the simulation # OrdinaryDiffEq's `solve` method evolves the solution in time and executes the passed callbacks -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks) +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks) # Print the timer summary -summary_callback() \ No newline at end of file +summary_callback() diff --git a/examples/tree_2d_dgsem/elixir_advection_amr.jl b/examples/tree_2d_dgsem/elixir_advection_amr.jl index 84841877448..c3f971d2ffc 100644 --- a/examples/tree_2d_dgsem/elixir_advection_amr.jl +++ b/examples/tree_2d_dgsem/elixir_advection_amr.jl @@ -9,18 +9,16 @@ advection_velocity = (0.2, -0.7) equations = LinearScalarAdvectionEquation2D(advection_velocity) initial_condition = initial_condition_gauss -solver = DGSEM(polydeg=3, surface_flux=flux_lax_friedrichs) +solver = DGSEM(polydeg = 3, surface_flux = flux_lax_friedrichs) coordinates_min = (-5.0, -5.0) -coordinates_max = ( 5.0, 5.0) +coordinates_max = (5.0, 5.0) mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=4, - n_cells_max=30_000) - + initial_refinement_level = 4, + n_cells_max = 30_000) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver) - ############################################################################### # ODE solvers, callbacks etc. @@ -30,37 +28,36 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval, - extra_analysis_integrals=(entropy,)) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval, + extra_analysis_integrals = (entropy,)) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=100, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 100, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) -amr_controller = ControllerThreeLevel(semi, IndicatorMax(semi, variable=first), - base_level=4, - med_level=5, med_threshold=0.1, - max_level=6, max_threshold=0.6) +amr_controller = ControllerThreeLevel(semi, IndicatorMax(semi, variable = first), + base_level = 4, + med_level = 5, med_threshold = 0.1, + max_level = 6, max_threshold = 0.6) amr_callback = AMRCallback(semi, amr_controller, - interval=5, - adapt_initial_condition=true, - adapt_initial_condition_only_refine=true) + interval = 5, + adapt_initial_condition = true, + adapt_initial_condition_only_refine = true) -stepsize_callback = StepsizeCallback(cfl=1.6) +stepsize_callback = StepsizeCallback(cfl = 1.6) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, save_solution, amr_callback, stepsize_callback); - ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/tree_2d_dgsem/elixir_advection_amr_coarsen_twice.jl b/examples/tree_2d_dgsem/elixir_advection_amr_coarsen_twice.jl index 897d3569e10..aa042e7500e 100644 --- a/examples/tree_2d_dgsem/elixir_advection_amr_coarsen_twice.jl +++ b/examples/tree_2d_dgsem/elixir_advection_amr_coarsen_twice.jl @@ -3,7 +3,6 @@ using OrdinaryDiffEq using Trixi - # Define new structs inside a module to allow re-evaluating the file. # This module name needs to be unique among all examples, otherwise Julia will throw warnings # if multiple test cases using the same module name are run in the same session. @@ -11,27 +10,27 @@ module TrixiExtensionCoarsen using Trixi -struct IndicatorAlwaysCoarsen{Cache<:NamedTuple} <: Trixi.AbstractIndicator - cache::Cache +struct IndicatorAlwaysCoarsen{Cache <: NamedTuple} <: Trixi.AbstractIndicator + cache::Cache end function IndicatorAlwaysCoarsen(semi) - basis = semi.solver.basis - alpha = Vector{real(basis)}() - cache = (; semi.mesh, alpha) + basis = semi.solver.basis + alpha = Vector{real(basis)}() + cache = (; semi.mesh, alpha) - return IndicatorAlwaysCoarsen{typeof(cache)}(cache) + return IndicatorAlwaysCoarsen{typeof(cache)}(cache) end -function (indicator::IndicatorAlwaysCoarsen)(u::AbstractArray{<:Any,4}, +function (indicator::IndicatorAlwaysCoarsen)(u::AbstractArray{<:Any, 4}, mesh, equations, dg, cache; t, kwargs...) - alpha = indicator.cache.alpha - resize!(alpha, nelements(dg, cache)) + alpha = indicator.cache.alpha + resize!(alpha, nelements(dg, cache)) - alpha .= -1.0 + alpha .= -1.0 - return alpha + return alpha end end # module TrixiExtensionCoarsen @@ -46,18 +45,16 @@ equations = LinearScalarAdvectionEquation2D(advection_velocity) initial_condition = initial_condition_gauss -solver = DGSEM(polydeg=3, surface_flux=flux_lax_friedrichs) +solver = DGSEM(polydeg = 3, surface_flux = flux_lax_friedrichs) coordinates_min = (-5.0, -5.0) -coordinates_max = ( 5.0, 5.0) +coordinates_max = (5.0, 5.0) mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=4, - n_cells_max=30_000) - + initial_refinement_level = 4, + n_cells_max = 30_000) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver) - ############################################################################### # ODE solvers, callbacks etc. @@ -67,37 +64,37 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval, - extra_analysis_integrals=(entropy,)) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval, + extra_analysis_integrals = (entropy,)) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=100, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 100, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) -amr_controller = ControllerThreeLevel(semi, TrixiExtensionCoarsen.IndicatorAlwaysCoarsen(semi), - base_level=2, max_level=2, - med_threshold=0.1, max_threshold=0.6) +amr_controller = ControllerThreeLevel(semi, + TrixiExtensionCoarsen.IndicatorAlwaysCoarsen(semi), + base_level = 2, max_level = 2, + med_threshold = 0.1, max_threshold = 0.6) amr_callback = AMRCallback(semi, amr_controller, - interval=5, - adapt_initial_condition=true, - adapt_initial_condition_only_refine=true) + interval = 5, + adapt_initial_condition = true, + adapt_initial_condition_only_refine = true) -stepsize_callback = StepsizeCallback(cfl=1.6) +stepsize_callback = StepsizeCallback(cfl = 1.6) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, save_solution, amr_callback, stepsize_callback); - ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/tree_2d_dgsem/elixir_advection_amr_nonperiodic.jl b/examples/tree_2d_dgsem/elixir_advection_amr_nonperiodic.jl index 42aee985889..abb8a5035be 100644 --- a/examples/tree_2d_dgsem/elixir_advection_amr_nonperiodic.jl +++ b/examples/tree_2d_dgsem/elixir_advection_amr_nonperiodic.jl @@ -14,19 +14,17 @@ initial_condition = initial_condition_gauss # 2*ndims == 4 directions or you can pass a tuple containing BCs for each direction boundary_conditions = BoundaryConditionDirichlet(initial_condition) -solver = DGSEM(polydeg=3, surface_flux=flux_lax_friedrichs) +solver = DGSEM(polydeg = 3, surface_flux = flux_lax_friedrichs) coordinates_min = (-5.0, -5.0) -coordinates_max = ( 5.0, 5.0) +coordinates_max = (5.0, 5.0) mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=4, - n_cells_max=30_000, - periodicity=false) - + initial_refinement_level = 4, + n_cells_max = 30_000, + periodicity = false) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver, - boundary_conditions=boundary_conditions) - + boundary_conditions = boundary_conditions) ############################################################################### # ODE solvers, callbacks etc. @@ -37,26 +35,26 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval, - extra_analysis_integrals=(entropy,)) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval, + extra_analysis_integrals = (entropy,)) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=100, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 100, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) -amr_controller = ControllerThreeLevel(semi, IndicatorMax(semi, variable=first), - base_level=4, - med_level=5, med_threshold=0.1, - max_level=6, max_threshold=0.6) +amr_controller = ControllerThreeLevel(semi, IndicatorMax(semi, variable = first), + base_level = 4, + med_level = 5, med_threshold = 0.1, + max_level = 6, max_threshold = 0.6) amr_callback = AMRCallback(semi, amr_controller, - interval=5, - adapt_initial_condition=true, - adapt_initial_condition_only_refine=true) + interval = 5, + adapt_initial_condition = true, + adapt_initial_condition_only_refine = true) -stepsize_callback = StepsizeCallback(cfl=1.6) +stepsize_callback = StepsizeCallback(cfl = 1.6) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, @@ -65,7 +63,7 @@ callbacks = CallbackSet(summary_callback, ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=stepsize_callback(ode), # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = stepsize_callback(ode), # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/tree_2d_dgsem/elixir_advection_amr_refine_twice.jl b/examples/tree_2d_dgsem/elixir_advection_amr_refine_twice.jl index e69cab29bb6..7b441775204 100644 --- a/examples/tree_2d_dgsem/elixir_advection_amr_refine_twice.jl +++ b/examples/tree_2d_dgsem/elixir_advection_amr_refine_twice.jl @@ -3,7 +3,6 @@ using OrdinaryDiffEq using Trixi - # Define new structs inside a module to allow re-evaluating the file. # This module name needs to be unique among all examples, otherwise Julia will throw warnings # if multiple test cases using the same module name are run in the same session. @@ -11,27 +10,27 @@ module TrixiExtensionRefine using Trixi -struct IndicatorAlwaysRefine{Cache<:NamedTuple} <: Trixi.AbstractIndicator - cache::Cache +struct IndicatorAlwaysRefine{Cache <: NamedTuple} <: Trixi.AbstractIndicator + cache::Cache end function IndicatorAlwaysRefine(semi) - basis = semi.solver.basis - alpha = Vector{real(basis)}() - cache = (; semi.mesh, alpha) + basis = semi.solver.basis + alpha = Vector{real(basis)}() + cache = (; semi.mesh, alpha) - return IndicatorAlwaysRefine{typeof(cache)}(cache) + return IndicatorAlwaysRefine{typeof(cache)}(cache) end -function (indicator::IndicatorAlwaysRefine)(u::AbstractArray{<:Any,4}, +function (indicator::IndicatorAlwaysRefine)(u::AbstractArray{<:Any, 4}, mesh, equations, dg, cache; t, kwargs...) - alpha = indicator.cache.alpha - resize!(alpha, nelements(dg, cache)) + alpha = indicator.cache.alpha + resize!(alpha, nelements(dg, cache)) - alpha .= 1.0 + alpha .= 1.0 - return alpha + return alpha end end # module TrixiExtensionRefine @@ -46,18 +45,16 @@ equations = LinearScalarAdvectionEquation2D(advection_velocity) initial_condition = initial_condition_gauss -solver = DGSEM(polydeg=3, surface_flux=flux_lax_friedrichs) +solver = DGSEM(polydeg = 3, surface_flux = flux_lax_friedrichs) coordinates_min = (-5.0, -5.0) -coordinates_max = ( 5.0, 5.0) +coordinates_max = (5.0, 5.0) mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=2, - n_cells_max=30_000) - + initial_refinement_level = 2, + n_cells_max = 30_000) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver) - ############################################################################### # ODE solvers, callbacks etc. @@ -67,37 +64,37 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval, - extra_analysis_integrals=(entropy,)) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval, + extra_analysis_integrals = (entropy,)) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=100, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 100, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) -amr_controller = ControllerThreeLevel(semi, TrixiExtensionRefine.IndicatorAlwaysRefine(semi), - base_level=4, max_level=4, - med_threshold=0.1, max_threshold=0.6) +amr_controller = ControllerThreeLevel(semi, + TrixiExtensionRefine.IndicatorAlwaysRefine(semi), + base_level = 4, max_level = 4, + med_threshold = 0.1, max_threshold = 0.6) amr_callback = AMRCallback(semi, amr_controller, - interval=5, - adapt_initial_condition=true, - adapt_initial_condition_only_refine=true) + interval = 5, + adapt_initial_condition = true, + adapt_initial_condition_only_refine = true) -stepsize_callback = StepsizeCallback(cfl=1.6) +stepsize_callback = StepsizeCallback(cfl = 1.6) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, save_solution, amr_callback, stepsize_callback); - ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/tree_2d_dgsem/elixir_advection_amr_solution_independent.jl b/examples/tree_2d_dgsem/elixir_advection_amr_solution_independent.jl index efd282dab1f..03a213689ec 100644 --- a/examples/tree_2d_dgsem/elixir_advection_amr_solution_independent.jl +++ b/examples/tree_2d_dgsem/elixir_advection_amr_solution_independent.jl @@ -7,69 +7,68 @@ module TrixiExtension using Trixi -struct IndicatorSolutionIndependent{Cache<:NamedTuple} <: Trixi.AbstractIndicator - cache::Cache +struct IndicatorSolutionIndependent{Cache <: NamedTuple} <: Trixi.AbstractIndicator + cache::Cache end function IndicatorSolutionIndependent(semi) - basis = semi.solver.basis - alpha = Vector{real(basis)}() - cache = (; semi.mesh, alpha) - return IndicatorSolutionIndependent{typeof(cache)}(cache) + basis = semi.solver.basis + alpha = Vector{real(basis)}() + cache = (; semi.mesh, alpha) + return IndicatorSolutionIndependent{typeof(cache)}(cache) end -function (indicator::IndicatorSolutionIndependent)(u::AbstractArray{<:Any,4}, +function (indicator::IndicatorSolutionIndependent)(u::AbstractArray{<:Any, 4}, mesh, equations, dg, cache; t, kwargs...) - - mesh = indicator.cache.mesh - alpha = indicator.cache.alpha - resize!(alpha, nelements(dg, cache)) - - #Predict the theoretical center. - advection_velocity = (0.2, -0.7) - center = t.*advection_velocity - - inner_distance = 1 - outer_distance = 1.85 - - #Iterate over all elements - for element in 1:length(alpha) - #Calculate periodic distance between cell and center. - cell_id = cache.elements.cell_ids[element] - coordinates = mesh.tree.coordinates[1:2, cell_id] - - #The geometric shape of the amr should be preserved when the base_level is increased. - #This is done by looking at the original coordinates of each cell. - cell_coordinates = original_coordinates(coordinates, 5/8) - cell_distance = periodic_distance_2d(cell_coordinates, center, 10) - if cell_distance < (inner_distance+outer_distance)/2 - cell_coordinates = original_coordinates(coordinates, 5/16) - cell_distance = periodic_distance_2d(cell_coordinates, center, 10) + mesh = indicator.cache.mesh + alpha = indicator.cache.alpha + resize!(alpha, nelements(dg, cache)) + + #Predict the theoretical center. + advection_velocity = (0.2, -0.7) + center = t .* advection_velocity + + inner_distance = 1 + outer_distance = 1.85 + + #Iterate over all elements + for element in 1:length(alpha) + #Calculate periodic distance between cell and center. + cell_id = cache.elements.cell_ids[element] + coordinates = mesh.tree.coordinates[1:2, cell_id] + + #The geometric shape of the amr should be preserved when the base_level is increased. + #This is done by looking at the original coordinates of each cell. + cell_coordinates = original_coordinates(coordinates, 5 / 8) + cell_distance = periodic_distance_2d(cell_coordinates, center, 10) + if cell_distance < (inner_distance + outer_distance) / 2 + cell_coordinates = original_coordinates(coordinates, 5 / 16) + cell_distance = periodic_distance_2d(cell_coordinates, center, 10) + end + + #Set alpha according to cells position inside the circles. + target_level = (cell_distance < inner_distance) + (cell_distance < outer_distance) + alpha[element] = target_level / 2 end - - #Set alpha according to cells position inside the circles. - target_level = (cell_distance < inner_distance) + (cell_distance < outer_distance) - alpha[element] = target_level/2 - end - return alpha + return alpha end # For periodic domains, distance between two points must take into account # periodic extensions of the domain function periodic_distance_2d(coordinates, center, domain_length) - dx = coordinates .- center - dx_shifted = abs.(dx .% domain_length) - dx_periodic = min.(dx_shifted, domain_length .- dx_shifted) - return sqrt(sum(dx_periodic.^2)) + dx = coordinates .- center + dx_shifted = abs.(dx .% domain_length) + dx_periodic = min.(dx_shifted, domain_length .- dx_shifted) + return sqrt(sum(dx_periodic .^ 2)) end #This takes a cells coordinates and transforms them into the coordinates of a parent-cell it originally refined from. #It does it so that the parent-cell has given cell_length. function original_coordinates(coordinates, cell_length) - offset = coordinates .% cell_length - offset_sign = sign.(offset) - border = coordinates - offset - center = border + (offset_sign .* cell_length/2) - return center + offset = coordinates .% cell_length + offset_sign = sign.(offset) + border = coordinates - offset + center = border + (offset_sign .* cell_length / 2) + return center end end # module TrixiExtension @@ -83,18 +82,16 @@ equations = LinearScalarAdvectionEquation2D(advection_velocity) initial_condition = initial_condition_gauss -solver = DGSEM(polydeg=3, surface_flux=flux_lax_friedrichs) +solver = DGSEM(polydeg = 3, surface_flux = flux_lax_friedrichs) coordinates_min = (-5.0, -5.0) -coordinates_max = ( 5.0, 5.0) +coordinates_max = (5.0, 5.0) mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=4, - n_cells_max=30_000) - + initial_refinement_level = 4, + n_cells_max = 30_000) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver) - ############################################################################### # ODE solvers, callbacks etc. @@ -104,38 +101,38 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval, - extra_analysis_integrals=(entropy,)) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval, + extra_analysis_integrals = (entropy,)) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=100, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 100, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) -amr_controller = ControllerThreeLevel(semi, TrixiExtension.IndicatorSolutionIndependent(semi), - base_level=4, - med_level=5, med_threshold=0.1, - max_level=6, max_threshold=0.6) +amr_controller = ControllerThreeLevel(semi, + TrixiExtension.IndicatorSolutionIndependent(semi), + base_level = 4, + med_level = 5, med_threshold = 0.1, + max_level = 6, max_threshold = 0.6) amr_callback = AMRCallback(semi, amr_controller, - interval=5, - adapt_initial_condition=true, - adapt_initial_condition_only_refine=true) + interval = 5, + adapt_initial_condition = true, + adapt_initial_condition_only_refine = true) -stepsize_callback = StepsizeCallback(cfl=1.6) +stepsize_callback = StepsizeCallback(cfl = 1.6) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, save_solution, amr_callback, stepsize_callback); - ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/tree_2d_dgsem/elixir_advection_amr_visualization.jl b/examples/tree_2d_dgsem/elixir_advection_amr_visualization.jl index f517b4eb1cf..7b67b811177 100644 --- a/examples/tree_2d_dgsem/elixir_advection_amr_visualization.jl +++ b/examples/tree_2d_dgsem/elixir_advection_amr_visualization.jl @@ -9,27 +9,26 @@ using Plots advection_velocity = (0.2, -0.7) equations = LinearScalarAdvectionEquation2D(advection_velocity) -function initial_condition_gauss_largedomain(x, t, equation::LinearScalarAdvectionEquation2D) - # Store translated coordinate for easy use of exact solution - domain_length = SVector(10, 10) - x_trans = Trixi.x_trans_periodic_2d(x - equation.advection_velocity * t, domain_length) +function initial_condition_gauss_largedomain(x, t, + equation::LinearScalarAdvectionEquation2D) + # Store translated coordinate for easy use of exact solution + domain_length = SVector(10, 10) + x_trans = Trixi.x_trans_periodic_2d(x - equation.advection_velocity * t, domain_length) - return SVector(exp(-(x_trans[1]^2 + x_trans[2]^2))) + return SVector(exp(-(x_trans[1]^2 + x_trans[2]^2))) end initial_condition = initial_condition_gauss_largedomain -solver = DGSEM(polydeg=3, surface_flux=flux_lax_friedrichs) +solver = DGSEM(polydeg = 3, surface_flux = flux_lax_friedrichs) coordinates_min = (-5.0, -5.0) -coordinates_max = ( 5.0, 5.0) +coordinates_max = (5.0, 5.0) mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=3, - n_cells_max=30_000) - + initial_refinement_level = 3, + n_cells_max = 30_000) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver) - ############################################################################### # ODE solvers, callbacks etc. @@ -39,41 +38,40 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval, - extra_analysis_integrals=(entropy,)) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval, + extra_analysis_integrals = (entropy,)) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=100, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 100, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) # Enable in-situ visualization with a new plot generated every 20 time steps # and additional plotting options passed as keyword arguments -visualization = VisualizationCallback(interval=20, clims=(0,1)) +visualization = VisualizationCallback(interval = 20, clims = (0, 1)) -amr_controller = ControllerThreeLevel(semi, IndicatorMax(semi, variable=first), - base_level=3, - med_level=4, med_threshold=0.1, - max_level=5, max_threshold=0.6) +amr_controller = ControllerThreeLevel(semi, IndicatorMax(semi, variable = first), + base_level = 3, + med_level = 4, med_threshold = 0.1, + max_level = 5, max_threshold = 0.6) amr_callback = AMRCallback(semi, amr_controller, - interval=5, - adapt_initial_condition=true, - adapt_initial_condition_only_refine=true) + interval = 5, + adapt_initial_condition = true, + adapt_initial_condition_only_refine = true) -stepsize_callback = StepsizeCallback(cfl=1.6) +stepsize_callback = StepsizeCallback(cfl = 1.6) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, save_solution, visualization, amr_callback, stepsize_callback); - ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/tree_2d_dgsem/elixir_advection_basic.jl b/examples/tree_2d_dgsem/elixir_advection_basic.jl index 269ab8cdd04..0ec0bc3629a 100644 --- a/examples/tree_2d_dgsem/elixir_advection_basic.jl +++ b/examples/tree_2d_dgsem/elixir_advection_basic.jl @@ -9,19 +9,19 @@ advection_velocity = (0.2, -0.7) equations = LinearScalarAdvectionEquation2D(advection_velocity) # Create DG solver with polynomial degree = 3 and (local) Lax-Friedrichs/Rusanov flux as surface flux -solver = DGSEM(polydeg=3, surface_flux=flux_lax_friedrichs) +solver = DGSEM(polydeg = 3, surface_flux = flux_lax_friedrichs) coordinates_min = (-1.0, -1.0) # minimum coordinates (min(x), min(y)) -coordinates_max = ( 1.0, 1.0) # maximum coordinates (max(x), max(y)) +coordinates_max = (1.0, 1.0) # maximum coordinates (max(x), max(y)) # Create a uniformly refined mesh with periodic boundaries mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=4, - n_cells_max=30_000) # set maximum capacity of tree data structure + initial_refinement_level = 4, + n_cells_max = 30_000) # set maximum capacity of tree data structure # A semidiscretization collects data structures and functions for the spatial discretization -semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition_convergence_test, solver) - +semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition_convergence_test, + solver) ############################################################################### # ODE solvers, callbacks etc. @@ -34,26 +34,26 @@ ode = semidiscretize(semi, (0.0, 1.0)); summary_callback = SummaryCallback() # The AnalysisCallback allows to analyse the solution in regular intervals and prints the results -analysis_callback = AnalysisCallback(semi, interval=100) +analysis_callback = AnalysisCallback(semi, interval = 100) # The SaveSolutionCallback allows to save the solution to a file in regular intervals -save_solution = SaveSolutionCallback(interval=100, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 100, + solution_variables = cons2prim) # The StepsizeCallback handles the re-calculation of the maximum Δt after each time step -stepsize_callback = StepsizeCallback(cfl=1.6) +stepsize_callback = StepsizeCallback(cfl = 1.6) # Create a CallbackSet to collect all callbacks such that they can be passed to the ODE solver -callbacks = CallbackSet(summary_callback, analysis_callback, save_solution, stepsize_callback) - +callbacks = CallbackSet(summary_callback, analysis_callback, save_solution, + stepsize_callback) ############################################################################### # run the simulation # OrdinaryDiffEq's `solve` method evolves the solution in time and executes the passed callbacks -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); # Print the timer summary summary_callback() diff --git a/examples/tree_2d_dgsem/elixir_advection_callbacks.jl b/examples/tree_2d_dgsem/elixir_advection_callbacks.jl index 2ddd3e92ed2..708cd0aa3a3 100644 --- a/examples/tree_2d_dgsem/elixir_advection_callbacks.jl +++ b/examples/tree_2d_dgsem/elixir_advection_callbacks.jl @@ -2,7 +2,6 @@ using OrdinaryDiffEq using Trixi - # define new structs inside a module to allow re-evaluating the file module TrixiExtensionExample @@ -14,83 +13,81 @@ using OrdinaryDiffEq: DiscreteCallback, u_modified! # each time it is called. Its sole purpose here is to showcase how to implement # a stage callback for Trixi.jl. struct ExampleStageCallback - times::Vector{Float64} - min_values::Vector{Float64} - max_values::Vector{Float64} - - # You can optionally define an inner constructor like the one below to set up - # some required stuff. You can also create outer constructors (not demonstrated - # here) for further customization options. - function ExampleStageCallback() - new(Float64[], Float64[], Float64[]) - end + times::Vector{Float64} + min_values::Vector{Float64} + max_values::Vector{Float64} + + # You can optionally define an inner constructor like the one below to set up + # some required stuff. You can also create outer constructors (not demonstrated + # here) for further customization options. + function ExampleStageCallback() + new(Float64[], Float64[], Float64[]) + end end # This method is called when the `ExampleStageCallback` is used as `stage_limiter!` # which gets called after every RK stage. There is no specific initialization # method for such `stage_limiter!`s in OrdinaryDiffEq.jl. function (example_stage_callback::ExampleStageCallback)(u_ode, _, semi, t) + min_val, max_val = extrema(u_ode) + push!(example_stage_callback.times, t) + push!(example_stage_callback.min_values, min_val) + push!(example_stage_callback.max_values, max_val) - min_val, max_val = extrema(u_ode) - push!(example_stage_callback.times, t) - push!(example_stage_callback.min_values, min_val) - push!(example_stage_callback.max_values, max_val) - - return nothing + return nothing end - # This is an example implementation for a simple step callback (i.e., a callable # that is potentially executed after each Runge-Kutta *step*), which records # some values each time it is called. Its sole purpose here is to showcase # how to implement a step callback for Trixi.jl. struct ExampleStepCallback - message::String - times::Vector{Float64} - min_values::Vector{Float64} - max_values::Vector{Float64} - - # You can optionally define an inner constructor like the one below to set up - # some required stuff. You can also create outer constructors (not demonstrated - # here) for further customization options. - function ExampleStepCallback(message::String) - new(message, Float64[], Float64[], Float64[]) - end + message::String + times::Vector{Float64} + min_values::Vector{Float64} + max_values::Vector{Float64} + + # You can optionally define an inner constructor like the one below to set up + # some required stuff. You can also create outer constructors (not demonstrated + # here) for further customization options. + function ExampleStepCallback(message::String) + new(message, Float64[], Float64[], Float64[]) + end end # This method is called when the `ExampleStepCallback` is used as callback # which gets called after RK steps. function (example_callback::ExampleStepCallback)(integrator) - u_ode = integrator.u - t = integrator.t - # You can also access semi = integrator.p - - min_val, max_val = extrema(u_ode) - push!(example_callback.times, t) - push!(example_callback.min_values, min_val) - push!(example_callback.max_values, max_val) - - # avoid re-evaluating possible FSAL stages - u_modified!(integrator, false) - return nothing + u_ode = integrator.u + t = integrator.t + # You can also access semi = integrator.p + + min_val, max_val = extrema(u_ode) + push!(example_callback.times, t) + push!(example_callback.min_values, min_val) + push!(example_callback.max_values, max_val) + + # avoid re-evaluating possible FSAL stages + u_modified!(integrator, false) + return nothing end # This method is used to wrap an `ExampleStepCallback` inside a `DiscreteCallback` # which gets called after every RK step. You can pass an additional initialization # method and a separate condition specifying whether the callback shall be called. function ExampleStepCallback(; message::String) - # Call the `ExampleStepCallback` after every RK step. - condition = (u_ode, t, integrator) -> true + # Call the `ExampleStepCallback` after every RK step. + condition = (u_ode, t, integrator) -> true - # You can optionally pass an initialization method. There, you can access the - # `ExampleStepCallback` as `cb.affect!`. - initialize = (cb, u_ode, t, integrator) -> println(cb.affect!.message) + # You can optionally pass an initialization method. There, you can access the + # `ExampleStepCallback` as `cb.affect!`. + initialize = (cb, u_ode, t, integrator) -> println(cb.affect!.message) - example_callback = ExampleStepCallback(message) + example_callback = ExampleStepCallback(message) - DiscreteCallback(condition, example_callback, - save_positions=(false,false), - initialize=initialize) + DiscreteCallback(condition, example_callback, + save_positions = (false, false), + initialize = initialize) end end # module TrixiExtensionExample @@ -104,18 +101,16 @@ advection_velocity = (0.2, -0.7) equations = LinearScalarAdvectionEquation2D(advection_velocity) initial_condition = initial_condition_convergence_test -solver = DGSEM(polydeg=3, surface_flux=flux_lax_friedrichs) +solver = DGSEM(polydeg = 3, surface_flux = flux_lax_friedrichs) coordinates_min = (-1.0, -1.0) -coordinates_max = ( 1.0, 1.0) +coordinates_max = (1.0, 1.0) mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=4, - n_cells_max=30_000) - + initial_refinement_level = 4, + n_cells_max = 30_000) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver) - ############################################################################### # ODE solvers, callbacks etc. @@ -125,19 +120,19 @@ ode = semidiscretize(semi, tspan); summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval, - extra_analysis_integrals=(entropy, energy_total)) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval, + extra_analysis_integrals = (entropy, energy_total)) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=100, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2cons) +save_solution = SaveSolutionCallback(interval = 100, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2cons) -example_callback = TrixiExtensionExample.ExampleStepCallback(message="안녕하세요?") +example_callback = TrixiExtensionExample.ExampleStepCallback(message = "안녕하세요?") -stepsize_callback = StepsizeCallback(cfl=1.6) +stepsize_callback = StepsizeCallback(cfl = 1.6) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, @@ -158,9 +153,10 @@ example_stage_callback! = TrixiExtensionExample.ExampleStageCallback() ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(example_stage_callback!, williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, + CarpenterKennedy2N54(example_stage_callback!, williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary # Check whether we recorded the same values. diff --git a/examples/tree_2d_dgsem/elixir_advection_diffusion.jl b/examples/tree_2d_dgsem/elixir_advection_diffusion.jl index a716bd278b8..1f765ff3564 100644 --- a/examples/tree_2d_dgsem/elixir_advection_diffusion.jl +++ b/examples/tree_2d_dgsem/elixir_advection_diffusion.jl @@ -10,30 +10,31 @@ diffusivity() = 5.0e-2 equations_parabolic = LaplaceDiffusion2D(diffusivity(), equations) # Create DG solver with polynomial degree = 3 and (local) Lax-Friedrichs/Rusanov flux as surface flux -solver = DGSEM(polydeg=3, surface_flux=flux_lax_friedrichs) +solver = DGSEM(polydeg = 3, surface_flux = flux_lax_friedrichs) coordinates_min = (-1.0, -1.0) # minimum coordinates (min(x), min(y)) -coordinates_max = ( 1.0, 1.0) # maximum coordinates (max(x), max(y)) +coordinates_max = (1.0, 1.0) # maximum coordinates (max(x), max(y)) # Create a uniformly refined mesh with periodic boundaries mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=4, - periodicity=true, - n_cells_max=30_000) # set maximum capacity of tree data structure + initial_refinement_level = 4, + periodicity = true, + n_cells_max = 30_000) # set maximum capacity of tree data structure # Define initial condition -function initial_condition_diffusive_convergence_test(x, t, equation::LinearScalarAdvectionEquation2D) - # Store translated coordinate for easy use of exact solution - x_trans = x - equation.advection_velocity * t - - nu = diffusivity() - c = 1.0 - A = 0.5 - L = 2 - f = 1/L - omega = 2 * pi * f - scalar = c + A * sin(omega * sum(x_trans)) * exp(-2 * nu * omega^2 * t) - return SVector(scalar) +function initial_condition_diffusive_convergence_test(x, t, + equation::LinearScalarAdvectionEquation2D) + # Store translated coordinate for easy use of exact solution + x_trans = x - equation.advection_velocity * t + + nu = diffusivity() + c = 1.0 + A = 0.5 + L = 2 + f = 1 / L + omega = 2 * pi * f + scalar = c + A * sin(omega * sum(x_trans)) * exp(-2 * nu * omega^2 * t) + return SVector(scalar) end initial_condition = initial_condition_diffusive_convergence_test @@ -45,9 +46,8 @@ boundary_conditions_parabolic = boundary_condition_periodic semi = SemidiscretizationHyperbolicParabolic(mesh, (equations, equations_parabolic), initial_condition, solver; - boundary_conditions=(boundary_conditions, - boundary_conditions_parabolic)) - + boundary_conditions = (boundary_conditions, + boundary_conditions_parabolic)) ############################################################################### # ODE solvers, callbacks etc. @@ -62,23 +62,22 @@ summary_callback = SummaryCallback() # The AnalysisCallback allows to analyse the solution in regular intervals and prints the results analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) # The AliveCallback prints short status information in regular intervals -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) # Create a CallbackSet to collect all callbacks such that they can be passed to the ODE solver callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback) - ############################################################################### # run the simulation # OrdinaryDiffEq's `solve` method evolves the solution in time and executes the passed callbacks alg = RDPK3SpFSAL49() time_int_tol = 1.0e-11 -sol = solve(ode, alg; abstol=time_int_tol, reltol=time_int_tol, - ode_default_options()..., callback=callbacks) +sol = solve(ode, alg; abstol = time_int_tol, reltol = time_int_tol, + ode_default_options()..., callback = callbacks) # Print the timer summary summary_callback() diff --git a/examples/tree_2d_dgsem/elixir_advection_diffusion_nonperiodic.jl b/examples/tree_2d_dgsem/elixir_advection_diffusion_nonperiodic.jl index c3cd2ebeb20..8da542b0b5d 100644 --- a/examples/tree_2d_dgsem/elixir_advection_diffusion_nonperiodic.jl +++ b/examples/tree_2d_dgsem/elixir_advection_diffusion_nonperiodic.jl @@ -10,16 +10,16 @@ equations = LinearScalarAdvectionEquation2D(advection_velocity) equations_parabolic = LaplaceDiffusion2D(diffusivity(), equations) # Create DG solver with polynomial degree = 3 and (local) Lax-Friedrichs/Rusanov flux as surface flux -solver = DGSEM(polydeg=3, surface_flux=flux_lax_friedrichs) +solver = DGSEM(polydeg = 3, surface_flux = flux_lax_friedrichs) coordinates_min = (-1.0, -0.5) # minimum coordinates (min(x), min(y)) -coordinates_max = ( 0.0, 0.5) # maximum coordinates (max(x), max(y)) +coordinates_max = (0.0, 0.5) # maximum coordinates (max(x), max(y)) # Create a uniformly refined mesh with periodic boundaries mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=4, - periodicity=false, - n_cells_max=30_000) # set maximum capacity of tree data structure + initial_refinement_level = 4, + periodicity = false, + n_cells_max = 30_000) # set maximum capacity of tree data structure # Example setup taken from # - Truman Ellis, Jesse Chan, and Leszek Demkowicz (2016). @@ -28,22 +28,22 @@ mesh = TreeMesh(coordinates_min, coordinates_max, # to numerical partial differential equations. # [DOI](https://doi.org/10.1007/978-3-319-41640-3_6). function initial_condition_eriksson_johnson(x, t, equations) - l = 4 - epsilon = diffusivity() # TODO: this requires epsilon < .6 due to sqrt - lambda_1 = (-1 + sqrt(1 - 4 * epsilon * l)) / (-2 * epsilon) - lambda_2 = (-1 - sqrt(1 - 4 * epsilon * l)) / (-2 * epsilon) - r1 = (1 + sqrt(1 + 4 * pi^2 * epsilon^2)) / (2 * epsilon) - s1 = (1 - sqrt(1 + 4 * pi^2 * epsilon^2)) / (2 * epsilon) - u = exp(-l * t) * (exp(lambda_1 * x[1]) - exp(lambda_2 * x[1])) + - cos(pi * x[2]) * (exp(s1 * x[1]) - exp(r1 * x[1])) / (exp(-s1) - exp(-r1)) - return SVector{1}(u) + l = 4 + epsilon = diffusivity() # TODO: this requires epsilon < .6 due to sqrt + lambda_1 = (-1 + sqrt(1 - 4 * epsilon * l)) / (-2 * epsilon) + lambda_2 = (-1 - sqrt(1 - 4 * epsilon * l)) / (-2 * epsilon) + r1 = (1 + sqrt(1 + 4 * pi^2 * epsilon^2)) / (2 * epsilon) + s1 = (1 - sqrt(1 + 4 * pi^2 * epsilon^2)) / (2 * epsilon) + u = exp(-l * t) * (exp(lambda_1 * x[1]) - exp(lambda_2 * x[1])) + + cos(pi * x[2]) * (exp(s1 * x[1]) - exp(r1 * x[1])) / (exp(-s1) - exp(-r1)) + return SVector{1}(u) end initial_condition = initial_condition_eriksson_johnson boundary_conditions = (; x_neg = BoundaryConditionDirichlet(initial_condition), - y_neg = BoundaryConditionDirichlet(initial_condition), - y_pos = BoundaryConditionDirichlet(initial_condition), - x_pos = boundary_condition_do_nothing) + y_neg = BoundaryConditionDirichlet(initial_condition), + y_pos = BoundaryConditionDirichlet(initial_condition), + x_pos = boundary_condition_do_nothing) boundary_conditions_parabolic = BoundaryConditionDirichlet(initial_condition) @@ -51,9 +51,8 @@ boundary_conditions_parabolic = BoundaryConditionDirichlet(initial_condition) semi = SemidiscretizationHyperbolicParabolic(mesh, (equations, equations_parabolic), initial_condition, solver; - boundary_conditions=(boundary_conditions, - boundary_conditions_parabolic)) - + boundary_conditions = (boundary_conditions, + boundary_conditions_parabolic)) ############################################################################### # ODE solvers, callbacks etc. @@ -68,22 +67,21 @@ summary_callback = SummaryCallback() # The AnalysisCallback allows to analyse the solution in regular intervals and prints the results analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) # The AliveCallback prints short status information in regular intervals -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) # Create a CallbackSet to collect all callbacks such that they can be passed to the ODE solver callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback) - ############################################################################### # run the simulation # OrdinaryDiffEq's `solve` method evolves the solution in time and executes the passed callbacks time_int_tol = 1.0e-11 -sol = solve(ode, RDPK3SpFSAL49(); abstol=time_int_tol, reltol=time_int_tol, - ode_default_options()..., callback=callbacks) +sol = solve(ode, RDPK3SpFSAL49(); abstol = time_int_tol, reltol = time_int_tol, + ode_default_options()..., callback = callbacks) # Print the timer summary summary_callback() diff --git a/examples/tree_2d_dgsem/elixir_advection_extended.jl b/examples/tree_2d_dgsem/elixir_advection_extended.jl index 278dc85386d..4d3da47b04a 100644 --- a/examples/tree_2d_dgsem/elixir_advection_extended.jl +++ b/examples/tree_2d_dgsem/elixir_advection_extended.jl @@ -18,21 +18,20 @@ initial_condition = initial_condition_convergence_test boundary_conditions = boundary_condition_periodic # Create DG solver with polynomial degree = 3 and (local) Lax-Friedrichs/Rusanov flux as surface flux -solver = DGSEM(polydeg=3, surface_flux=flux_lax_friedrichs) +solver = DGSEM(polydeg = 3, surface_flux = flux_lax_friedrichs) coordinates_min = (-1.0, -1.0) # minimum coordinates (min(x), min(y)) -coordinates_max = ( 1.0, 1.0) # maximum coordinates (max(x), max(y)) +coordinates_max = (1.0, 1.0) # maximum coordinates (max(x), max(y)) # Create a uniformly refined mesh with periodic boundaries mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=4, - n_cells_max=30_000, # set maximum capacity of tree data structure - periodicity=true) + initial_refinement_level = 4, + n_cells_max = 30_000, # set maximum capacity of tree data structure + periodicity = true) # A semidiscretization collects data structures and functions for the spatial discretization semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver, - boundary_conditions=boundary_conditions) - + boundary_conditions = boundary_conditions) ############################################################################### # ODE solvers, callbacks etc. @@ -47,24 +46,24 @@ summary_callback = SummaryCallback() # The AnalysisCallback allows to analyse the solution in regular intervals and prints the results analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval, - extra_analysis_integrals=(entropy, energy_total)) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval, + extra_analysis_integrals = (entropy, energy_total)) # The AliveCallback prints short status information in regular intervals -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) # The SaveRestartCallback allows to save a file from which a Trixi.jl simulation can be restarted -save_restart = SaveRestartCallback(interval=40, - save_final_restart=true) +save_restart = SaveRestartCallback(interval = 40, + save_final_restart = true) # The SaveSolutionCallback allows to save the solution to a file in regular intervals -save_solution = SaveSolutionCallback(interval=100, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 100, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) # The StepsizeCallback handles the re-calculation of the maximum Δt after each time step -stepsize_callback = StepsizeCallback(cfl=1.6) +stepsize_callback = StepsizeCallback(cfl = 1.6) # Create a CallbackSet to collect all callbacks such that they can be passed to the ODE solver callbacks = CallbackSet(summary_callback, @@ -72,15 +71,14 @@ callbacks = CallbackSet(summary_callback, save_restart, save_solution, stepsize_callback) - ############################################################################### # run the simulation # OrdinaryDiffEq's `solve` method evolves the solution in time and executes the passed callbacks -alg = CarpenterKennedy2N54(williamson_condition=false) +alg = CarpenterKennedy2N54(williamson_condition = false) sol = solve(ode, alg, - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks; ode_default_options()...); + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks; ode_default_options()...); # Print the timer summary summary_callback() diff --git a/examples/tree_2d_dgsem/elixir_advection_mortar.jl b/examples/tree_2d_dgsem/elixir_advection_mortar.jl index 2a283fb9008..645c55ba438 100644 --- a/examples/tree_2d_dgsem/elixir_advection_mortar.jl +++ b/examples/tree_2d_dgsem/elixir_advection_mortar.jl @@ -9,22 +9,19 @@ advection_velocity = (0.2, -0.7) equations = LinearScalarAdvectionEquation2D(advection_velocity) initial_condition = initial_condition_convergence_test -solver = DGSEM(polydeg=3, surface_flux=flux_lax_friedrichs) +solver = DGSEM(polydeg = 3, surface_flux = flux_lax_friedrichs) coordinates_min = (-1.0, -1.0) -coordinates_max = ( 1.0, 1.0) -refinement_patches = ( - (type="box", coordinates_min=(0.0, -1.0), coordinates_max=(1.0, 1.0)), -) +coordinates_max = (1.0, 1.0) +refinement_patches = ((type = "box", coordinates_min = (0.0, -1.0), + coordinates_max = (1.0, 1.0)),) mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=2, - refinement_patches=refinement_patches, - n_cells_max=10_000,) - + initial_refinement_level = 2, + refinement_patches = refinement_patches, + n_cells_max = 10_000) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver) - ############################################################################### # ODE solvers, callbacks etc. @@ -34,28 +31,27 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval, - extra_analysis_integrals=(entropy,)) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval, + extra_analysis_integrals = (entropy,)) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=100, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 100, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) -stepsize_callback = StepsizeCallback(cfl=1.6) +stepsize_callback = StepsizeCallback(cfl = 1.6) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, save_solution, stepsize_callback) - ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/tree_2d_dgsem/elixir_advection_restart.jl b/examples/tree_2d_dgsem/elixir_advection_restart.jl index b63a8d1f7bc..770629bb15e 100644 --- a/examples/tree_2d_dgsem/elixir_advection_restart.jl +++ b/examples/tree_2d_dgsem/elixir_advection_restart.jl @@ -4,10 +4,10 @@ using Trixi ############################################################################### # Define time integration algorithm -alg = CarpenterKennedy2N54(williamson_condition=false) +alg = CarpenterKennedy2N54(williamson_condition = false) # Create a restart file -trixi_include(@__MODULE__, joinpath(@__DIR__, "elixir_advection_extended.jl"), alg = alg, tspan = (0.0, 10.0)) - +trixi_include(@__MODULE__, joinpath(@__DIR__, "elixir_advection_extended.jl"), alg = alg, + tspan = (0.0, 10.0)) ############################################################################### # adapt the parameters that have changed compared to "elixir_advection_extended.jl" @@ -28,8 +28,8 @@ ode = semidiscretize(semi, tspan, restart_filename); save_solution.condition.save_initial_solution = false integrator = init(ode, alg, - dt=dt, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks; ode_default_options()...) + dt = dt, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks; ode_default_options()...) # Load saved context for adaptive time integrator if integrator.opts.adaptive diff --git a/examples/tree_2d_dgsem/elixir_advection_timeintegration.jl b/examples/tree_2d_dgsem/elixir_advection_timeintegration.jl index be87f24f817..06982bb9a27 100644 --- a/examples/tree_2d_dgsem/elixir_advection_timeintegration.jl +++ b/examples/tree_2d_dgsem/elixir_advection_timeintegration.jl @@ -9,18 +9,16 @@ advection_velocity = (0.2, -0.7) equations = LinearScalarAdvectionEquation2D(advection_velocity) initial_condition = initial_condition_gauss -solver = DGSEM(polydeg=3, surface_flux=flux_lax_friedrichs) +solver = DGSEM(polydeg = 3, surface_flux = flux_lax_friedrichs) coordinates_min = (-5.0, -5.0) -coordinates_max = ( 5.0, 5.0) +coordinates_max = (5.0, 5.0) mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=4, - n_cells_max=30_000) - + initial_refinement_level = 4, + n_cells_max = 30_000) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver) - ############################################################################### # ODE solvers, callbacks etc. @@ -30,39 +28,38 @@ ode = semidiscretize(semi, tspan); summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval, - extra_analysis_integrals=(entropy,)) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval, + extra_analysis_integrals = (entropy,)) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=100, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2cons) +save_solution = SaveSolutionCallback(interval = 100, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2cons) -amr_controller = ControllerThreeLevel(semi, IndicatorMax(semi, variable=first), - base_level=4, - med_level=5, med_threshold=0.1, - max_level=6, max_threshold=0.6) +amr_controller = ControllerThreeLevel(semi, IndicatorMax(semi, variable = first), + base_level = 4, + med_level = 5, med_threshold = 0.1, + max_level = 6, max_threshold = 0.6) amr_callback = AMRCallback(semi, amr_controller, - interval=5, - adapt_initial_condition=true, - adapt_initial_condition_only_refine=true) + interval = 5, + adapt_initial_condition = true, + adapt_initial_condition_only_refine = true) -stepsize_callback = StepsizeCallback(cfl=1.6) +stepsize_callback = StepsizeCallback(cfl = 1.6) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, save_solution, amr_callback, stepsize_callback) - ############################################################################### # run the simulation # sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), ode_algorithm = Trixi.CarpenterKennedy2N54() sol = Trixi.solve(ode, ode_algorithm, - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/tree_2d_dgsem/elixir_euler_astro_jet_MCL.jl b/examples/tree_2d_dgsem/elixir_euler_astro_jet_MCL.jl index f51b73dd497..69148f5bdb6 100644 --- a/examples/tree_2d_dgsem/elixir_euler_astro_jet_MCL.jl +++ b/examples/tree_2d_dgsem/elixir_euler_astro_jet_MCL.jl @@ -4,7 +4,7 @@ using Trixi ############################################################################### # semidiscretization of the compressible Euler equations -gamma = 5/3 +gamma = 5 / 3 equations = CompressibleEulerEquations2D(gamma) # Initial condition adopted from @@ -13,57 +13,56 @@ equations = CompressibleEulerEquations2D(gamma) # https://tinyurl.com/c76fjtx4 # Mach = 2000 jet function initial_condition_astro_jet(x, t, equations::CompressibleEulerEquations2D) - @unpack gamma = equations - rho = 0.5 - v1 = 0 - v2 = 0 - p = 0.4127 - # add inflow for t>0 at x=-0.5 - # domain size is [-0.5,+0.5]^2 - if (x[1] ≈ -0.5) && (abs(x[2]) < 0.05) - rho = 5 - v1 = 800 # about Mach number Ma = 2000 + @unpack gamma = equations + rho = 0.5 + v1 = 0 v2 = 0 p = 0.4127 - end - return prim2cons(SVector(rho, v1, v2, p), equations) + # add inflow for t>0 at x=-0.5 + # domain size is [-0.5,+0.5]^2 + if (x[1] ≈ -0.5) && (abs(x[2]) < 0.05) + rho = 5 + v1 = 800 # about Mach number Ma = 2000 + v2 = 0 + p = 0.4127 + end + return prim2cons(SVector(rho, v1, v2, p), equations) end initial_condition = initial_condition_astro_jet -boundary_conditions = ( - x_neg=BoundaryConditionCharacteristic(initial_condition_astro_jet), - x_pos=BoundaryConditionCharacteristic(initial_condition_astro_jet), - y_neg=boundary_condition_periodic, - y_pos=boundary_condition_periodic, - ) +boundary_conditions = (x_neg = BoundaryConditionCharacteristic(initial_condition_astro_jet), + x_pos = BoundaryConditionCharacteristic(initial_condition_astro_jet), + y_neg = boundary_condition_periodic, + y_pos = boundary_condition_periodic) surface_flux = flux_lax_friedrichs # HLLC needs more shock capturing (alpha_max) -volume_flux = flux_chandrashekar # works with Ranocha flux as well +volume_flux = flux_chandrashekar # works with Ranocha flux as well polydeg = 3 basis = LobattoLegendreBasis(polydeg) # shock capturing necessary for this tough example limiter_mcl = SubcellLimiterMCL(equations, basis; - DensityLimiter=true, - DensityAlphaForAll=true, - SequentialLimiter=true, - PressurePositivityLimiterKuzmin=true, - DensityPositivityLimiter=false, - SemiDiscEntropyLimiter=false, - Plotting=true) + DensityLimiter = true, + DensityAlphaForAll = true, + SequentialLimiter = true, + PressurePositivityLimiterKuzmin = true, + DensityPositivityLimiter = false, + SemiDiscEntropyLimiter = false, + Plotting = true) volume_integral = VolumeIntegralSubcellLimiting(limiter_mcl; - volume_flux_dg=volume_flux, - volume_flux_fv=surface_flux) + volume_flux_dg = volume_flux, + volume_flux_fv = surface_flux) solver = DGSEM(basis, surface_flux, volume_integral) coordinates_min = (-0.5, -0.5) -coordinates_max = ( 0.5, 0.5) +coordinates_max = (0.5, 0.5) mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=8, - periodicity=(false,true), - n_cells_max=100_000) -semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver, boundary_conditions=boundary_conditions) + initial_refinement_level = 8, + periodicity = (false, true), + n_cells_max = 100_000) +semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver, + boundary_conditions = boundary_conditions) ############################################################################### # ODE solvers, callbacks etc. @@ -74,16 +73,16 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 1000 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=5000, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 5000, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) -stepsize_callback = StepsizeCallback(cfl=0.9) +stepsize_callback = StepsizeCallback(cfl = 0.9) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, @@ -93,9 +92,9 @@ callbacks = CallbackSet(summary_callback, ############################################################################### # run the simulation -stage_callbacks = (BoundsCheckCallback(save_errors=false),) +stage_callbacks = (BoundsCheckCallback(save_errors = false),) -sol = Trixi.solve(ode, Trixi.SimpleSSPRK33(stage_callbacks=stage_callbacks); - maxiters=1e6, dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - callback=callbacks); +sol = Trixi.solve(ode, Trixi.SimpleSSPRK33(stage_callbacks = stage_callbacks); + maxiters = 1e6, dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/tree_2d_dgsem/elixir_euler_astro_jet_amr.jl b/examples/tree_2d_dgsem/elixir_euler_astro_jet_amr.jl index c5790e455bc..1393f4a6cc8 100644 --- a/examples/tree_2d_dgsem/elixir_euler_astro_jet_amr.jl +++ b/examples/tree_2d_dgsem/elixir_euler_astro_jet_amr.jl @@ -4,7 +4,7 @@ using Trixi ############################################################################### # semidiscretization of the compressible Euler equations -gamma = 5/3 +gamma = 5 / 3 equations = CompressibleEulerEquations2D(gamma) # Initial condition adopted from @@ -13,55 +13,54 @@ equations = CompressibleEulerEquations2D(gamma) # https://tinyurl.com/c76fjtx4 # Mach = 2000 jet function initial_condition_astro_jet(x, t, equations::CompressibleEulerEquations2D) - @unpack gamma = equations - rho = 0.5 - v1 = 0 - v2 = 0 - p = 0.4127 - # add inflow for t>0 at x=-0.5 - # domain size is [-0.5,+0.5]^2 - if (t > 0) && (x[1] ≈ -0.5) && (abs(x[2]) < 0.05) - rho = 5 - v1 = 800 # about Mach number Ma = 2000 + @unpack gamma = equations + rho = 0.5 + v1 = 0 v2 = 0 p = 0.4127 - end - return prim2cons(SVector(rho, v1, v2, p), equations) + # add inflow for t>0 at x=-0.5 + # domain size is [-0.5,+0.5]^2 + if (t > 0) && (x[1] ≈ -0.5) && (abs(x[2]) < 0.05) + rho = 5 + v1 = 800 # about Mach number Ma = 2000 + v2 = 0 + p = 0.4127 + end + return prim2cons(SVector(rho, v1, v2, p), equations) end initial_condition = initial_condition_astro_jet -boundary_conditions = ( - x_neg=BoundaryConditionDirichlet(initial_condition_astro_jet), - x_pos=BoundaryConditionDirichlet(initial_condition_astro_jet), - y_neg=boundary_condition_periodic, - y_pos=boundary_condition_periodic, - ) +boundary_conditions = (x_neg = BoundaryConditionDirichlet(initial_condition_astro_jet), + x_pos = BoundaryConditionDirichlet(initial_condition_astro_jet), + y_neg = boundary_condition_periodic, + y_pos = boundary_condition_periodic) surface_flux = flux_lax_friedrichs # HLLC needs more shock capturing (alpha_max) -volume_flux = flux_ranocha # works with Chandrashekar flux as well +volume_flux = flux_ranocha # works with Chandrashekar flux as well polydeg = 3 basis = LobattoLegendreBasis(polydeg) # shock capturing necessary for this tough example indicator_sc = IndicatorHennemannGassner(equations, basis, - alpha_max=0.3, - alpha_min=0.0001, - alpha_smooth=true, - variable=density_pressure) + alpha_max = 0.3, + alpha_min = 0.0001, + alpha_smooth = true, + variable = density_pressure) volume_integral = VolumeIntegralShockCapturingHG(indicator_sc; - volume_flux_dg=volume_flux, - volume_flux_fv=surface_flux) + volume_flux_dg = volume_flux, + volume_flux_fv = surface_flux) solver = DGSEM(basis, surface_flux, volume_integral) coordinates_min = (-0.5, -0.5) -coordinates_max = ( 0.5, 0.5) +coordinates_max = (0.5, 0.5) mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=6, - periodicity=(false,true), - n_cells_max=100_000) -semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver, boundary_conditions=boundary_conditions) + initial_refinement_level = 6, + periodicity = (false, true), + n_cells_max = 100_000) +semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver, + boundary_conditions = boundary_conditions) ############################################################################### # ODE solvers, callbacks etc. @@ -72,43 +71,43 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 5000 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) - -alive_callback = AliveCallback(analysis_interval=analysis_interval) - -save_solution = SaveSolutionCallback(interval=5000, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) - -amr_indicator = IndicatorHennemannGassner(semi, - alpha_max=1.0, - alpha_min=0.0001, - alpha_smooth=false, - variable=Trixi.density) - -amr_controller = ControllerThreeLevelCombined(semi, amr_indicator, indicator_sc, - base_level=2, - med_level =0, med_threshold=0.0003, # med_level = current level - max_level =8, max_threshold=0.003, - max_threshold_secondary=indicator_sc.alpha_max) - -amr_callback = AMRCallback(semi, amr_controller, - interval=1, - adapt_initial_condition=true, - adapt_initial_condition_only_refine=true) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) + +alive_callback = AliveCallback(analysis_interval = analysis_interval) + +save_solution = SaveSolutionCallback(interval = 5000, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) + +amr_indicator = IndicatorHennemannGassner(semi, + alpha_max = 1.0, + alpha_min = 0.0001, + alpha_smooth = false, + variable = Trixi.density) + +amr_controller = ControllerThreeLevelCombined(semi, amr_indicator, indicator_sc, + base_level = 2, + med_level = 0, med_threshold = 0.0003, # med_level = current level + max_level = 8, max_threshold = 0.003, + max_threshold_secondary = indicator_sc.alpha_max) + +amr_callback = AMRCallback(semi, amr_controller, + interval = 1, + adapt_initial_condition = true, + adapt_initial_condition_only_refine = true) callbacks = CallbackSet(summary_callback, - analysis_callback, alive_callback, + analysis_callback, alive_callback, amr_callback, save_solution) # positivity limiter necessary for this tough example -stage_limiter! = PositivityPreservingLimiterZhangShu(thresholds=(5.0e-6, 5.0e-6), - variables=(Trixi.density, pressure)) +stage_limiter! = PositivityPreservingLimiterZhangShu(thresholds = (5.0e-6, 5.0e-6), + variables = (Trixi.density, pressure)) ############################################################################### # run the simulation # use adaptive time stepping based on error estimates, time step roughly dt = 1e-7 sol = solve(ode, SSPRK43(stage_limiter!); - ode_default_options()..., callback=callbacks); + ode_default_options()..., callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/tree_2d_dgsem/elixir_euler_astro_jet_subcell.jl b/examples/tree_2d_dgsem/elixir_euler_astro_jet_subcell.jl index 5b95fef374e..3bf4f230d44 100644 --- a/examples/tree_2d_dgsem/elixir_euler_astro_jet_subcell.jl +++ b/examples/tree_2d_dgsem/elixir_euler_astro_jet_subcell.jl @@ -4,7 +4,7 @@ using Trixi ############################################################################### # semidiscretization of the compressible Euler equations -gamma = 5/3 +gamma = 5 / 3 equations = CompressibleEulerEquations2D(gamma) # Initial condition adopted from @@ -13,54 +13,53 @@ equations = CompressibleEulerEquations2D(gamma) # https://tinyurl.com/c76fjtx4 # Mach = 2000 jet function initial_condition_astro_jet(x, t, equations::CompressibleEulerEquations2D) - @unpack gamma = equations - rho = 0.5 - v1 = 0 - v2 = 0 - p = 0.4127 - # add inflow for t>0 at x=-0.5 - # domain size is [-0.5,+0.5]^2 - if (x[1] ≈ -0.5) && (abs(x[2]) < 0.05) - rho = 5 - v1 = 800 # about Mach number Ma = 2000 + @unpack gamma = equations + rho = 0.5 + v1 = 0 v2 = 0 p = 0.4127 - end - return prim2cons(SVector(rho, v1, v2, p), equations) + # add inflow for t>0 at x=-0.5 + # domain size is [-0.5,+0.5]^2 + if (x[1] ≈ -0.5) && (abs(x[2]) < 0.05) + rho = 5 + v1 = 800 # about Mach number Ma = 2000 + v2 = 0 + p = 0.4127 + end + return prim2cons(SVector(rho, v1, v2, p), equations) end initial_condition = initial_condition_astro_jet -boundary_conditions = ( - x_neg=BoundaryConditionCharacteristic(initial_condition_astro_jet), - x_pos=BoundaryConditionCharacteristic(initial_condition_astro_jet), - y_neg=boundary_condition_periodic, - y_pos=boundary_condition_periodic, - ) +boundary_conditions = (x_neg = BoundaryConditionCharacteristic(initial_condition_astro_jet), + x_pos = BoundaryConditionCharacteristic(initial_condition_astro_jet), + y_neg = boundary_condition_periodic, + y_pos = boundary_condition_periodic) surface_flux = flux_lax_friedrichs # HLLC needs more shock capturing (alpha_max) -volume_flux = flux_chandrashekar # works with Ranocha flux as well +volume_flux = flux_chandrashekar # works with Ranocha flux as well polydeg = 3 basis = LobattoLegendreBasis(polydeg) # shock capturing necessary for this tough example limiter_idp = SubcellLimiterIDP(equations, basis; - local_minmax_variables_cons=[1], - spec_entropy=true, - bar_states=true, - max_iterations_newton=25) + local_minmax_variables_cons = [1], + spec_entropy = true, + bar_states = true, + max_iterations_newton = 25) volume_integral = VolumeIntegralSubcellLimiting(limiter_idp; - volume_flux_dg=volume_flux, - volume_flux_fv=surface_flux) + volume_flux_dg = volume_flux, + volume_flux_fv = surface_flux) solver = DGSEM(basis, surface_flux, volume_integral) coordinates_min = (-0.5, -0.5) -coordinates_max = ( 0.5, 0.5) +coordinates_max = (0.5, 0.5) mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=8, - periodicity=(false,true), - n_cells_max=100_000) -semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver, boundary_conditions=boundary_conditions) + initial_refinement_level = 8, + periodicity = (false, true), + n_cells_max = 100_000) +semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver, + boundary_conditions = boundary_conditions) ############################################################################### # ODE solvers, callbacks etc. @@ -71,16 +70,16 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 1000 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=1000, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 1000, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) -stepsize_callback = StepsizeCallback(cfl=0.9) +stepsize_callback = StepsizeCallback(cfl = 0.9) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, @@ -89,9 +88,9 @@ callbacks = CallbackSet(summary_callback, ############################################################################### # run the simulation -stage_callbacks = (SubcellLimiterIDPCorrection(), BoundsCheckCallback(save_errors=false)) +stage_callbacks = (SubcellLimiterIDPCorrection(), BoundsCheckCallback(save_errors = false)) -sol = Trixi.solve(ode, Trixi.SimpleSSPRK33(stage_callbacks=stage_callbacks); - maxiters=1e6, dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - callback=callbacks); +sol = Trixi.solve(ode, Trixi.SimpleSSPRK33(stage_callbacks = stage_callbacks); + maxiters = 1e6, dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/tree_2d_dgsem/elixir_euler_blast_wave.jl b/examples/tree_2d_dgsem/elixir_euler_blast_wave.jl index 0da18b7120d..ccd7b54086b 100644 --- a/examples/tree_2d_dgsem/elixir_euler_blast_wave.jl +++ b/examples/tree_2d_dgsem/elixir_euler_blast_wave.jl @@ -16,48 +16,46 @@ A medium blast wave taken from [arXiv: 2008.12044](https://arxiv.org/abs/2008.12044) """ function initial_condition_blast_wave(x, t, equations::CompressibleEulerEquations2D) - # Modified From Hennemann & Gassner JCP paper 2020 (Sec. 6.3) -> "medium blast wave" - # Set up polar coordinates - inicenter = SVector(0.0, 0.0) - x_norm = x[1] - inicenter[1] - y_norm = x[2] - inicenter[2] - r = sqrt(x_norm^2 + y_norm^2) - phi = atan(y_norm, x_norm) - sin_phi, cos_phi = sincos(phi) - - # Calculate primitive variables - rho = r > 0.5 ? 1.0 : 1.1691 - v1 = r > 0.5 ? 0.0 : 0.1882 * cos_phi - v2 = r > 0.5 ? 0.0 : 0.1882 * sin_phi - p = r > 0.5 ? 1.0E-3 : 1.245 - - return prim2cons(SVector(rho, v1, v2, p), equations) + # Modified From Hennemann & Gassner JCP paper 2020 (Sec. 6.3) -> "medium blast wave" + # Set up polar coordinates + inicenter = SVector(0.0, 0.0) + x_norm = x[1] - inicenter[1] + y_norm = x[2] - inicenter[2] + r = sqrt(x_norm^2 + y_norm^2) + phi = atan(y_norm, x_norm) + sin_phi, cos_phi = sincos(phi) + + # Calculate primitive variables + rho = r > 0.5 ? 1.0 : 1.1691 + v1 = r > 0.5 ? 0.0 : 0.1882 * cos_phi + v2 = r > 0.5 ? 0.0 : 0.1882 * sin_phi + p = r > 0.5 ? 1.0E-3 : 1.245 + + return prim2cons(SVector(rho, v1, v2, p), equations) end initial_condition = initial_condition_blast_wave surface_flux = flux_lax_friedrichs -volume_flux = flux_ranocha +volume_flux = flux_ranocha basis = LobattoLegendreBasis(3) indicator_sc = IndicatorHennemannGassner(equations, basis, - alpha_max=0.5, - alpha_min=0.001, - alpha_smooth=true, - variable=density_pressure) + alpha_max = 0.5, + alpha_min = 0.001, + alpha_smooth = true, + variable = density_pressure) volume_integral = VolumeIntegralShockCapturingHG(indicator_sc; - volume_flux_dg=volume_flux, - volume_flux_fv=surface_flux) + volume_flux_dg = volume_flux, + volume_flux_fv = surface_flux) solver = DGSEM(basis, surface_flux, volume_integral) coordinates_min = (-2.0, -2.0) -coordinates_max = ( 2.0, 2.0) +coordinates_max = (2.0, 2.0) mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=6, - n_cells_max=10_000) - + initial_refinement_level = 6, + n_cells_max = 10_000) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver) - ############################################################################### # ODE solvers, callbacks etc. @@ -67,27 +65,26 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=100, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 100, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) -stepsize_callback = StepsizeCallback(cfl=0.9) +stepsize_callback = StepsizeCallback(cfl = 0.9) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, save_solution, stepsize_callback) - ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/tree_2d_dgsem/elixir_euler_blast_wave_MCL.jl b/examples/tree_2d_dgsem/elixir_euler_blast_wave_MCL.jl index 0e5a85e00a8..3e90ef7da2e 100644 --- a/examples/tree_2d_dgsem/elixir_euler_blast_wave_MCL.jl +++ b/examples/tree_2d_dgsem/elixir_euler_blast_wave_MCL.jl @@ -16,54 +16,52 @@ A medium blast wave taken from [arXiv: 2008.12044](https://arxiv.org/abs/2008.12044) """ function initial_condition_blast_wave(x, t, equations::CompressibleEulerEquations2D) - # Modified From Hennemann & Gassner JCP paper 2020 (Sec. 6.3) -> "medium blast wave" - # Set up polar coordinates - inicenter = SVector(0.0, 0.0) - x_norm = x[1] - inicenter[1] - y_norm = x[2] - inicenter[2] - r = sqrt(x_norm^2 + y_norm^2) - phi = atan(y_norm, x_norm) - sin_phi, cos_phi = sincos(phi) - - # Calculate primitive variables - rho = r > 0.5 ? 1.0 : 1.1691 - v1 = r > 0.5 ? 0.0 : 0.1882 * cos_phi - v2 = r > 0.5 ? 0.0 : 0.1882 * sin_phi - p = r > 0.5 ? 1.0E-3 : 1.245 - - return prim2cons(SVector(rho, v1, v2, p), equations) + # Modified From Hennemann & Gassner JCP paper 2020 (Sec. 6.3) -> "medium blast wave" + # Set up polar coordinates + inicenter = SVector(0.0, 0.0) + x_norm = x[1] - inicenter[1] + y_norm = x[2] - inicenter[2] + r = sqrt(x_norm^2 + y_norm^2) + phi = atan(y_norm, x_norm) + sin_phi, cos_phi = sincos(phi) + + # Calculate primitive variables + rho = r > 0.5 ? 1.0 : 1.1691 + v1 = r > 0.5 ? 0.0 : 0.1882 * cos_phi + v2 = r > 0.5 ? 0.0 : 0.1882 * sin_phi + p = r > 0.5 ? 1.0E-3 : 1.245 + + return prim2cons(SVector(rho, v1, v2, p), equations) end initial_condition = initial_condition_blast_wave surface_flux = flux_lax_friedrichs -volume_flux = flux_ranocha +volume_flux = flux_ranocha basis = LobattoLegendreBasis(3) limiter_mcl = SubcellLimiterMCL(equations, basis; - DensityLimiter=true, - DensityAlphaForAll=true, - SequentialLimiter=false, - ConservativeLimiter=true, - DensityPositivityLimiter=true, - PressurePositivityLimiterKuzmin=true, - PressurePositivityLimiterKuzminExact=false, - SemiDiscEntropyLimiter=true, - smoothness_indicator=true, - Plotting=false) + DensityLimiter = true, + DensityAlphaForAll = true, + SequentialLimiter = false, + ConservativeLimiter = true, + DensityPositivityLimiter = true, + PressurePositivityLimiterKuzmin = true, + PressurePositivityLimiterKuzminExact = false, + SemiDiscEntropyLimiter = true, + smoothness_indicator = true, + Plotting = false) volume_integral = VolumeIntegralSubcellLimiting(limiter_mcl; - volume_flux_dg=volume_flux, - volume_flux_fv=surface_flux) + volume_flux_dg = volume_flux, + volume_flux_fv = surface_flux) solver = DGSEM(basis, surface_flux, volume_integral) coordinates_min = (-2.0, -2.0) -coordinates_max = ( 2.0, 2.0) +coordinates_max = (2.0, 2.0) mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=6, - n_cells_max=10_000) - + initial_refinement_level = 6, + n_cells_max = 10_000) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver) - ############################################################################### # ODE solvers, callbacks etc. @@ -73,29 +71,28 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=500, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 500, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) -stepsize_callback = StepsizeCallback(cfl=0.9) +stepsize_callback = StepsizeCallback(cfl = 0.9) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, save_solution, stepsize_callback) - ############################################################################### # run the simulation -stage_callbacks = (BoundsCheckCallback(save_errors=false),) +stage_callbacks = (BoundsCheckCallback(save_errors = false),) -sol = Trixi.solve(ode, Trixi.SimpleSSPRK33(stage_callbacks=stage_callbacks); - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = Trixi.solve(ode, Trixi.SimpleSSPRK33(stage_callbacks = stage_callbacks); + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/tree_2d_dgsem/elixir_euler_blast_wave_amr.jl b/examples/tree_2d_dgsem/elixir_euler_blast_wave_amr.jl index 6ce9268486c..d32c2e51b06 100644 --- a/examples/tree_2d_dgsem/elixir_euler_blast_wave_amr.jl +++ b/examples/tree_2d_dgsem/elixir_euler_blast_wave_amr.jl @@ -16,48 +16,46 @@ A medium blast wave taken from [arXiv: 2008.12044](https://arxiv.org/abs/2008.12044) """ function initial_condition_blast_wave(x, t, equations::CompressibleEulerEquations2D) - # Modified From Hennemann & Gassner JCP paper 2020 (Sec. 6.3) -> "medium blast wave" - # Set up polar coordinates - inicenter = SVector(0.0, 0.0) - x_norm = x[1] - inicenter[1] - y_norm = x[2] - inicenter[2] - r = sqrt(x_norm^2 + y_norm^2) - phi = atan(y_norm, x_norm) - sin_phi, cos_phi = sincos(phi) - - # Calculate primitive variables - rho = r > 0.5 ? 1.0 : 1.1691 - v1 = r > 0.5 ? 0.0 : 0.1882 * cos_phi - v2 = r > 0.5 ? 0.0 : 0.1882 * sin_phi - p = r > 0.5 ? 1.0E-3 : 1.245 - - return prim2cons(SVector(rho, v1, v2, p), equations) + # Modified From Hennemann & Gassner JCP paper 2020 (Sec. 6.3) -> "medium blast wave" + # Set up polar coordinates + inicenter = SVector(0.0, 0.0) + x_norm = x[1] - inicenter[1] + y_norm = x[2] - inicenter[2] + r = sqrt(x_norm^2 + y_norm^2) + phi = atan(y_norm, x_norm) + sin_phi, cos_phi = sincos(phi) + + # Calculate primitive variables + rho = r > 0.5 ? 1.0 : 1.1691 + v1 = r > 0.5 ? 0.0 : 0.1882 * cos_phi + v2 = r > 0.5 ? 0.0 : 0.1882 * sin_phi + p = r > 0.5 ? 1.0E-3 : 1.245 + + return prim2cons(SVector(rho, v1, v2, p), equations) end initial_condition = initial_condition_blast_wave surface_flux = flux_lax_friedrichs -volume_flux = flux_ranocha +volume_flux = flux_ranocha basis = LobattoLegendreBasis(3) indicator_sc = IndicatorHennemannGassner(equations, basis, - alpha_max=0.5, - alpha_min=0.001, - alpha_smooth=true, - variable=density_pressure) + alpha_max = 0.5, + alpha_min = 0.001, + alpha_smooth = true, + variable = density_pressure) volume_integral = VolumeIntegralShockCapturingHG(indicator_sc; - volume_flux_dg=volume_flux, - volume_flux_fv=surface_flux) + volume_flux_dg = volume_flux, + volume_flux_fv = surface_flux) solver = DGSEM(basis, surface_flux, volume_integral) coordinates_min = (-2.0, -2.0) -coordinates_max = ( 2.0, 2.0) +coordinates_max = (2.0, 2.0) mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=6, - n_cells_max=10_000) - + initial_refinement_level = 6, + n_cells_max = 10_000) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver) - ############################################################################### # ODE solvers, callbacks etc. @@ -67,40 +65,39 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=100, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 100, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) amr_indicator = IndicatorHennemannGassner(semi, - alpha_max=0.5, - alpha_min=0.001, - alpha_smooth=true, - variable=density_pressure) + alpha_max = 0.5, + alpha_min = 0.001, + alpha_smooth = true, + variable = density_pressure) amr_controller = ControllerThreeLevel(semi, amr_indicator, - base_level=4, - max_level =6, max_threshold=0.01) + base_level = 4, + max_level = 6, max_threshold = 0.01) amr_callback = AMRCallback(semi, amr_controller, - interval=5, - adapt_initial_condition=true, - adapt_initial_condition_only_refine=true) + interval = 5, + adapt_initial_condition = true, + adapt_initial_condition_only_refine = true) -stepsize_callback = StepsizeCallback(cfl=0.9) +stepsize_callback = StepsizeCallback(cfl = 0.9) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, save_solution, amr_callback, stepsize_callback) - ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/tree_2d_dgsem/elixir_euler_blast_wave_neuralnetwork_cnn.jl b/examples/tree_2d_dgsem/elixir_euler_blast_wave_neuralnetwork_cnn.jl index 659788f2f5c..79d7474dc66 100644 --- a/examples/tree_2d_dgsem/elixir_euler_blast_wave_neuralnetwork_cnn.jl +++ b/examples/tree_2d_dgsem/elixir_euler_blast_wave_neuralnetwork_cnn.jl @@ -2,7 +2,8 @@ using Downloads: download using Flux using BSON: load network = joinpath(@__DIR__, "modelcnn-0.964-0.001.bson") -download("https://github.com/trixi-framework/Trixi_IndicatorNeuralNetwork_networks/raw/main/networks/modelcnn-0.964-0.001.bson", network) +download("https://github.com/trixi-framework/Trixi_IndicatorNeuralNetwork_networks/raw/main/networks/modelcnn-0.964-0.001.bson", + network) model2dcnn = load(network, @__MODULE__)[:model2dcnn] using OrdinaryDiffEq @@ -28,52 +29,50 @@ A medium blast wave taken from [arXiv: 2008.12044](https://arxiv.org/abs/2008.12044) """ function initial_condition_blast_wave(x, t, equations::CompressibleEulerEquations2D) - # Modified From Hennemann & Gassner JCP paper 2020 (Sec. 6.3) -> "medium blast wave" - # Set up polar coordinates - inicenter = SVector(0.0, 0.0) - x_norm = x[1] - inicenter[1] - y_norm = x[2] - inicenter[2] - r = sqrt(x_norm^2 + y_norm^2) - phi = atan(y_norm, x_norm) - sin_phi, cos_phi = sincos(phi) - - # Calculate primitive variables - rho = r > 0.5 ? 1.0 : 1.1691 - v1 = r > 0.5 ? 0.0 : 0.1882 * cos_phi - v2 = r > 0.5 ? 0.0 : 0.1882 * sin_phi - p = r > 0.5 ? 1.0E-3 : 1.245 - - return prim2cons(SVector(rho, v1, v2, p), equations) + # Modified From Hennemann & Gassner JCP paper 2020 (Sec. 6.3) -> "medium blast wave" + # Set up polar coordinates + inicenter = SVector(0.0, 0.0) + x_norm = x[1] - inicenter[1] + y_norm = x[2] - inicenter[2] + r = sqrt(x_norm^2 + y_norm^2) + phi = atan(y_norm, x_norm) + sin_phi, cos_phi = sincos(phi) + + # Calculate primitive variables + rho = r > 0.5 ? 1.0 : 1.1691 + v1 = r > 0.5 ? 0.0 : 0.1882 * cos_phi + v2 = r > 0.5 ? 0.0 : 0.1882 * sin_phi + p = r > 0.5 ? 1.0E-3 : 1.245 + + return prim2cons(SVector(rho, v1, v2, p), equations) end initial_condition = initial_condition_blast_wave surface_flux = flux_lax_friedrichs -volume_flux = flux_chandrashekar +volume_flux = flux_chandrashekar basis = LobattoLegendreBasis(3) indicator_sc = IndicatorNeuralNetwork(equations, basis, - indicator_type=NeuralNetworkCNN(), - alpha_max=0.5, - alpha_min=0.001, - alpha_smooth=true, - alpha_continuous=true, - alpha_amr=false, - variable=density_pressure, - network=model2dcnn) + indicator_type = NeuralNetworkCNN(), + alpha_max = 0.5, + alpha_min = 0.001, + alpha_smooth = true, + alpha_continuous = true, + alpha_amr = false, + variable = density_pressure, + network = model2dcnn) volume_integral = VolumeIntegralShockCapturingHG(indicator_sc; - volume_flux_dg=volume_flux, - volume_flux_fv=surface_flux) + volume_flux_dg = volume_flux, + volume_flux_fv = surface_flux) solver = DGSEM(basis, surface_flux, volume_integral) coordinates_min = (-2.0, -2.0) -coordinates_max = ( 2.0, 2.0) +coordinates_max = (2.0, 2.0) mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=6, - n_cells_max=10_000) - + initial_refinement_level = 6, + n_cells_max = 10_000) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver) - ############################################################################### # ODE solvers, callbacks etc. @@ -83,27 +82,26 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=100, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 100, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) -stepsize_callback = StepsizeCallback(cfl=0.9) +stepsize_callback = StepsizeCallback(cfl = 0.9) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, save_solution, stepsize_callback) - ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/tree_2d_dgsem/elixir_euler_blast_wave_neuralnetwork_perssonperaire.jl b/examples/tree_2d_dgsem/elixir_euler_blast_wave_neuralnetwork_perssonperaire.jl index 3f4862674d2..27398593efd 100644 --- a/examples/tree_2d_dgsem/elixir_euler_blast_wave_neuralnetwork_perssonperaire.jl +++ b/examples/tree_2d_dgsem/elixir_euler_blast_wave_neuralnetwork_perssonperaire.jl @@ -2,7 +2,8 @@ using Downloads: download using Flux using BSON: load network = joinpath(@__DIR__, "modelnnpp-0.904-0.0005.bson") -download("https://github.com/trixi-framework/Trixi_IndicatorNeuralNetwork_networks/raw/main/networks/modelnnpp-0.904-0.0005.bson", network) +download("https://github.com/trixi-framework/Trixi_IndicatorNeuralNetwork_networks/raw/main/networks/modelnnpp-0.904-0.0005.bson", + network) model2d = load(network, @__MODULE__)[:model2d] using OrdinaryDiffEq @@ -28,52 +29,50 @@ A medium blast wave taken from [arXiv: 2008.12044](https://arxiv.org/abs/2008.12044) """ function initial_condition_blast_wave(x, t, equations::CompressibleEulerEquations2D) - # Modified From Hennemann & Gassner JCP paper 2020 (Sec. 6.3) -> "medium blast wave" - # Set up polar coordinates - inicenter = SVector(0.0, 0.0) - x_norm = x[1] - inicenter[1] - y_norm = x[2] - inicenter[2] - r = sqrt(x_norm^2 + y_norm^2) - phi = atan(y_norm, x_norm) - sin_phi, cos_phi = sincos(phi) - - # Calculate primitive variables - rho = r > 0.5 ? 1.0 : 1.1691 - v1 = r > 0.5 ? 0.0 : 0.1882 * cos_phi - v2 = r > 0.5 ? 0.0 : 0.1882 * sin_phi - p = r > 0.5 ? 1.0E-3 : 1.245 - - return prim2cons(SVector(rho, v1, v2, p), equations) + # Modified From Hennemann & Gassner JCP paper 2020 (Sec. 6.3) -> "medium blast wave" + # Set up polar coordinates + inicenter = SVector(0.0, 0.0) + x_norm = x[1] - inicenter[1] + y_norm = x[2] - inicenter[2] + r = sqrt(x_norm^2 + y_norm^2) + phi = atan(y_norm, x_norm) + sin_phi, cos_phi = sincos(phi) + + # Calculate primitive variables + rho = r > 0.5 ? 1.0 : 1.1691 + v1 = r > 0.5 ? 0.0 : 0.1882 * cos_phi + v2 = r > 0.5 ? 0.0 : 0.1882 * sin_phi + p = r > 0.5 ? 1.0E-3 : 1.245 + + return prim2cons(SVector(rho, v1, v2, p), equations) end initial_condition = initial_condition_blast_wave surface_flux = flux_lax_friedrichs -volume_flux = flux_chandrashekar +volume_flux = flux_chandrashekar basis = LobattoLegendreBasis(3) indicator_sc = IndicatorNeuralNetwork(equations, basis, - indicator_type=NeuralNetworkPerssonPeraire(), - alpha_max=0.5, - alpha_min=0.001, - alpha_smooth=true, - alpha_continuous=true, - alpha_amr=false, - variable=density_pressure, - network=model2d) + indicator_type = NeuralNetworkPerssonPeraire(), + alpha_max = 0.5, + alpha_min = 0.001, + alpha_smooth = true, + alpha_continuous = true, + alpha_amr = false, + variable = density_pressure, + network = model2d) volume_integral = VolumeIntegralShockCapturingHG(indicator_sc; - volume_flux_dg=volume_flux, - volume_flux_fv=surface_flux) + volume_flux_dg = volume_flux, + volume_flux_fv = surface_flux) solver = DGSEM(basis, surface_flux, volume_integral) coordinates_min = (-2.0, -2.0) -coordinates_max = ( 2.0, 2.0) +coordinates_max = (2.0, 2.0) mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=6, - n_cells_max=10_000) - + initial_refinement_level = 6, + n_cells_max = 10_000) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver) - ############################################################################### # ODE solvers, callbacks etc. @@ -83,27 +82,26 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=100, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 100, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) -stepsize_callback = StepsizeCallback(cfl=0.9) +stepsize_callback = StepsizeCallback(cfl = 0.9) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, save_solution, stepsize_callback) - ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/tree_2d_dgsem/elixir_euler_blast_wave_neuralnetwork_rayhesthaven.jl b/examples/tree_2d_dgsem/elixir_euler_blast_wave_neuralnetwork_rayhesthaven.jl index db2fffacb36..6c67f948636 100644 --- a/examples/tree_2d_dgsem/elixir_euler_blast_wave_neuralnetwork_rayhesthaven.jl +++ b/examples/tree_2d_dgsem/elixir_euler_blast_wave_neuralnetwork_rayhesthaven.jl @@ -3,7 +3,8 @@ using Flux using Random using BSON: load network = joinpath(@__DIR__, "modelnnrhs-0.973-0.001.bson") -download("https://github.com/trixi-framework/Trixi_IndicatorNeuralNetwork_networks/raw/main/networks/modelnnrhs-0.973-0.001.bson", network) +download("https://github.com/trixi-framework/Trixi_IndicatorNeuralNetwork_networks/raw/main/networks/modelnnrhs-0.973-0.001.bson", + network) model2d = load(network, @__MODULE__)[:model2d] using OrdinaryDiffEq @@ -29,54 +30,52 @@ A medium blast wave taken from [arXiv: 2008.12044](https://arxiv.org/abs/2008.12044) """ function initial_condition_blast_wave(x, t, equations::CompressibleEulerEquations2D) - # Modified From Hennemann & Gassner JCP paper 2020 (Sec. 6.3) -> "medium blast wave" - # Set up polar coordinates - inicenter = SVector(0.0, 0.0) - x_norm = x[1] - inicenter[1] - y_norm = x[2] - inicenter[2] - r = sqrt(x_norm^2 + y_norm^2) - phi = atan(y_norm, x_norm) - sin_phi, cos_phi = sincos(phi) - - # Calculate primitive variables - rho = r > 0.5 ? 1.0 : 1.1691 - v1 = r > 0.5 ? 0.0 : 0.1882 * cos_phi - v2 = r > 0.5 ? 0.0 : 0.1882 * sin_phi - p = r > 0.5 ? 1.0E-3 : 1.245 - - return prim2cons(SVector(rho, v1, v2, p), equations) + # Modified From Hennemann & Gassner JCP paper 2020 (Sec. 6.3) -> "medium blast wave" + # Set up polar coordinates + inicenter = SVector(0.0, 0.0) + x_norm = x[1] - inicenter[1] + y_norm = x[2] - inicenter[2] + r = sqrt(x_norm^2 + y_norm^2) + phi = atan(y_norm, x_norm) + sin_phi, cos_phi = sincos(phi) + + # Calculate primitive variables + rho = r > 0.5 ? 1.0 : 1.1691 + v1 = r > 0.5 ? 0.0 : 0.1882 * cos_phi + v2 = r > 0.5 ? 0.0 : 0.1882 * sin_phi + p = r > 0.5 ? 1.0E-3 : 1.245 + + return prim2cons(SVector(rho, v1, v2, p), equations) end initial_condition = initial_condition_blast_wave surface_flux = flux_lax_friedrichs -volume_flux = flux_chandrashekar +volume_flux = flux_chandrashekar basis = LobattoLegendreBasis(3) indicator_sc = IndicatorNeuralNetwork(equations, basis, - indicator_type=NeuralNetworkRayHesthaven(), - alpha_max=0.5, - alpha_min=0.001, - alpha_smooth=true, - alpha_continuous=true, - alpha_amr=false, - variable=density_pressure, - network=model2d) + indicator_type = NeuralNetworkRayHesthaven(), + alpha_max = 0.5, + alpha_min = 0.001, + alpha_smooth = true, + alpha_continuous = true, + alpha_amr = false, + variable = density_pressure, + network = model2d) volume_integral = VolumeIntegralShockCapturingHG(indicator_sc; - volume_flux_dg=volume_flux, - volume_flux_fv=surface_flux) + volume_flux_dg = volume_flux, + volume_flux_fv = surface_flux) solver = DGSEM(basis, surface_flux, volume_integral) coordinates_min = (-2.0, -2.0) -coordinates_max = ( 2.0, 2.0) +coordinates_max = (2.0, 2.0) refinement_patches = () # To allow for specifying them via `trixi_include` mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=6, - refinement_patches=refinement_patches, - n_cells_max=10_000) - + initial_refinement_level = 6, + refinement_patches = refinement_patches, + n_cells_max = 10_000) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver) - ############################################################################### # ODE solvers, callbacks etc. @@ -86,27 +85,26 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=100, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 100, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) -stepsize_callback = StepsizeCallback(cfl=0.9) +stepsize_callback = StepsizeCallback(cfl = 0.9) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, save_solution, stepsize_callback) - ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/tree_2d_dgsem/elixir_euler_blast_wave_pure_fv.jl b/examples/tree_2d_dgsem/elixir_euler_blast_wave_pure_fv.jl index a0fc9349696..a2392d05e5a 100644 --- a/examples/tree_2d_dgsem/elixir_euler_blast_wave_pure_fv.jl +++ b/examples/tree_2d_dgsem/elixir_euler_blast_wave_pure_fv.jl @@ -16,40 +16,38 @@ A medium blast wave taken from [arXiv: 2008.12044](https://arxiv.org/abs/2008.12044) """ function initial_condition_blast_wave(x, t, equations::CompressibleEulerEquations2D) - # Modified From Hennemann & Gassner JCP paper 2020 (Sec. 6.3) -> "medium blast wave" - # Set up polar coordinates - inicenter = SVector(0.0, 0.0) - x_norm = x[1] - inicenter[1] - y_norm = x[2] - inicenter[2] - r = sqrt(x_norm^2 + y_norm^2) - phi = atan(y_norm, x_norm) - sin_phi, cos_phi = sincos(phi) - - # Calculate primitive variables - rho = r > 0.5 ? 1.0 : 1.1691 - v1 = r > 0.5 ? 0.0 : 0.1882 * cos_phi - v2 = r > 0.5 ? 0.0 : 0.1882 * sin_phi - p = r > 0.5 ? 1.0E-3 : 1.245 - - return prim2cons(SVector(rho, v1, v2, p), equations) + # Modified From Hennemann & Gassner JCP paper 2020 (Sec. 6.3) -> "medium blast wave" + # Set up polar coordinates + inicenter = SVector(0.0, 0.0) + x_norm = x[1] - inicenter[1] + y_norm = x[2] - inicenter[2] + r = sqrt(x_norm^2 + y_norm^2) + phi = atan(y_norm, x_norm) + sin_phi, cos_phi = sincos(phi) + + # Calculate primitive variables + rho = r > 0.5 ? 1.0 : 1.1691 + v1 = r > 0.5 ? 0.0 : 0.1882 * cos_phi + v2 = r > 0.5 ? 0.0 : 0.1882 * sin_phi + p = r > 0.5 ? 1.0E-3 : 1.245 + + return prim2cons(SVector(rho, v1, v2, p), equations) end initial_condition = initial_condition_blast_wave -surface_flux = flux_hllc +surface_flux = flux_hllc basis = LobattoLegendreBasis(3) volume_integral = VolumeIntegralPureLGLFiniteVolume(flux_hllc) solver = DGSEM(basis, surface_flux, volume_integral) coordinates_min = (-2.0, -2.0) -coordinates_max = ( 2.0, 2.0) +coordinates_max = (2.0, 2.0) mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=6, - n_cells_max=10_000) - + initial_refinement_level = 6, + n_cells_max = 10_000) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver) - ############################################################################### # ODE solvers, callbacks etc. @@ -59,27 +57,26 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=100, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 100, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) -stepsize_callback = StepsizeCallback(cfl=0.9) +stepsize_callback = StepsizeCallback(cfl = 0.9) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, save_solution, stepsize_callback) - ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/tree_2d_dgsem/elixir_euler_blast_wave_sc_subcell.jl b/examples/tree_2d_dgsem/elixir_euler_blast_wave_sc_subcell.jl index 0e44f62c7bd..fab3a86e531 100644 --- a/examples/tree_2d_dgsem/elixir_euler_blast_wave_sc_subcell.jl +++ b/examples/tree_2d_dgsem/elixir_euler_blast_wave_sc_subcell.jl @@ -16,48 +16,46 @@ A medium blast wave taken from [arXiv: 2008.12044](https://arxiv.org/abs/2008.12044) """ function initial_condition_blast_wave(x, t, equations::CompressibleEulerEquations2D) - # Modified From Hennemann & Gassner JCP paper 2020 (Sec. 6.3) -> "medium blast wave" - # Set up polar coordinates - inicenter = SVector(0.0, 0.0) - x_norm = x[1] - inicenter[1] - y_norm = x[2] - inicenter[2] - r = sqrt(x_norm^2 + y_norm^2) - phi = atan(y_norm, x_norm) - sin_phi, cos_phi = sincos(phi) - - # Calculate primitive variables - rho = r > 0.5 ? 1.0 : 1.1691 - v1 = r > 0.5 ? 0.0 : 0.1882 * cos_phi - v2 = r > 0.5 ? 0.0 : 0.1882 * sin_phi - p = r > 0.5 ? 1.0E-3 : 1.245 - - return prim2cons(SVector(rho, v1, v2, p), equations) + # Modified From Hennemann & Gassner JCP paper 2020 (Sec. 6.3) -> "medium blast wave" + # Set up polar coordinates + inicenter = SVector(0.0, 0.0) + x_norm = x[1] - inicenter[1] + y_norm = x[2] - inicenter[2] + r = sqrt(x_norm^2 + y_norm^2) + phi = atan(y_norm, x_norm) + sin_phi, cos_phi = sincos(phi) + + # Calculate primitive variables + rho = r > 0.5 ? 1.0 : 1.1691 + v1 = r > 0.5 ? 0.0 : 0.1882 * cos_phi + v2 = r > 0.5 ? 0.0 : 0.1882 * sin_phi + p = r > 0.5 ? 1.0E-3 : 1.245 + + return prim2cons(SVector(rho, v1, v2, p), equations) end initial_condition = initial_condition_blast_wave surface_flux = flux_lax_friedrichs -volume_flux = flux_ranocha +volume_flux = flux_ranocha basis = LobattoLegendreBasis(3) limiter_idp = SubcellLimiterIDP(equations, basis; - local_minmax_variables_cons=[1], - math_entropy=true, - bar_states=false, - smoothness_indicator=true) + local_minmax_variables_cons = [1], + math_entropy = true, + bar_states = false, + smoothness_indicator = true) volume_integral = VolumeIntegralSubcellLimiting(limiter_idp; - volume_flux_dg=volume_flux, - volume_flux_fv=surface_flux) + volume_flux_dg = volume_flux, + volume_flux_fv = surface_flux) solver = DGSEM(basis, surface_flux, volume_integral) coordinates_min = (-2.0, -2.0) -coordinates_max = ( 2.0, 2.0) +coordinates_max = (2.0, 2.0) mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=6, - n_cells_max=10_000) - + initial_refinement_level = 6, + n_cells_max = 10_000) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver) - ############################################################################### # ODE solvers, callbacks etc. @@ -67,29 +65,28 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=100, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 100, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) -stepsize_callback = StepsizeCallback(cfl=0.6) +stepsize_callback = StepsizeCallback(cfl = 0.6) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, save_solution, stepsize_callback) - ############################################################################### # run the simulation -stage_callbacks = (SubcellLimiterIDPCorrection(), BoundsCheckCallback(save_errors=false)) +stage_callbacks = (SubcellLimiterIDPCorrection(), BoundsCheckCallback(save_errors = false)) -sol = Trixi.solve(ode, Trixi.SimpleSSPRK33(stage_callbacks=stage_callbacks); - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = Trixi.solve(ode, Trixi.SimpleSSPRK33(stage_callbacks = stage_callbacks); + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/tree_2d_dgsem/elixir_euler_blob_amr.jl b/examples/tree_2d_dgsem/elixir_euler_blob_amr.jl index f4040732667..2b3659017a3 100644 --- a/examples/tree_2d_dgsem/elixir_euler_blob_amr.jl +++ b/examples/tree_2d_dgsem/elixir_euler_blob_amr.jl @@ -4,7 +4,7 @@ using Trixi ############################################################################### # semidiscretization of the compressible Euler equations -gamma = 5/3 +gamma = 5 / 3 equations = CompressibleEulerEquations2D(gamma) """ @@ -16,67 +16,67 @@ The blob test case taken from [arXiv: astro-ph/0610051](https://arxiv.org/abs/astro-ph/0610051) """ function initial_condition_blob(x, t, equations::CompressibleEulerEquations2D) - # blob test case, see Agertz et al. https://arxiv.org/pdf/astro-ph/0610051.pdf - # other reference: https://arxiv.org/pdf/astro-ph/0610051.pdf - # change discontinuity to tanh - # typical domain is rectangular, we change it to a square - # resolution 128^2, 256^2 - # domain size is [-20.0,20.0]^2 - # gamma = 5/3 for this test case - R = 1.0 # radius of the blob - # background density - dens0 = 1.0 - Chi = 10.0 # density contrast - # reference time of characteristic growth of KH instability equal to 1.0 - tau_kh = 1.0 - tau_cr = tau_kh/1.6 # crushing time - # determine background velocity - velx0 = 2*R*sqrt(Chi)/tau_cr - vely0 = 0.0 - Ma0 = 2.7 # background flow Mach number Ma=v/c - c = velx0/Ma0 # sound speed - # use perfect gas assumption to compute background pressure via the sound speed c^2 = gamma * pressure/density - p0 = c*c*dens0/equations.gamma - # initial center of the blob - inicenter = [-15,0] - x_rel = x-inicenter - r = sqrt(x_rel[1]^2 + x_rel[2]^2) - # steepness of the tanh transition zone - slope = 2 - # density blob - dens = dens0 + (Chi-1) * 0.5*(1+(tanh(slope*(r+R)) - (tanh(slope*(r-R)) + 1))) - # velocity blob is zero - velx = velx0 - velx0 * 0.5*(1+(tanh(slope*(r+R)) - (tanh(slope*(r-R)) + 1))) - return prim2cons(SVector(dens, velx, vely0, p0), equations) + # blob test case, see Agertz et al. https://arxiv.org/pdf/astro-ph/0610051.pdf + # other reference: https://arxiv.org/pdf/astro-ph/0610051.pdf + # change discontinuity to tanh + # typical domain is rectangular, we change it to a square + # resolution 128^2, 256^2 + # domain size is [-20.0,20.0]^2 + # gamma = 5/3 for this test case + R = 1.0 # radius of the blob + # background density + dens0 = 1.0 + Chi = 10.0 # density contrast + # reference time of characteristic growth of KH instability equal to 1.0 + tau_kh = 1.0 + tau_cr = tau_kh / 1.6 # crushing time + # determine background velocity + velx0 = 2 * R * sqrt(Chi) / tau_cr + vely0 = 0.0 + Ma0 = 2.7 # background flow Mach number Ma=v/c + c = velx0 / Ma0 # sound speed + # use perfect gas assumption to compute background pressure via the sound speed c^2 = gamma * pressure/density + p0 = c * c * dens0 / equations.gamma + # initial center of the blob + inicenter = [-15, 0] + x_rel = x - inicenter + r = sqrt(x_rel[1]^2 + x_rel[2]^2) + # steepness of the tanh transition zone + slope = 2 + # density blob + dens = dens0 + + (Chi - 1) * 0.5 * (1 + (tanh(slope * (r + R)) - (tanh(slope * (r - R)) + 1))) + # velocity blob is zero + velx = velx0 - velx0 * 0.5 * (1 + (tanh(slope * (r + R)) - (tanh(slope * (r - R)) + 1))) + return prim2cons(SVector(dens, velx, vely0, p0), equations) end initial_condition = initial_condition_blob surface_flux = flux_lax_friedrichs -volume_flux = flux_ranocha +volume_flux = flux_ranocha basis = LobattoLegendreBasis(4) indicator_sc = IndicatorHennemannGassner(equations, basis, - alpha_max=0.4, - alpha_min=0.0001, - alpha_smooth=true, - variable=pressure) + alpha_max = 0.4, + alpha_min = 0.0001, + alpha_smooth = true, + variable = pressure) volume_integral = VolumeIntegralShockCapturingHG(indicator_sc; - volume_flux_dg=volume_flux, - volume_flux_fv=surface_flux) + volume_flux_dg = volume_flux, + volume_flux_fv = surface_flux) solver = DGSEM(basis, surface_flux, volume_integral) coordinates_min = (-20.0, -20.0) -coordinates_max = ( 20.0, 20.0) +coordinates_max = (20.0, 20.0) mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=6, - n_cells_max=100_000,) + initial_refinement_level = 6, + n_cells_max = 100_000) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver) - ############################################################################### # ODE solvers, callbacks etc. @@ -86,42 +86,41 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=100, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 100, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) amr_indicator = IndicatorHennemannGassner(semi, - alpha_max=1.0, - alpha_min=0.0001, - alpha_smooth=false, - variable=Trixi.density) + alpha_max = 1.0, + alpha_min = 0.0001, + alpha_smooth = false, + variable = Trixi.density) amr_controller = ControllerThreeLevelCombined(semi, amr_indicator, indicator_sc, - base_level=4, - med_level =0, med_threshold=0.0003, # med_level = current level - max_level =7, max_threshold=0.003, - max_threshold_secondary=indicator_sc.alpha_max) + base_level = 4, + med_level = 0, med_threshold = 0.0003, # med_level = current level + max_level = 7, max_threshold = 0.003, + max_threshold_secondary = indicator_sc.alpha_max) amr_callback = AMRCallback(semi, amr_controller, - interval=1, - adapt_initial_condition=true, - adapt_initial_condition_only_refine=true) + interval = 1, + adapt_initial_condition = true, + adapt_initial_condition_only_refine = true) -stepsize_callback = StepsizeCallback(cfl=0.25) +stepsize_callback = StepsizeCallback(cfl = 0.25) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, save_solution, amr_callback, stepsize_callback) - ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/tree_2d_dgsem/elixir_euler_blob_mortar.jl b/examples/tree_2d_dgsem/elixir_euler_blob_mortar.jl index 5b7365f860f..8bd5db00c9a 100644 --- a/examples/tree_2d_dgsem/elixir_euler_blob_mortar.jl +++ b/examples/tree_2d_dgsem/elixir_euler_blob_mortar.jl @@ -4,7 +4,7 @@ using Trixi ############################################################################### # semidiscretization of the compressible Euler equations -gamma = 5/3 +gamma = 5 / 3 equations = CompressibleEulerEquations2D(gamma) """ @@ -16,71 +16,71 @@ The blob test case taken from [arXiv: astro-ph/0610051](https://arxiv.org/abs/astro-ph/0610051) """ function initial_condition_blob(x, t, equations::CompressibleEulerEquations2D) - # blob test case, see Agertz et al. https://arxiv.org/pdf/astro-ph/0610051.pdf - # other reference: https://arxiv.org/pdf/astro-ph/0610051.pdf - # change discontinuity to tanh - # typical domain is rectangular, we change it to a square - # resolution 128^2, 256^2 - # domain size is [-20.0,20.0]^2 - # gamma = 5/3 for this test case - R = 1.0 # radius of the blob - # background density - dens0 = 1.0 - Chi = 10.0 # density contrast - # reference time of characteristic growth of KH instability equal to 1.0 - tau_kh = 1.0 - tau_cr = tau_kh/1.6 # crushing time - # determine background velocity - velx0 = 2*R*sqrt(Chi)/tau_cr - vely0 = 0.0 - Ma0 = 2.7 # background flow Mach number Ma=v/c - c = velx0/Ma0 # sound speed - # use perfect gas assumption to compute background pressure via the sound speed c^2 = gamma * pressure/density - p0 = c*c*dens0/equations.gamma - # initial center of the blob - inicenter = [-15,0] - x_rel = x-inicenter - r = sqrt(x_rel[1]^2 + x_rel[2]^2) - # steepness of the tanh transition zone - slope = 2 - # density blob - dens = dens0 + (Chi-1) * 0.5*(1+(tanh(slope*(r+R)) - (tanh(slope*(r-R)) + 1))) - # velocity blob is zero - velx = velx0 - velx0 * 0.5*(1+(tanh(slope*(r+R)) - (tanh(slope*(r-R)) + 1))) - return prim2cons(SVector(dens, velx, vely0, p0), equations) + # blob test case, see Agertz et al. https://arxiv.org/pdf/astro-ph/0610051.pdf + # other reference: https://arxiv.org/pdf/astro-ph/0610051.pdf + # change discontinuity to tanh + # typical domain is rectangular, we change it to a square + # resolution 128^2, 256^2 + # domain size is [-20.0,20.0]^2 + # gamma = 5/3 for this test case + R = 1.0 # radius of the blob + # background density + dens0 = 1.0 + Chi = 10.0 # density contrast + # reference time of characteristic growth of KH instability equal to 1.0 + tau_kh = 1.0 + tau_cr = tau_kh / 1.6 # crushing time + # determine background velocity + velx0 = 2 * R * sqrt(Chi) / tau_cr + vely0 = 0.0 + Ma0 = 2.7 # background flow Mach number Ma=v/c + c = velx0 / Ma0 # sound speed + # use perfect gas assumption to compute background pressure via the sound speed c^2 = gamma * pressure/density + p0 = c * c * dens0 / equations.gamma + # initial center of the blob + inicenter = [-15, 0] + x_rel = x - inicenter + r = sqrt(x_rel[1]^2 + x_rel[2]^2) + # steepness of the tanh transition zone + slope = 2 + # density blob + dens = dens0 + + (Chi - 1) * 0.5 * (1 + (tanh(slope * (r + R)) - (tanh(slope * (r - R)) + 1))) + # velocity blob is zero + velx = velx0 - velx0 * 0.5 * (1 + (tanh(slope * (r + R)) - (tanh(slope * (r - R)) + 1))) + return prim2cons(SVector(dens, velx, vely0, p0), equations) end initial_condition = initial_condition_blob surface_flux = flux_lax_friedrichs -volume_flux = flux_ranocha +volume_flux = flux_ranocha basis = LobattoLegendreBasis(3) indicator_sc = IndicatorHennemannGassner(equations, basis, - alpha_max=0.05, - alpha_min=0.0001, - alpha_smooth=true, - variable=pressure) + alpha_max = 0.05, + alpha_min = 0.0001, + alpha_smooth = true, + variable = pressure) volume_integral = VolumeIntegralShockCapturingHG(indicator_sc; - volume_flux_dg=volume_flux, - volume_flux_fv=surface_flux) + volume_flux_dg = volume_flux, + volume_flux_fv = surface_flux) solver = DGSEM(basis, surface_flux, volume_integral) coordinates_min = (-32.0, -32.0) -coordinates_max = ( 32.0, 32.0) -refinement_patches = ( - (type="box", coordinates_min=(-40.0, -5.0), coordinates_max=(40.0, 5.0)), - (type="box", coordinates_min=(-40.0, -5.0), coordinates_max=(40.0, 5.0)), -) +coordinates_max = (32.0, 32.0) +refinement_patches = ((type = "box", coordinates_min = (-40.0, -5.0), + coordinates_max = (40.0, 5.0)), + (type = "box", coordinates_min = (-40.0, -5.0), + coordinates_max = (40.0, 5.0))) mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=4, - refinement_patches=refinement_patches, - n_cells_max=100_000,) + initial_refinement_level = 4, + refinement_patches = refinement_patches, + n_cells_max = 100_000) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver) - ############################################################################### # ODE solvers, callbacks etc. @@ -90,27 +90,26 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=100, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 100, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) -stepsize_callback = StepsizeCallback(cfl=0.7) +stepsize_callback = StepsizeCallback(cfl = 0.7) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, save_solution, stepsize_callback) - ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/tree_2d_dgsem/elixir_euler_colliding_flow.jl b/examples/tree_2d_dgsem/elixir_euler_colliding_flow.jl index cb2a5b16816..984ac3ff1f6 100644 --- a/examples/tree_2d_dgsem/elixir_euler_colliding_flow.jl +++ b/examples/tree_2d_dgsem/elixir_euler_colliding_flow.jl @@ -10,71 +10,71 @@ equations = CompressibleEulerEquations2D(gamma) # This is a hand made colliding flow setup without reference. Features Mach=70 inflow from both # sides, with relative low temperature, such that pressure keeps relatively small # Computed with gamma close to 1, to simulate isothermal gas -function initial_condition_colliding_flow_astro(x, t, equations::CompressibleEulerEquations2D) - # change discontinuity to tanh - # resolution 128^2 elements (refined close to the interface) and polydeg=3 (total of 512^2 DOF) - # domain size is [-64,+64]^2 - @unpack gamma = equations - # the quantities are chosen such, that they are as close as possible to the astro examples - # keep in mind, that in the astro example, the physical units are weird (parsec, mega years, ...) - rho = 0.0247 - c = 0.2 - p = c^2 / gamma * rho - vel = 13.907432274789372 - slope = 1.0 - v1 = -vel*tanh(slope * x[1]) - # add small initial disturbance to the field, but only close to the interface - if abs(x[1]) < 10 - v1 = v1 * (1 + 0.01 * sin(pi * x[2])) - end - v2 = 0.0 - return prim2cons(SVector(rho, v1, v2, p), equations) +function initial_condition_colliding_flow_astro(x, t, + equations::CompressibleEulerEquations2D) + # change discontinuity to tanh + # resolution 128^2 elements (refined close to the interface) and polydeg=3 (total of 512^2 DOF) + # domain size is [-64,+64]^2 + @unpack gamma = equations + # the quantities are chosen such, that they are as close as possible to the astro examples + # keep in mind, that in the astro example, the physical units are weird (parsec, mega years, ...) + rho = 0.0247 + c = 0.2 + p = c^2 / gamma * rho + vel = 13.907432274789372 + slope = 1.0 + v1 = -vel * tanh(slope * x[1]) + # add small initial disturbance to the field, but only close to the interface + if abs(x[1]) < 10 + v1 = v1 * (1 + 0.01 * sin(pi * x[2])) + end + v2 = 0.0 + return prim2cons(SVector(rho, v1, v2, p), equations) end initial_condition = initial_condition_colliding_flow_astro - -boundary_conditions = ( - x_neg=BoundaryConditionDirichlet(initial_condition_colliding_flow_astro), - x_pos=BoundaryConditionDirichlet(initial_condition_colliding_flow_astro), - y_neg=boundary_condition_periodic, - y_pos=boundary_condition_periodic, - ) - - +boundary_conditions = (x_neg = BoundaryConditionDirichlet(initial_condition_colliding_flow_astro), + x_pos = BoundaryConditionDirichlet(initial_condition_colliding_flow_astro), + y_neg = boundary_condition_periodic, + y_pos = boundary_condition_periodic) surface_flux = flux_lax_friedrichs # HLLC needs more shock capturing (alpha_max) -volume_flux = flux_ranocha # works with Chandrashekar flux as well +volume_flux = flux_ranocha # works with Chandrashekar flux as well polydeg = 3 basis = LobattoLegendreBasis(polydeg) # shock capturing necessary for this tough example, however alpha_max = 0.5 is fine indicator_sc = IndicatorHennemannGassner(equations, basis, - alpha_max=0.5, - alpha_min=0.0001, - alpha_smooth=true, - variable=density_pressure) + alpha_max = 0.5, + alpha_min = 0.0001, + alpha_smooth = true, + variable = density_pressure) volume_integral = VolumeIntegralShockCapturingHG(indicator_sc; - volume_flux_dg=volume_flux, - volume_flux_fv=surface_flux) + volume_flux_dg = volume_flux, + volume_flux_fv = surface_flux) solver = DGSEM(basis, surface_flux, volume_integral) coordinates_min = (-64.0, -64.0) -coordinates_max = ( 64.0, 64.0) +coordinates_max = (64.0, 64.0) # only refinement in a patch. Needs x=-17/+17 to trigger refinement due to coarse base mesh -refinement_patches = ( - (type="box", coordinates_min=(-17, -64), coordinates_max=(17, 64)), - (type="box", coordinates_min=(-17, -64), coordinates_max=(17, 64)), - (type="box", coordinates_min=(-17, -64), coordinates_max=(17, 64)), - (type="box", coordinates_min=(-17, -64), coordinates_max=(17, 64)), - #(type="box", coordinates_min=(-17, -64), coordinates_max=(17, 64)), # very high resolution, takes about 1000s on 2 cores -) +refinement_patches = ((type = "box", coordinates_min = (-17, -64), + coordinates_max = (17, 64)), + (type = "box", coordinates_min = (-17, -64), + coordinates_max = (17, 64)), + (type = "box", coordinates_min = (-17, -64), + coordinates_max = (17, 64)), + (type = "box", coordinates_min = (-17, -64), + coordinates_max = (17, 64)) + #(type="box", coordinates_min=(-17, -64), coordinates_max=(17, 64)), # very high resolution, takes about 1000s on 2 cores + ) mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=3, - refinement_patches=refinement_patches, - periodicity=(false,true), - n_cells_max=100_000) -semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver, boundary_conditions=boundary_conditions) + initial_refinement_level = 3, + refinement_patches = refinement_patches, + periodicity = (false, true), + n_cells_max = 100_000) +semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver, + boundary_conditions = boundary_conditions) ############################################################################### # ODE solvers, callbacks etc. @@ -85,26 +85,26 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 1000 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=1000, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 1000, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) callbacks = CallbackSet(summary_callback, - analysis_callback, alive_callback, + analysis_callback, alive_callback, save_solution) # positivity limiter necessary for this tough example -stage_limiter! = PositivityPreservingLimiterZhangShu(thresholds=(5.0e-6, 5.0e-6), - variables=(Trixi.density, pressure)) +stage_limiter! = PositivityPreservingLimiterZhangShu(thresholds = (5.0e-6, 5.0e-6), + variables = (Trixi.density, pressure)) ############################################################################### # run the simulation # use adaptive time stepping based on error estimates, time step roughly dt = 5e-3 sol = solve(ode, SSPRK43(stage_limiter!); - ode_default_options()..., callback=callbacks); + ode_default_options()..., callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/tree_2d_dgsem/elixir_euler_colliding_flow_amr.jl b/examples/tree_2d_dgsem/elixir_euler_colliding_flow_amr.jl index 21de07147ca..a9eb671929f 100644 --- a/examples/tree_2d_dgsem/elixir_euler_colliding_flow_amr.jl +++ b/examples/tree_2d_dgsem/elixir_euler_colliding_flow_amr.jl @@ -10,62 +10,59 @@ equations = CompressibleEulerEquations2D(gamma) # This is a hand made colliding flow setup without reference. Features Mach=70 inflow from both # sides, with relative low temperature, such that pressure keeps relatively small # Computed with gamma close to 1, to simulate isothermal gas -function initial_condition_colliding_flow_astro(x, t, equations::CompressibleEulerEquations2D) - # change discontinuity to tanh - # resolution 128^2 elements (refined close to the interface) and polydeg=3 (total of 512^2 DOF) - # domain size is [-64,+64]^2 - @unpack gamma = equations - # the quantities are chosen such, that they are as close as possible to the astro examples - # keep in mind, that in the astro example, the physical units are weird (parsec, mega years, ...) - rho = 0.0247 - c = 0.2 - p = c^2 / gamma * rho - vel = 13.907432274789372 - slope = 1.0 - v1 = -vel*tanh(slope * x[1]) - # add small initial disturbance to the field, but only close to the interface - if abs(x[1]) < 10 - v1 = v1 * (1 + 0.01 * sin(pi*x[2])) - end - v2 = 0.0 - return prim2cons(SVector(rho, v1, v2, p), equations) +function initial_condition_colliding_flow_astro(x, t, + equations::CompressibleEulerEquations2D) + # change discontinuity to tanh + # resolution 128^2 elements (refined close to the interface) and polydeg=3 (total of 512^2 DOF) + # domain size is [-64,+64]^2 + @unpack gamma = equations + # the quantities are chosen such, that they are as close as possible to the astro examples + # keep in mind, that in the astro example, the physical units are weird (parsec, mega years, ...) + rho = 0.0247 + c = 0.2 + p = c^2 / gamma * rho + vel = 13.907432274789372 + slope = 1.0 + v1 = -vel * tanh(slope * x[1]) + # add small initial disturbance to the field, but only close to the interface + if abs(x[1]) < 10 + v1 = v1 * (1 + 0.01 * sin(pi * x[2])) + end + v2 = 0.0 + return prim2cons(SVector(rho, v1, v2, p), equations) end initial_condition = initial_condition_colliding_flow_astro - -boundary_conditions = ( - x_neg=BoundaryConditionDirichlet(initial_condition_colliding_flow_astro), - x_pos=BoundaryConditionDirichlet(initial_condition_colliding_flow_astro), - y_neg=boundary_condition_periodic, - y_pos=boundary_condition_periodic, - ) - - +boundary_conditions = (x_neg = BoundaryConditionDirichlet(initial_condition_colliding_flow_astro), + x_pos = BoundaryConditionDirichlet(initial_condition_colliding_flow_astro), + y_neg = boundary_condition_periodic, + y_pos = boundary_condition_periodic) surface_flux = flux_lax_friedrichs # HLLC needs more shock capturing (alpha_max) -volume_flux = flux_ranocha # works with Chandrashekar flux as well +volume_flux = flux_ranocha # works with Chandrashekar flux as well polydeg = 3 basis = LobattoLegendreBasis(polydeg) # shock capturing necessary for this tough example, however alpha_max = 0.5 is fine indicator_sc = IndicatorHennemannGassner(equations, basis, - alpha_max=0.5, - alpha_min=0.0001, - alpha_smooth=true, - variable=density_pressure) + alpha_max = 0.5, + alpha_min = 0.0001, + alpha_smooth = true, + variable = density_pressure) volume_integral = VolumeIntegralShockCapturingHG(indicator_sc; - volume_flux_dg=volume_flux, - volume_flux_fv=surface_flux) + volume_flux_dg = volume_flux, + volume_flux_fv = surface_flux) solver = DGSEM(basis, surface_flux, volume_integral) coordinates_min = (-64.0, -64.0) -coordinates_max = ( 64.0, 64.0) +coordinates_max = (64.0, 64.0) mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=4, - periodicity=(false,true), - n_cells_max=100_000) -semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver, boundary_conditions=boundary_conditions) + initial_refinement_level = 4, + periodicity = (false, true), + n_cells_max = 100_000) +semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver, + boundary_conditions = boundary_conditions) ############################################################################### # ODE solvers, callbacks etc. @@ -76,44 +73,44 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 1000 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=1000, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 1000, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) # Simulation also feasible without AMR: AMR reduces CPU time by a factor of about 2 amr_indicator = IndicatorHennemannGassner(semi, - alpha_max=1.0, - alpha_min=0.0001, - alpha_smooth=false, - variable=Trixi.density) + alpha_max = 1.0, + alpha_min = 0.0001, + alpha_smooth = false, + variable = Trixi.density) amr_controller = ControllerThreeLevelCombined(semi, amr_indicator, indicator_sc, - base_level=2, - med_level =0, med_threshold=0.0003, # med_level = current level - max_level =8, max_threshold=0.003, - max_threshold_secondary=indicator_sc.alpha_max) + base_level = 2, + med_level = 0, med_threshold = 0.0003, # med_level = current level + max_level = 8, max_threshold = 0.003, + max_threshold_secondary = indicator_sc.alpha_max) amr_callback = AMRCallback(semi, amr_controller, - interval=1, - adapt_initial_condition=true, - adapt_initial_condition_only_refine=true) + interval = 1, + adapt_initial_condition = true, + adapt_initial_condition_only_refine = true) callbacks = CallbackSet(summary_callback, - analysis_callback, alive_callback, + analysis_callback, alive_callback, amr_callback, save_solution) # positivity limiter necessary for this tough example -stage_limiter! = PositivityPreservingLimiterZhangShu(thresholds=(5.0e-6, 5.0e-6), - variables=(Trixi.density, pressure)) +stage_limiter! = PositivityPreservingLimiterZhangShu(thresholds = (5.0e-6, 5.0e-6), + variables = (Trixi.density, pressure)) ############################################################################### # run the simulation # use adaptive time stepping based on error estimates, time step roughly dt = 5e-3 sol = solve(ode, SSPRK43(stage_limiter!); - ode_default_options()..., callback=callbacks); + ode_default_options()..., callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/tree_2d_dgsem/elixir_euler_convergence_IDP.jl b/examples/tree_2d_dgsem/elixir_euler_convergence_IDP.jl index bf6064dc219..eccf13c6d2c 100644 --- a/examples/tree_2d_dgsem/elixir_euler_convergence_IDP.jl +++ b/examples/tree_2d_dgsem/elixir_euler_convergence_IDP.jl @@ -14,29 +14,28 @@ volume_flux = flux_ranocha polydeg = 3 basis = LobattoLegendreBasis(polydeg) limiter_idp = SubcellLimiterIDP(equations, basis; - positivity_variables_cons=[1], - positivity_variables_nonlinear=(pressure,), - positivity_correction_factor=0.1, - spec_entropy=false, - max_iterations_newton=10, - newton_tolerances=(1.0e-12, 1.0e-14), - bar_states=true, - smoothness_indicator=false) + positivity_variables_cons = [1], + positivity_variables_nonlinear = (pressure,), + positivity_correction_factor = 0.1, + spec_entropy = false, + max_iterations_newton = 10, + newton_tolerances = (1.0e-12, 1.0e-14), + bar_states = true, + smoothness_indicator = false) volume_integral = VolumeIntegralSubcellLimiting(limiter_idp; - volume_flux_dg=volume_flux, - volume_flux_fv=surface_flux) + volume_flux_dg = volume_flux, + volume_flux_fv = surface_flux) solver = DGSEM(basis, surface_flux, volume_integral) coordinates_min = (-1.0, -1.0) coordinates_max = (1.0, 1.0) mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=2, - n_cells_max=10_000) + initial_refinement_level = 2, + n_cells_max = 10_000) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver) - ############################################################################### # ODE solvers, callbacks etc. @@ -46,16 +45,16 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=100000, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 100000, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) -stepsize_callback = StepsizeCallback(cfl=0.9) +stepsize_callback = StepsizeCallback(cfl = 0.9) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, @@ -64,9 +63,9 @@ callbacks = CallbackSet(summary_callback, ############################################################################### # run the simulation -stage_callbacks = (SubcellLimiterIDPCorrection(), BoundsCheckCallback(save_errors=false)) +stage_callbacks = (SubcellLimiterIDPCorrection(), BoundsCheckCallback(save_errors = false)) -sol = Trixi.solve(ode, Trixi.SimpleSSPRK33(stage_callbacks=stage_callbacks); - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = Trixi.solve(ode, Trixi.SimpleSSPRK33(stage_callbacks = stage_callbacks); + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/tree_2d_dgsem/elixir_euler_convergence_MCL.jl b/examples/tree_2d_dgsem/elixir_euler_convergence_MCL.jl index d7e4250bb67..d82aed8ba32 100644 --- a/examples/tree_2d_dgsem/elixir_euler_convergence_MCL.jl +++ b/examples/tree_2d_dgsem/elixir_euler_convergence_MCL.jl @@ -14,28 +14,28 @@ volume_flux = flux_ranocha polydeg = 3 basis = LobattoLegendreBasis(polydeg) limiter_mcl = SubcellLimiterMCL(equations, basis; - DensityLimiter=false, - DensityAlphaForAll=false, - SequentialLimiter=false, - ConservativeLimiter=false, - DensityPositivityLimiter=true, - PressurePositivityLimiterKuzmin=true, PressurePositivityLimiterKuzminExact=true, - Plotting=true) + DensityLimiter = false, + DensityAlphaForAll = false, + SequentialLimiter = false, + ConservativeLimiter = false, + DensityPositivityLimiter = true, + PressurePositivityLimiterKuzmin = true, + PressurePositivityLimiterKuzminExact = true, + Plotting = true) volume_integral = VolumeIntegralSubcellLimiting(limiter_mcl; - volume_flux_dg=volume_flux, - volume_flux_fv=surface_flux) + volume_flux_dg = volume_flux, + volume_flux_fv = surface_flux) solver = DGSEM(basis, surface_flux, volume_integral) coordinates_min = (-1.0, -1.0) -coordinates_max = ( 1.0, 1.0) +coordinates_max = (1.0, 1.0) mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=2, - n_cells_max=10_000) + initial_refinement_level = 2, + n_cells_max = 10_000) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver) - ############################################################################### # ODE solvers, callbacks etc. @@ -45,16 +45,16 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=100000, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 100000, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) -stepsize_callback = StepsizeCallback(cfl=0.9) +stepsize_callback = StepsizeCallback(cfl = 0.9) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, @@ -63,9 +63,9 @@ callbacks = CallbackSet(summary_callback, ############################################################################### # run the simulation -stage_callbacks = (BoundsCheckCallback(save_errors=false),) +stage_callbacks = (BoundsCheckCallback(save_errors = false),) -sol = Trixi.solve(ode, Trixi.SimpleSSPRK33(stage_callbacks=stage_callbacks); - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = Trixi.solve(ode, Trixi.SimpleSSPRK33(stage_callbacks = stage_callbacks); + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/tree_2d_dgsem/elixir_euler_convergence_pure_fv.jl b/examples/tree_2d_dgsem/elixir_euler_convergence_pure_fv.jl index 89d7422cfe6..96184b5ba47 100644 --- a/examples/tree_2d_dgsem/elixir_euler_convergence_pure_fv.jl +++ b/examples/tree_2d_dgsem/elixir_euler_convergence_pure_fv.jl @@ -18,13 +18,11 @@ solver = DGSEM(basis, surface_flux, volume_integral) coordinates_min = (0.0, 0.0) coordinates_max = (2.0, 2.0) mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=4, - n_cells_max=10_000) - + initial_refinement_level = 4, + n_cells_max = 10_000) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver, - source_terms=source_terms_convergence_test) - + source_terms = source_terms_convergence_test) ############################################################################### # ODE solvers, callbacks etc. @@ -35,16 +33,16 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=100, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 100, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) -stepsize_callback = StepsizeCallback(cfl=0.5) +stepsize_callback = StepsizeCallback(cfl = 0.5) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, @@ -54,7 +52,7 @@ callbacks = CallbackSet(summary_callback, ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/tree_2d_dgsem/elixir_euler_density_wave.jl b/examples/tree_2d_dgsem/elixir_euler_density_wave.jl index a5e9d30e389..0f9e232fa14 100644 --- a/examples/tree_2d_dgsem/elixir_euler_density_wave.jl +++ b/examples/tree_2d_dgsem/elixir_euler_density_wave.jl @@ -9,18 +9,16 @@ equations = CompressibleEulerEquations2D(gamma) initial_condition = initial_condition_density_wave -solver = DGSEM(polydeg=5, surface_flux=flux_central) +solver = DGSEM(polydeg = 5, surface_flux = flux_central) coordinates_min = (-1.0, -1.0) -coordinates_max = ( 1.0, 1.0) +coordinates_max = (1.0, 1.0) mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=2, - n_cells_max=30_000) - + initial_refinement_level = 2, + n_cells_max = 30_000) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver) - ############################################################################### # ODE solvers, callbacks etc. @@ -30,27 +28,26 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=100, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 100, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) -stepsize_callback = StepsizeCallback(cfl=1.6) +stepsize_callback = StepsizeCallback(cfl = 1.6) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, save_solution, stepsize_callback) - ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/tree_2d_dgsem/elixir_euler_ec.jl b/examples/tree_2d_dgsem/elixir_euler_ec.jl index 88f65c3d689..e634a383cdf 100644 --- a/examples/tree_2d_dgsem/elixir_euler_ec.jl +++ b/examples/tree_2d_dgsem/elixir_euler_ec.jl @@ -9,20 +9,18 @@ equations = CompressibleEulerEquations2D(1.4) initial_condition = initial_condition_weak_blast_wave volume_flux = flux_ranocha -solver = DGSEM(polydeg=3, surface_flux=flux_ranocha, - volume_integral=VolumeIntegralFluxDifferencing(volume_flux)) +solver = DGSEM(polydeg = 3, surface_flux = flux_ranocha, + volume_integral = VolumeIntegralFluxDifferencing(volume_flux)) coordinates_min = (-2.0, -2.0) -coordinates_max = ( 2.0, 2.0) +coordinates_max = (2.0, 2.0) mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=5, - n_cells_max=10_000, - periodicity=true) - + initial_refinement_level = 5, + n_cells_max = 10_000, + periodicity = true) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver, - boundary_conditions=boundary_condition_periodic) - + boundary_conditions = boundary_condition_periodic) ############################################################################### # ODE solvers, callbacks etc. @@ -33,27 +31,26 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=100, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 100, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) -stepsize_callback = StepsizeCallback(cfl=1.0) +stepsize_callback = StepsizeCallback(cfl = 1.0) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, save_solution, stepsize_callback) - ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/tree_2d_dgsem/elixir_euler_kelvin_helmholtz_instability.jl b/examples/tree_2d_dgsem/elixir_euler_kelvin_helmholtz_instability.jl index 4fdedf516ef..5e6b1e0cc0d 100644 --- a/examples/tree_2d_dgsem/elixir_euler_kelvin_helmholtz_instability.jl +++ b/examples/tree_2d_dgsem/elixir_euler_kelvin_helmholtz_instability.jl @@ -16,40 +16,41 @@ A version of the classical Kelvin-Helmholtz instability based on of the Euler Equations [arXiv: 2102.06017](https://arxiv.org/abs/2102.06017) """ -function initial_condition_kelvin_helmholtz_instability(x, t, equations::CompressibleEulerEquations2D) - # change discontinuity to tanh - # typical resolution 128^2, 256^2 - # domain size is [-1,+1]^2 - slope = 15 - amplitude = 0.02 - B = tanh(slope * x[2] + 7.5) - tanh(slope * x[2] - 7.5) - rho = 0.5 + 0.75 * B - v1 = 0.5 * (B - 1) - v2 = 0.1 * sin(2 * pi * x[1]) - p = 1.0 - return prim2cons(SVector(rho, v1, v2, p), equations) +function initial_condition_kelvin_helmholtz_instability(x, t, + equations::CompressibleEulerEquations2D) + # change discontinuity to tanh + # typical resolution 128^2, 256^2 + # domain size is [-1,+1]^2 + slope = 15 + amplitude = 0.02 + B = tanh(slope * x[2] + 7.5) - tanh(slope * x[2] - 7.5) + rho = 0.5 + 0.75 * B + v1 = 0.5 * (B - 1) + v2 = 0.1 * sin(2 * pi * x[1]) + p = 1.0 + return prim2cons(SVector(rho, v1, v2, p), equations) end initial_condition = initial_condition_kelvin_helmholtz_instability surface_flux = flux_lax_friedrichs -volume_flux = flux_ranocha +volume_flux = flux_ranocha polydeg = 3 basis = LobattoLegendreBasis(polydeg) indicator_sc = IndicatorHennemannGassner(equations, basis, - alpha_max=0.002, - alpha_min=0.0001, - alpha_smooth=true, - variable=density_pressure) + alpha_max = 0.002, + alpha_min = 0.0001, + alpha_smooth = true, + variable = density_pressure) volume_integral = VolumeIntegralShockCapturingHG(indicator_sc; - volume_flux_dg=volume_flux, - volume_flux_fv=surface_flux) + volume_flux_dg = volume_flux, + volume_flux_fv = surface_flux) solver = DGSEM(basis, surface_flux, volume_integral) coordinates_min = (-1.0, -1.0) -coordinates_max = ( 1.0, 1.0) +coordinates_max = (1.0, 1.0) mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=5, - n_cells_max=100_000) + initial_refinement_level = 5, + n_cells_max = 100_000) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver) ############################################################################### @@ -61,27 +62,26 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=20, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 20, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) -stepsize_callback = StepsizeCallback(cfl=1.3) +stepsize_callback = StepsizeCallback(cfl = 1.3) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, save_solution, stepsize_callback) - ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/tree_2d_dgsem/elixir_euler_kelvin_helmholtz_instability_MCL.jl b/examples/tree_2d_dgsem/elixir_euler_kelvin_helmholtz_instability_MCL.jl index 3be50d01995..548485a1abc 100644 --- a/examples/tree_2d_dgsem/elixir_euler_kelvin_helmholtz_instability_MCL.jl +++ b/examples/tree_2d_dgsem/elixir_euler_kelvin_helmholtz_instability_MCL.jl @@ -16,45 +16,47 @@ A version of the classical Kelvin-Helmholtz instability based on of the Euler Equations [arXiv: 2102.06017](https://arxiv.org/abs/2102.06017) """ -function initial_condition_kelvin_helmholtz_instability(x, t, equations::CompressibleEulerEquations2D) - # change discontinuity to tanh - # typical resolution 128^2, 256^2 - # domain size is [-1,+1]^2 - slope = 15 - amplitude = 0.02 - B = tanh(slope * x[2] + 7.5) - tanh(slope * x[2] - 7.5) - rho = 0.5 + 0.75 * B - v1 = 0.5 * (B - 1) - v2 = 0.1 * sin(2 * pi * x[1]) - p = 1.0 - return prim2cons(SVector(rho, v1, v2, p), equations) +function initial_condition_kelvin_helmholtz_instability(x, t, + equations::CompressibleEulerEquations2D) + # change discontinuity to tanh + # typical resolution 128^2, 256^2 + # domain size is [-1,+1]^2 + slope = 15 + amplitude = 0.02 + B = tanh(slope * x[2] + 7.5) - tanh(slope * x[2] - 7.5) + rho = 0.5 + 0.75 * B + v1 = 0.5 * (B - 1) + v2 = 0.1 * sin(2 * pi * x[1]) + p = 1.0 + return prim2cons(SVector(rho, v1, v2, p), equations) end initial_condition = initial_condition_kelvin_helmholtz_instability surface_flux = flux_lax_friedrichs -volume_flux = flux_ranocha +volume_flux = flux_ranocha polydeg = 3 basis = LobattoLegendreBasis(polydeg) limiter_mcl = SubcellLimiterMCL(equations, basis; - DensityLimiter=false, - DensityAlphaForAll=false, - SequentialLimiter=false, - ConservativeLimiter=false, - PressurePositivityLimiterKuzmin=true, PressurePositivityLimiterKuzminExact=true, - DensityPositivityLimiter=true, - SemiDiscEntropyLimiter=false, - Plotting=true) + DensityLimiter = false, + DensityAlphaForAll = false, + SequentialLimiter = false, + ConservativeLimiter = false, + PressurePositivityLimiterKuzmin = true, + PressurePositivityLimiterKuzminExact = true, + DensityPositivityLimiter = true, + SemiDiscEntropyLimiter = false, + Plotting = true) volume_integral = VolumeIntegralSubcellLimiting(limiter_mcl; - volume_flux_dg=volume_flux, - volume_flux_fv=surface_flux) + volume_flux_dg = volume_flux, + volume_flux_fv = surface_flux) solver = DGSEM(basis, surface_flux, volume_integral) coordinates_min = (-1.0, -1.0) -coordinates_max = ( 1.0, 1.0) +coordinates_max = (1.0, 1.0) mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=6, - n_cells_max=100_000) + initial_refinement_level = 6, + n_cells_max = 100_000) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver) ############################################################################### @@ -66,32 +68,31 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 1000 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=5000, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 5000, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) -save_restart = SaveRestartCallback(interval=50000, - save_final_restart=true) +save_restart = SaveRestartCallback(interval = 50000, + save_final_restart = true) -stepsize_callback = StepsizeCallback(cfl=0.9) +stepsize_callback = StepsizeCallback(cfl = 0.9) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, stepsize_callback, save_restart, save_solution) - ############################################################################### # run the simulation -stage_callbacks = (BoundsCheckCallback(save_errors=false),) +stage_callbacks = (BoundsCheckCallback(save_errors = false),) -sol = Trixi.solve(ode, Trixi.SimpleSSPRK33(stage_callbacks=stage_callbacks); - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - maxiters=1e7, callback=callbacks); +sol = Trixi.solve(ode, Trixi.SimpleSSPRK33(stage_callbacks = stage_callbacks); + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + maxiters = 1e7, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/tree_2d_dgsem/elixir_euler_kelvin_helmholtz_instability_amr.jl b/examples/tree_2d_dgsem/elixir_euler_kelvin_helmholtz_instability_amr.jl index b8927c3fd6b..5c237835cc5 100644 --- a/examples/tree_2d_dgsem/elixir_euler_kelvin_helmholtz_instability_amr.jl +++ b/examples/tree_2d_dgsem/elixir_euler_kelvin_helmholtz_instability_amr.jl @@ -16,45 +16,44 @@ A version of the classical Kelvin-Helmholtz instability based on of the Euler Equations [arXiv: 2102.06017](https://arxiv.org/abs/2102.06017) """ -function initial_condition_kelvin_helmholtz_instability(x, t, equations::CompressibleEulerEquations2D) - # change discontinuity to tanh - # typical resolution 128^2, 256^2 - # domain size is [-1,+1]^2 - slope = 15 - amplitude = 0.02 - B = tanh(slope * x[2] + 7.5) - tanh(slope * x[2] - 7.5) - rho = 0.5 + 0.75 * B - v1 = 0.5 * (B - 1) - v2 = 0.1 * sin(2 * pi * x[1]) - p = 1.0 - return prim2cons(SVector(rho, v1, v2, p), equations) +function initial_condition_kelvin_helmholtz_instability(x, t, + equations::CompressibleEulerEquations2D) + # change discontinuity to tanh + # typical resolution 128^2, 256^2 + # domain size is [-1,+1]^2 + slope = 15 + amplitude = 0.02 + B = tanh(slope * x[2] + 7.5) - tanh(slope * x[2] - 7.5) + rho = 0.5 + 0.75 * B + v1 = 0.5 * (B - 1) + v2 = 0.1 * sin(2 * pi * x[1]) + p = 1.0 + return prim2cons(SVector(rho, v1, v2, p), equations) end initial_condition = initial_condition_kelvin_helmholtz_instability surface_flux = flux_lax_friedrichs -volume_flux = flux_ranocha +volume_flux = flux_ranocha polydeg = 3 basis = LobattoLegendreBasis(polydeg) indicator_sc = IndicatorHennemannGassner(equations, basis, - alpha_max=0.002, - alpha_min=0.0001, - alpha_smooth=true, - variable=density_pressure) + alpha_max = 0.002, + alpha_min = 0.0001, + alpha_smooth = true, + variable = density_pressure) volume_integral = VolumeIntegralShockCapturingHG(indicator_sc; - volume_flux_dg=volume_flux, - volume_flux_fv=surface_flux) + volume_flux_dg = volume_flux, + volume_flux_fv = surface_flux) solver = DGSEM(basis, surface_flux, volume_integral) coordinates_min = (-1.0, -1.0) -coordinates_max = ( 1.0, 1.0) +coordinates_max = (1.0, 1.0) mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=5, - n_cells_max=100_000) - + initial_refinement_level = 5, + n_cells_max = 100_000) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver) - ############################################################################### # ODE solvers, callbacks etc. @@ -64,41 +63,40 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=100, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 100, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) amr_indicator = IndicatorHennemannGassner(semi, - alpha_max=1.0, - alpha_min=0.0001, - alpha_smooth=false, - variable=Trixi.density) + alpha_max = 1.0, + alpha_min = 0.0001, + alpha_smooth = false, + variable = Trixi.density) amr_controller = ControllerThreeLevel(semi, amr_indicator, - base_level=4, - med_level=0, med_threshold=0.0003, # med_level = current level - max_level=6, max_threshold=0.003) + base_level = 4, + med_level = 0, med_threshold = 0.0003, # med_level = current level + max_level = 6, max_threshold = 0.003) amr_callback = AMRCallback(semi, amr_controller, - interval=1, - adapt_initial_condition=true, - adapt_initial_condition_only_refine=true) + interval = 1, + adapt_initial_condition = true, + adapt_initial_condition_only_refine = true) -stepsize_callback = StepsizeCallback(cfl=1.3) +stepsize_callback = StepsizeCallback(cfl = 1.3) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, save_solution, amr_callback, stepsize_callback) - ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/tree_2d_dgsem/elixir_euler_kelvin_helmholtz_instability_amr_neuralnetwork_perssonperaire.jl b/examples/tree_2d_dgsem/elixir_euler_kelvin_helmholtz_instability_amr_neuralnetwork_perssonperaire.jl index 952fa372696..d2cab04223e 100644 --- a/examples/tree_2d_dgsem/elixir_euler_kelvin_helmholtz_instability_amr_neuralnetwork_perssonperaire.jl +++ b/examples/tree_2d_dgsem/elixir_euler_kelvin_helmholtz_instability_amr_neuralnetwork_perssonperaire.jl @@ -2,7 +2,8 @@ using Downloads: download using Flux using BSON: load network = joinpath(@__DIR__, "modelnnpp-0.904-0.0005.bson") -download("https://github.com/trixi-framework/Trixi_IndicatorNeuralNetwork_networks/raw/main/networks/modelnnpp-0.904-0.0005.bson", network) +download("https://github.com/trixi-framework/Trixi_IndicatorNeuralNetwork_networks/raw/main/networks/modelnnpp-0.904-0.0005.bson", + network) model2d = load(network, @__MODULE__)[:model2d] using Random: seed! @@ -28,55 +29,59 @@ equations = CompressibleEulerEquations2D(gamma) A version of the classical Kelvin-Helmholtz instability based on https://rsaa.anu.edu.au/research/established-projects/fyris/2-d-kelvin-helmholtz-test. """ -function initial_condition_kelvin_helmholtz_instability(x, t, equations::CompressibleEulerEquations2D) - # change discontinuity to tanh - # typical resolution 128^2, 256^2 - # domain size is [-0.5,0.5]^2 - dens0 = 1.0 # outside density - dens1 = 2.0 # inside density - velx0 = -0.5 # outside velocity - velx1 = 0.5 # inside velocity - slope = 50 # used for tanh instead of discontinuous initial condition - # pressure equilibrium - p = 2.5 - # y velocity v2 is only white noise - v2 = 0.01*(rand(Float64,1)[1]-0.5) - # density - rho = dens0 + (dens1-dens0) * 0.5*(1+(tanh(slope*(x[2]+0.25)) - (tanh(slope*(x[2]-0.25)) + 1))) - # x velocity is also augmented with noise - v1 = velx0 + (velx1-velx0) * 0.5*(1+(tanh(slope*(x[2]+0.25)) - (tanh(slope*(x[2]-0.25)) + 1)))+0.01*(rand(Float64,1)[1]-0.5) - return prim2cons(SVector(rho, v1, v2, p), equations) +function initial_condition_kelvin_helmholtz_instability(x, t, + equations::CompressibleEulerEquations2D) + # change discontinuity to tanh + # typical resolution 128^2, 256^2 + # domain size is [-0.5,0.5]^2 + dens0 = 1.0 # outside density + dens1 = 2.0 # inside density + velx0 = -0.5 # outside velocity + velx1 = 0.5 # inside velocity + slope = 50 # used for tanh instead of discontinuous initial condition + # pressure equilibrium + p = 2.5 + # y velocity v2 is only white noise + v2 = 0.01 * (rand(Float64, 1)[1] - 0.5) + # density + rho = dens0 + + (dens1 - dens0) * 0.5 * + (1 + (tanh(slope * (x[2] + 0.25)) - (tanh(slope * (x[2] - 0.25)) + 1))) + # x velocity is also augmented with noise + v1 = velx0 + + (velx1 - velx0) * 0.5 * + (1 + (tanh(slope * (x[2] + 0.25)) - (tanh(slope * (x[2] - 0.25)) + 1))) + + 0.01 * (rand(Float64, 1)[1] - 0.5) + return prim2cons(SVector(rho, v1, v2, p), equations) end initial_condition = initial_condition_kelvin_helmholtz_instability surface_flux = flux_lax_friedrichs -volume_flux = flux_chandrashekar +volume_flux = flux_chandrashekar polydeg = 3 basis = LobattoLegendreBasis(polydeg) indicator_sc = IndicatorNeuralNetwork(equations, basis, - indicator_type=NeuralNetworkPerssonPeraire(), - alpha_max=0.002, - alpha_min=0.0001, - alpha_smooth=true, - alpha_continuous=true, - alpha_amr=false, - variable=density_pressure, - network=model2d) + indicator_type = NeuralNetworkPerssonPeraire(), + alpha_max = 0.002, + alpha_min = 0.0001, + alpha_smooth = true, + alpha_continuous = true, + alpha_amr = false, + variable = density_pressure, + network = model2d) volume_integral = VolumeIntegralShockCapturingHG(indicator_sc; - volume_flux_dg=volume_flux, - volume_flux_fv=surface_flux) + volume_flux_dg = volume_flux, + volume_flux_fv = surface_flux) solver = DGSEM(basis, surface_flux, volume_integral) coordinates_min = (-0.5, -0.5) -coordinates_max = ( 0.5, 0.5) +coordinates_max = (0.5, 0.5) mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=5, - n_cells_max=100_000) - + initial_refinement_level = 5, + n_cells_max = 100_000) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver) - ############################################################################### # ODE solvers, callbacks etc. @@ -86,45 +91,44 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=100, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 100, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) amr_indicator = IndicatorNeuralNetwork(semi, - indicator_type=NeuralNetworkPerssonPeraire(), - alpha_max=1.0, - alpha_min=0.0001, - alpha_smooth=false, - alpha_continuous=true, - alpha_amr=true, - variable=density_pressure, - network=model2d) + indicator_type = NeuralNetworkPerssonPeraire(), + alpha_max = 1.0, + alpha_min = 0.0001, + alpha_smooth = false, + alpha_continuous = true, + alpha_amr = true, + variable = density_pressure, + network = model2d) amr_controller = ControllerThreeLevel(semi, amr_indicator, - base_level=4, - med_level=6, med_threshold=0.3, # med_level = current level - max_level=7, max_threshold=0.5) + base_level = 4, + med_level = 6, med_threshold = 0.3, # med_level = current level + max_level = 7, max_threshold = 0.5) amr_callback = AMRCallback(semi, amr_controller, - interval=1, - adapt_initial_condition=true, - adapt_initial_condition_only_refine=true) + interval = 1, + adapt_initial_condition = true, + adapt_initial_condition_only_refine = true) -stepsize_callback = StepsizeCallback(cfl=1.3) +stepsize_callback = StepsizeCallback(cfl = 1.3) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, save_solution, amr_callback, stepsize_callback) - ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/tree_2d_dgsem/elixir_euler_kelvin_helmholtz_instability_fjordholm_etal.jl b/examples/tree_2d_dgsem/elixir_euler_kelvin_helmholtz_instability_fjordholm_etal.jl index 8e7484a96d4..5b2b80d84f3 100644 --- a/examples/tree_2d_dgsem/elixir_euler_kelvin_helmholtz_instability_fjordholm_etal.jl +++ b/examples/tree_2d_dgsem/elixir_euler_kelvin_helmholtz_instability_fjordholm_etal.jl @@ -1,7 +1,6 @@ using OrdinaryDiffEq using Trixi - ############################################################################### # semidiscretization of the compressible Euler equations gamma = 1.4 @@ -16,83 +15,86 @@ A version of the classical Kelvin-Helmholtz instability based on solutions for hyperbolic systems of conservation laws [arXiv: 1402.0909](https://arxiv.org/abs/1402.0909) """ -function initial_condition_kelvin_helmholtz_instability_fjordholm_etal(x, t, equations::CompressibleEulerEquations2D) - # typical resolution 128^2, 256^2 - # domain size is [0,+1]^2 - # interface is sharp, but randomly perturbed - # The random numbers used in the initial conditions have been generated as follows: - # - # using StableRNGs - # - # rng = StableRNG(100) - # - # a1 = rand(rng, m) - # a2 = rand(rng, m) - # a1 .= a1 / sum(a1) - # a2 .= a2 / sum(a2) - # b1 = (rand(rng, m) .- 0.5) .* pi - # b2 = (rand(rng, m) .- 0.5) .* pi - - m = 10 - a1 = [0.04457096674422902, 0.03891512410182607, 0.0030191053979293433, 0.0993913172320319, +function initial_condition_kelvin_helmholtz_instability_fjordholm_etal(x, t, + equations::CompressibleEulerEquations2D) + # typical resolution 128^2, 256^2 + # domain size is [0,+1]^2 + # interface is sharp, but randomly perturbed + # The random numbers used in the initial conditions have been generated as follows: + # + # using StableRNGs + # + # rng = StableRNG(100) + # + # a1 = rand(rng, m) + # a2 = rand(rng, m) + # a1 .= a1 / sum(a1) + # a2 .= a2 / sum(a2) + # b1 = (rand(rng, m) .- 0.5) .* pi + # b2 = (rand(rng, m) .- 0.5) .* pi + + m = 10 + a1 = [0.04457096674422902, 0.03891512410182607, 0.0030191053979293433, + 0.0993913172320319, 0.1622302137588842, 0.1831383653456182, 0.11758003014101702, 0.07964318348142958, 0.0863245324711805, 0.18518716132585408] - a2 = [0.061688440856337096, 0.23000237877135882, 0.04453793881833177, 0.19251530387370916, + a2 = [0.061688440856337096, 0.23000237877135882, 0.04453793881833177, + 0.19251530387370916, 0.11107917357941084, 0.05898041974649702, 0.09949312336096268, 0.07022276346006465, 0.10670366489014596, 0.02477679264318211] - b1 = [0.06582340543754152, 0.9857886297001535, 0.8450452205037154, -1.279648120993805, + b1 = [0.06582340543754152, 0.9857886297001535, 0.8450452205037154, -1.279648120993805, 0.45454198915209526, -0.13359370986823993, 0.07062615913363897, -1.0097986278512623, 1.0810669017430343, -0.14207309803877177] - b2 = [-1.1376882185131414, -1.4798197129947765, 0.6139290513283818, -0.3319087388365522, + b2 = [-1.1376882185131414, -1.4798197129947765, 0.6139290513283818, -0.3319087388365522, 0.14633328999192285, -0.06373231463100072, -0.6270101051216724, 0.13941252226261905, -1.0337526453303645, 1.0441408867083155] - Y1 = 0.0 - Y2 = 0.0 - for n = 1:m - Y1 += a1[n] * cos(b1[n] + 2 * n * pi * x[1]) - Y2 += a2[n] * cos(b2[n] + 2 * n * pi * x[1]) - end - - J1 = 0.25 - J2 = 0.75 - epsilon = 0.01 - I1 = J1 + epsilon * Y1 - I2 = J2 + epsilon * Y2 - - if (x[2] > I1) && (x[2] < I2) - rho = 2 - v1 = -0.5 - else - rho = 1 - v1 = 0.5 - end - v2 = 0 - p = 2.5 - - return prim2cons(SVector(rho, v1, v2, p), equations) + Y1 = 0.0 + Y2 = 0.0 + for n in 1:m + Y1 += a1[n] * cos(b1[n] + 2 * n * pi * x[1]) + Y2 += a2[n] * cos(b2[n] + 2 * n * pi * x[1]) + end + + J1 = 0.25 + J2 = 0.75 + epsilon = 0.01 + I1 = J1 + epsilon * Y1 + I2 = J2 + epsilon * Y2 + + if (x[2] > I1) && (x[2] < I2) + rho = 2 + v1 = -0.5 + else + rho = 1 + v1 = 0.5 + end + v2 = 0 + p = 2.5 + + return prim2cons(SVector(rho, v1, v2, p), equations) end initial_condition = initial_condition_kelvin_helmholtz_instability_fjordholm_etal surface_flux = flux_hllc -volume_flux = flux_ranocha +volume_flux = flux_ranocha polydeg = 3 basis = LobattoLegendreBasis(polydeg) indicator_sc = IndicatorHennemannGassner(equations, basis, - alpha_max=0.001, - alpha_min=0.0001, - alpha_smooth=true, - variable=density_pressure) + alpha_max = 0.001, + alpha_min = 0.0001, + alpha_smooth = true, + variable = density_pressure) volume_integral = VolumeIntegralShockCapturingHG(indicator_sc; - volume_flux_dg=volume_flux, - volume_flux_fv=surface_flux) + volume_flux_dg = volume_flux, + volume_flux_fv = surface_flux) solver = DGSEM(basis, surface_flux, volume_integral) coordinates_min = (0.0, 0.0) coordinates_max = (1.0, 1.0) mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=6, - n_cells_max=100_000) + initial_refinement_level = 6, + n_cells_max = 100_000) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver) @@ -105,14 +107,14 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 400 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=400, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 400, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, @@ -121,5 +123,5 @@ callbacks = CallbackSet(summary_callback, ############################################################################### # run the simulation sol = solve(ode, SSPRK43(); - ode_default_options()..., callback=callbacks); + ode_default_options()..., callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/tree_2d_dgsem/elixir_euler_kelvin_helmholtz_instability_restart.jl b/examples/tree_2d_dgsem/elixir_euler_kelvin_helmholtz_instability_restart.jl index e31a0476a43..dc54bb1fb3d 100644 --- a/examples/tree_2d_dgsem/elixir_euler_kelvin_helmholtz_instability_restart.jl +++ b/examples/tree_2d_dgsem/elixir_euler_kelvin_helmholtz_instability_restart.jl @@ -11,15 +11,15 @@ new_path = path tspan = (load_time(restart_filename), 6.7) ode = semidiscretize(semi, tspan, restart_filename); -save_solution = SaveSolutionCallback(output_directory=path, - interval=5000, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(output_directory = path, + interval = 5000, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) -save_restart = SaveRestartCallback(output_directory=path, - interval=50000, - save_final_restart=true) +save_restart = SaveRestartCallback(output_directory = path, + interval = 50000, + save_final_restart = true) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, @@ -27,6 +27,6 @@ callbacks = CallbackSet(summary_callback, save_restart, save_solution) sol = Trixi.solve(ode, - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - callback=callbacks); + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/tree_2d_dgsem/elixir_euler_kelvin_helmholtz_instability_sc_subcell.jl b/examples/tree_2d_dgsem/elixir_euler_kelvin_helmholtz_instability_sc_subcell.jl index 42b529cb638..8f07b7ca920 100644 --- a/examples/tree_2d_dgsem/elixir_euler_kelvin_helmholtz_instability_sc_subcell.jl +++ b/examples/tree_2d_dgsem/elixir_euler_kelvin_helmholtz_instability_sc_subcell.jl @@ -16,41 +16,42 @@ A version of the classical Kelvin-Helmholtz instability based on of the Euler Equations [arXiv: 2102.06017](https://arxiv.org/abs/2102.06017) """ -function initial_condition_kelvin_helmholtz_instability(x, t, equations::CompressibleEulerEquations2D) - # change discontinuity to tanh - # typical resolution 128^2, 256^2 - # domain size is [-1,+1]^2 - slope = 15 - amplitude = 0.02 - B = tanh(slope * x[2] + 7.5) - tanh(slope * x[2] - 7.5) - rho = 0.5 + 0.75 * B - v1 = 0.5 * (B - 1) - v2 = 0.1 * sin(2 * pi * x[1]) - p = 1.0 - return prim2cons(SVector(rho, v1, v2, p), equations) +function initial_condition_kelvin_helmholtz_instability(x, t, + equations::CompressibleEulerEquations2D) + # change discontinuity to tanh + # typical resolution 128^2, 256^2 + # domain size is [-1,+1]^2 + slope = 15 + amplitude = 0.02 + B = tanh(slope * x[2] + 7.5) - tanh(slope * x[2] - 7.5) + rho = 0.5 + 0.75 * B + v1 = 0.5 * (B - 1) + v2 = 0.1 * sin(2 * pi * x[1]) + p = 1.0 + return prim2cons(SVector(rho, v1, v2, p), equations) end initial_condition = initial_condition_kelvin_helmholtz_instability surface_flux = flux_lax_friedrichs -volume_flux = flux_ranocha +volume_flux = flux_ranocha polydeg = 3 basis = LobattoLegendreBasis(polydeg) limiter_idp = SubcellLimiterIDP(equations, basis; - positivity_variables_cons=[1], - positivity_variables_nonlinear=(pressure,), - spec_entropy=false, - bar_states=true) + positivity_variables_cons = [1], + positivity_variables_nonlinear = (pressure,), + spec_entropy = false, + bar_states = true) volume_integral = VolumeIntegralSubcellLimiting(limiter_idp; - volume_flux_dg=volume_flux, - volume_flux_fv=surface_flux) + volume_flux_dg = volume_flux, + volume_flux_fv = surface_flux) solver = DGSEM(basis, surface_flux, volume_integral) coordinates_min = (-1.0, -1.0) -coordinates_max = ( 1.0, 1.0) +coordinates_max = (1.0, 1.0) mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=6, - n_cells_max=100_000) + initial_refinement_level = 6, + n_cells_max = 100_000) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver) ############################################################################### @@ -62,32 +63,31 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 1000 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=5000, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 5000, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) -save_restart = SaveRestartCallback(interval=50000, - save_final_restart=true) +save_restart = SaveRestartCallback(interval = 50000, + save_final_restart = true) -stepsize_callback = StepsizeCallback(cfl=0.9) +stepsize_callback = StepsizeCallback(cfl = 0.9) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, stepsize_callback, save_restart, save_solution) - ############################################################################### # run the simulation -stage_callbacks = (SubcellLimiterIDPCorrection(), BoundsCheckCallback(save_errors=false)) +stage_callbacks = (SubcellLimiterIDPCorrection(), BoundsCheckCallback(save_errors = false)) -sol = Trixi.solve(ode, Trixi.SimpleSSPRK33(stage_callbacks=stage_callbacks); - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - callback=callbacks); +sol = Trixi.solve(ode, Trixi.SimpleSSPRK33(stage_callbacks = stage_callbacks); + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/tree_2d_dgsem/elixir_euler_positivity.jl b/examples/tree_2d_dgsem/elixir_euler_positivity.jl index 4c7dd7eb6cf..6fec4c1bf9b 100644 --- a/examples/tree_2d_dgsem/elixir_euler_positivity.jl +++ b/examples/tree_2d_dgsem/elixir_euler_positivity.jl @@ -14,53 +14,51 @@ The Sedov blast wave setup based on Flash - https://flash.rochester.edu/site/flashcode/user_support/flash_ug_devel/node187.html#SECTION010114000000000000000 """ function initial_condition_sedov_blast_wave(x, t, equations::CompressibleEulerEquations2D) - # Set up polar coordinates - inicenter = SVector(0.0, 0.0) - x_norm = x[1] - inicenter[1] - y_norm = x[2] - inicenter[2] - r = sqrt(x_norm^2 + y_norm^2) - - # Setup based on https://flash.rochester.edu/site/flashcode/user_support/flash_ug_devel/node187.html#SECTION010114000000000000000 - r0 = 0.21875 # = 3.5 * smallest dx (for domain length=4 and max-ref=6) - # r0 = 0.5 # = more reasonable setup - E = 1.0 - p0_inner = 3 * (equations.gamma - 1) * E / (3 * pi * r0^2) - p0_outer = 1.0e-5 # = true Sedov setup - # p0_outer = 1.0e-3 # = more reasonable setup - - # Calculate primitive variables - rho = 1.0 - v1 = 0.0 - v2 = 0.0 - p = r > r0 ? p0_outer : p0_inner - - return prim2cons(SVector(rho, v1, v2, p), equations) + # Set up polar coordinates + inicenter = SVector(0.0, 0.0) + x_norm = x[1] - inicenter[1] + y_norm = x[2] - inicenter[2] + r = sqrt(x_norm^2 + y_norm^2) + + # Setup based on https://flash.rochester.edu/site/flashcode/user_support/flash_ug_devel/node187.html#SECTION010114000000000000000 + r0 = 0.21875 # = 3.5 * smallest dx (for domain length=4 and max-ref=6) + # r0 = 0.5 # = more reasonable setup + E = 1.0 + p0_inner = 3 * (equations.gamma - 1) * E / (3 * pi * r0^2) + p0_outer = 1.0e-5 # = true Sedov setup + # p0_outer = 1.0e-3 # = more reasonable setup + + # Calculate primitive variables + rho = 1.0 + v1 = 0.0 + v2 = 0.0 + p = r > r0 ? p0_outer : p0_inner + + return prim2cons(SVector(rho, v1, v2, p), equations) end initial_condition = initial_condition_sedov_blast_wave surface_flux = flux_lax_friedrichs -volume_flux = flux_ranocha +volume_flux = flux_ranocha basis = LobattoLegendreBasis(3) indicator_sc = IndicatorHennemannGassner(equations, basis, - alpha_max=0.5, - alpha_min=0.001, - alpha_smooth=true, - variable=density_pressure) + alpha_max = 0.5, + alpha_min = 0.001, + alpha_smooth = true, + variable = density_pressure) volume_integral = VolumeIntegralShockCapturingHG(indicator_sc; - volume_flux_dg=volume_flux, - volume_flux_fv=surface_flux) + volume_flux_dg = volume_flux, + volume_flux_fv = surface_flux) solver = DGSEM(basis, surface_flux, volume_integral) coordinates_min = (-2.0, -2.0) -coordinates_max = ( 2.0, 2.0) +coordinates_max = (2.0, 2.0) mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=6, - n_cells_max=100_000) - + initial_refinement_level = 6, + n_cells_max = 100_000) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver) - ############################################################################### # ODE solvers, callbacks etc. @@ -70,42 +68,40 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 500 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=100, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 100, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) amr_indicator = IndicatorLöhner(semi, - variable=density_pressure) + variable = density_pressure) amr_controller = ControllerThreeLevel(semi, amr_indicator, - base_level=4, - med_level =0, med_threshold=0.1, # med_level = current level - max_level =6, max_threshold=0.3) + base_level = 4, + med_level = 0, med_threshold = 0.1, # med_level = current level + max_level = 6, max_threshold = 0.3) amr_callback = AMRCallback(semi, amr_controller, - interval=2, - adapt_initial_condition=true, - adapt_initial_condition_only_refine=true) + interval = 2, + adapt_initial_condition = true, + adapt_initial_condition_only_refine = true) -stepsize_callback = StepsizeCallback(cfl=0.8) +stepsize_callback = StepsizeCallback(cfl = 0.8) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, save_solution, amr_callback, stepsize_callback) - -stage_limiter! = PositivityPreservingLimiterZhangShu(thresholds=(5.0e-6, 5.0e-6), - variables=(Trixi.density, pressure)) - +stage_limiter! = PositivityPreservingLimiterZhangShu(thresholds = (5.0e-6, 5.0e-6), + variables = (Trixi.density, pressure)) ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(stage_limiter!, williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(stage_limiter!, williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/tree_2d_dgsem/elixir_euler_sedov_blast_wave.jl b/examples/tree_2d_dgsem/elixir_euler_sedov_blast_wave.jl index 512e5822374..5b8959b97d1 100644 --- a/examples/tree_2d_dgsem/elixir_euler_sedov_blast_wave.jl +++ b/examples/tree_2d_dgsem/elixir_euler_sedov_blast_wave.jl @@ -14,53 +14,51 @@ The Sedov blast wave setup based on Flash - https://flash.rochester.edu/site/flashcode/user_support/flash_ug_devel/node187.html#SECTION010114000000000000000 """ function initial_condition_sedov_blast_wave(x, t, equations::CompressibleEulerEquations2D) - # Set up polar coordinates - inicenter = SVector(0.0, 0.0) - x_norm = x[1] - inicenter[1] - y_norm = x[2] - inicenter[2] - r = sqrt(x_norm^2 + y_norm^2) - - # Setup based on https://flash.rochester.edu/site/flashcode/user_support/flash_ug_devel/node187.html#SECTION010114000000000000000 - r0 = 0.21875 # = 3.5 * smallest dx (for domain length=4 and max-ref=6) - # r0 = 0.5 # = more reasonable setup - E = 1.0 - p0_inner = 3 * (equations.gamma - 1) * E / (3 * pi * r0^2) - p0_outer = 1.0e-5 # = true Sedov setup - # p0_outer = 1.0e-3 # = more reasonable setup - - # Calculate primitive variables - rho = 1.0 - v1 = 0.0 - v2 = 0.0 - p = r > r0 ? p0_outer : p0_inner - - return prim2cons(SVector(rho, v1, v2, p), equations) + # Set up polar coordinates + inicenter = SVector(0.0, 0.0) + x_norm = x[1] - inicenter[1] + y_norm = x[2] - inicenter[2] + r = sqrt(x_norm^2 + y_norm^2) + + # Setup based on https://flash.rochester.edu/site/flashcode/user_support/flash_ug_devel/node187.html#SECTION010114000000000000000 + r0 = 0.21875 # = 3.5 * smallest dx (for domain length=4 and max-ref=6) + # r0 = 0.5 # = more reasonable setup + E = 1.0 + p0_inner = 3 * (equations.gamma - 1) * E / (3 * pi * r0^2) + p0_outer = 1.0e-5 # = true Sedov setup + # p0_outer = 1.0e-3 # = more reasonable setup + + # Calculate primitive variables + rho = 1.0 + v1 = 0.0 + v2 = 0.0 + p = r > r0 ? p0_outer : p0_inner + + return prim2cons(SVector(rho, v1, v2, p), equations) end initial_condition = initial_condition_sedov_blast_wave surface_flux = flux_lax_friedrichs -volume_flux = flux_chandrashekar +volume_flux = flux_chandrashekar basis = LobattoLegendreBasis(3) indicator_sc = IndicatorHennemannGassner(equations, basis, - alpha_max=0.5, - alpha_min=0.001, - alpha_smooth=true, - variable=density_pressure) + alpha_max = 0.5, + alpha_min = 0.001, + alpha_smooth = true, + variable = density_pressure) volume_integral = VolumeIntegralShockCapturingHG(indicator_sc; - volume_flux_dg=volume_flux, - volume_flux_fv=surface_flux) + volume_flux_dg = volume_flux, + volume_flux_fv = surface_flux) solver = DGSEM(basis, surface_flux, volume_integral) coordinates_min = (-2.0, -2.0) -coordinates_max = ( 2.0, 2.0) +coordinates_max = (2.0, 2.0) mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=6, - n_cells_max=100_000) - + initial_refinement_level = 6, + n_cells_max = 100_000) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver) - ############################################################################### # ODE solvers, callbacks etc. @@ -70,29 +68,29 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=100, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 100, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) amr_indicator = IndicatorHennemannGassner(semi, - alpha_max=0.5, - alpha_min=0.001, - alpha_smooth=true, - variable=density_pressure) + alpha_max = 0.5, + alpha_min = 0.001, + alpha_smooth = true, + variable = density_pressure) amr_controller = ControllerThreeLevel(semi, amr_indicator, - base_level=4, - max_level =6, max_threshold=0.01) + base_level = 4, + max_level = 6, max_threshold = 0.01) amr_callback = AMRCallback(semi, amr_controller, - interval=5, - adapt_initial_condition=true, - adapt_initial_condition_only_refine=true) + interval = 5, + adapt_initial_condition = true, + adapt_initial_condition_only_refine = true) -stepsize_callback = StepsizeCallback(cfl=0.8) +stepsize_callback = StepsizeCallback(cfl = 0.8) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, @@ -101,7 +99,7 @@ callbacks = CallbackSet(summary_callback, ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/tree_2d_dgsem/elixir_euler_sedov_blast_wave_MCL.jl b/examples/tree_2d_dgsem/elixir_euler_sedov_blast_wave_MCL.jl index af239b7c1a3..a5e7532854e 100644 --- a/examples/tree_2d_dgsem/elixir_euler_sedov_blast_wave_MCL.jl +++ b/examples/tree_2d_dgsem/elixir_euler_sedov_blast_wave_MCL.jl @@ -14,57 +14,57 @@ The Sedov blast wave setup based on Flash - http://flash.uchicago.edu/site/flashcode/user_support/flash_ug_devel/node184.html#SECTION010114000000000000000 """ function initial_condition_sedov_blast_wave(x, t, equations::CompressibleEulerEquations2D) - # Set up polar coordinates - inicenter = SVector(0.0, 0.0) - x_norm = x[1] - inicenter[1] - y_norm = x[2] - inicenter[2] - r = sqrt(x_norm^2 + y_norm^2) - - # Setup based on http://flash.uchicago.edu/site/flashcode/user_support/flash_ug_devel/node184.html#SECTION010114000000000000000 - r0 = 0.21875 # = 3.5 * smallest dx (for domain length=4 and max-ref=6) - # r0 = 0.5 # = more reasonable setup - E = 1.0 - p0_inner = 3 * (equations.gamma - 1) * E / (3 * pi * r0^2) - p0_outer = 1.0e-5 # = true Sedov setup - # p0_outer = 1.0e-3 # = more reasonable setup - - # Calculate primitive variables - rho = 1.0 - v1 = 0.0 - v2 = 0.0 - p = r > r0 ? p0_outer : p0_inner - - return prim2cons(SVector(rho, v1, v2, p), equations) + # Set up polar coordinates + inicenter = SVector(0.0, 0.0) + x_norm = x[1] - inicenter[1] + y_norm = x[2] - inicenter[2] + r = sqrt(x_norm^2 + y_norm^2) + + # Setup based on http://flash.uchicago.edu/site/flashcode/user_support/flash_ug_devel/node184.html#SECTION010114000000000000000 + r0 = 0.21875 # = 3.5 * smallest dx (for domain length=4 and max-ref=6) + # r0 = 0.5 # = more reasonable setup + E = 1.0 + p0_inner = 3 * (equations.gamma - 1) * E / (3 * pi * r0^2) + p0_outer = 1.0e-5 # = true Sedov setup + # p0_outer = 1.0e-3 # = more reasonable setup + + # Calculate primitive variables + rho = 1.0 + v1 = 0.0 + v2 = 0.0 + p = r > r0 ? p0_outer : p0_inner + + return prim2cons(SVector(rho, v1, v2, p), equations) end initial_condition = initial_condition_sedov_blast_wave surface_flux = flux_lax_friedrichs -volume_flux = flux_chandrashekar +volume_flux = flux_chandrashekar basis = LobattoLegendreBasis(3) limiter_mcl = SubcellLimiterMCL(equations, basis; - DensityLimiter=true, - DensityAlphaForAll=false, - SequentialLimiter=true, - ConservativeLimiter=false, - DensityPositivityLimiter=false, - PressurePositivityLimiterKuzmin=true, PressurePositivityLimiterKuzminExact=true, - SemiDiscEntropyLimiter=true, - smoothness_indicator=false, - Plotting=true) + DensityLimiter = true, + DensityAlphaForAll = false, + SequentialLimiter = true, + ConservativeLimiter = false, + DensityPositivityLimiter = false, + PressurePositivityLimiterKuzmin = true, + PressurePositivityLimiterKuzminExact = true, + SemiDiscEntropyLimiter = true, + smoothness_indicator = false, + Plotting = true) volume_integral = VolumeIntegralSubcellLimiting(limiter_mcl; - volume_flux_dg=volume_flux, - volume_flux_fv=surface_flux) + volume_flux_dg = volume_flux, + volume_flux_fv = surface_flux) solver = DGSEM(basis, surface_flux, volume_integral) coordinates_min = (-2.0, -2.0) -coordinates_max = ( 2.0, 2.0) +coordinates_max = (2.0, 2.0) mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=3, - n_cells_max=100_000) + initial_refinement_level = 3, + n_cells_max = 100_000) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver) - ############################################################################### # ODE solvers, callbacks etc. @@ -74,18 +74,19 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 1000 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=1000, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 1000, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) -stepsize_callback = StepsizeCallback(cfl=0.9) +stepsize_callback = StepsizeCallback(cfl = 0.9) -limiting_analysis_callback = LimitingAnalysisCallback(output_directory="out", interval=1) +limiting_analysis_callback = LimitingAnalysisCallback(output_directory = "out", + interval = 1) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, @@ -94,9 +95,11 @@ callbacks = CallbackSet(summary_callback, ############################################################################### # run the simulation -stage_callbacks = (BoundsCheckCallback(save_errors=false),) +output_directory = "out" +stage_callbacks = (BoundsCheckCallback(save_errors = true, interval = 100, + output_directory = output_directory),) -sol = Trixi.solve(ode, Trixi.SimpleSSPRK33(stage_callbacks=stage_callbacks); - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = Trixi.solve(ode, Trixi.SimpleSSPRK33(stage_callbacks = stage_callbacks); + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/tree_2d_dgsem/elixir_euler_sedov_blast_wave_neuralnetwork_perssonperaire.jl b/examples/tree_2d_dgsem/elixir_euler_sedov_blast_wave_neuralnetwork_perssonperaire.jl index 5fd32da2e5c..39ea947f872 100644 --- a/examples/tree_2d_dgsem/elixir_euler_sedov_blast_wave_neuralnetwork_perssonperaire.jl +++ b/examples/tree_2d_dgsem/elixir_euler_sedov_blast_wave_neuralnetwork_perssonperaire.jl @@ -2,7 +2,8 @@ using Downloads: download using Flux using BSON: load network = joinpath(@__DIR__, "modelnnpp-0.904-0.0005.bson") -download("https://github.com/trixi-framework/Trixi_IndicatorNeuralNetwork_networks/raw/main/networks/modelnnpp-0.904-0.0005.bson", network) +download("https://github.com/trixi-framework/Trixi_IndicatorNeuralNetwork_networks/raw/main/networks/modelnnpp-0.904-0.0005.bson", + network) model2d = load(network, @__MODULE__)[:model2d] using OrdinaryDiffEq @@ -26,57 +27,55 @@ The Sedov blast wave setup based on Flash - https://flash.rochester.edu/site/flashcode/user_support/flash_ug_devel/node187.html#SECTION010114000000000000000 """ function initial_condition_sedov_blast_wave(x, t, equations::CompressibleEulerEquations2D) - # Set up polar coordinates - inicenter = SVector(0.0, 0.0) - x_norm = x[1] - inicenter[1] - y_norm = x[2] - inicenter[2] - r = sqrt(x_norm^2 + y_norm^2) - - # Setup based on https://flash.rochester.edu/site/flashcode/user_support/flash_ug_devel/node187.html#SECTION010114000000000000000 - r0 = 0.21875 # = 3.5 * smallest dx (for domain length=4 and max-ref=6) - # r0 = 0.5 # = more reasonable setup - E = 1.0 - p0_inner = 3 * (equations.gamma - 1) * E / (3 * pi * r0^2) - p0_outer = 1.0e-5 # = true Sedov setup - # p0_outer = 1.0e-3 # = more reasonable setup - - # Calculate primitive variables - rho = 1.0 - v1 = 0.0 - v2 = 0.0 - p = r > r0 ? p0_outer : p0_inner - - return prim2cons(SVector(rho, v1, v2, p), equations) + # Set up polar coordinates + inicenter = SVector(0.0, 0.0) + x_norm = x[1] - inicenter[1] + y_norm = x[2] - inicenter[2] + r = sqrt(x_norm^2 + y_norm^2) + + # Setup based on https://flash.rochester.edu/site/flashcode/user_support/flash_ug_devel/node187.html#SECTION010114000000000000000 + r0 = 0.21875 # = 3.5 * smallest dx (for domain length=4 and max-ref=6) + # r0 = 0.5 # = more reasonable setup + E = 1.0 + p0_inner = 3 * (equations.gamma - 1) * E / (3 * pi * r0^2) + p0_outer = 1.0e-5 # = true Sedov setup + # p0_outer = 1.0e-3 # = more reasonable setup + + # Calculate primitive variables + rho = 1.0 + v1 = 0.0 + v2 = 0.0 + p = r > r0 ? p0_outer : p0_inner + + return prim2cons(SVector(rho, v1, v2, p), equations) end initial_condition = initial_condition_sedov_blast_wave surface_flux = flux_lax_friedrichs -volume_flux = flux_chandrashekar +volume_flux = flux_chandrashekar basis = LobattoLegendreBasis(3) indicator_sc = IndicatorNeuralNetwork(equations, basis, - indicator_type=NeuralNetworkPerssonPeraire(), - alpha_max=0.5, - alpha_min=0.001, - alpha_smooth=true, - alpha_continuous=true, - alpha_amr=false, - variable=density_pressure, - network=model2d) + indicator_type = NeuralNetworkPerssonPeraire(), + alpha_max = 0.5, + alpha_min = 0.001, + alpha_smooth = true, + alpha_continuous = true, + alpha_amr = false, + variable = density_pressure, + network = model2d) volume_integral = VolumeIntegralShockCapturingHG(indicator_sc; - volume_flux_dg=volume_flux, - volume_flux_fv=surface_flux) + volume_flux_dg = volume_flux, + volume_flux_fv = surface_flux) solver = DGSEM(basis, surface_flux, volume_integral) coordinates_min = (-2.0, -2.0) -coordinates_max = ( 2.0, 2.0) +coordinates_max = (2.0, 2.0) mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=6, - n_cells_max=100_000) - + initial_refinement_level = 6, + n_cells_max = 100_000) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver) - ############################################################################### # ODE solvers, callbacks etc. @@ -86,33 +85,33 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=100, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 100, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) amr_indicator = IndicatorNeuralNetwork(semi, - indicator_type=NeuralNetworkPerssonPeraire(), - alpha_max=0.5, - alpha_min=0.001, - alpha_smooth=true, - alpha_continuous=true, - alpha_amr=true, - variable=density_pressure, - network=model2d) + indicator_type = NeuralNetworkPerssonPeraire(), + alpha_max = 0.5, + alpha_min = 0.001, + alpha_smooth = true, + alpha_continuous = true, + alpha_amr = true, + variable = density_pressure, + network = model2d) amr_controller = ControllerThreeLevel(semi, amr_indicator, - base_level=4, - max_level =6, max_threshold=0.22) + base_level = 4, + max_level = 6, max_threshold = 0.22) amr_callback = AMRCallback(semi, amr_controller, - interval=5, - adapt_initial_condition=true, - adapt_initial_condition_only_refine=true) + interval = 5, + adapt_initial_condition = true, + adapt_initial_condition_only_refine = true) -stepsize_callback = StepsizeCallback(cfl=0.9) +stepsize_callback = StepsizeCallback(cfl = 0.9) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, @@ -121,7 +120,7 @@ callbacks = CallbackSet(summary_callback, ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/tree_2d_dgsem/elixir_euler_sedov_blast_wave_sc_subcell.jl b/examples/tree_2d_dgsem/elixir_euler_sedov_blast_wave_sc_subcell.jl index 98861064415..b460b7a507b 100644 --- a/examples/tree_2d_dgsem/elixir_euler_sedov_blast_wave_sc_subcell.jl +++ b/examples/tree_2d_dgsem/elixir_euler_sedov_blast_wave_sc_subcell.jl @@ -14,53 +14,51 @@ The Sedov blast wave setup based on Flash - http://flash.uchicago.edu/site/flashcode/user_support/flash_ug_devel/node184.html#SECTION010114000000000000000 """ function initial_condition_sedov_blast_wave(x, t, equations::CompressibleEulerEquations2D) - # Set up polar coordinates - inicenter = SVector(0.0, 0.0) - x_norm = x[1] - inicenter[1] - y_norm = x[2] - inicenter[2] - r = sqrt(x_norm^2 + y_norm^2) - - # Setup based on http://flash.uchicago.edu/site/flashcode/user_support/flash_ug_devel/node184.html#SECTION010114000000000000000 - r0 = 0.21875 # = 3.5 * smallest dx (for domain length=4 and max-ref=6) - # r0 = 0.5 # = more reasonable setup - E = 1.0 - p0_inner = 3 * (equations.gamma - 1) * E / (3 * pi * r0^2) - p0_outer = 1.0e-5 # = true Sedov setup - # p0_outer = 1.0e-3 # = more reasonable setup - - # Calculate primitive variables - rho = 1.0 - v1 = 0.0 - v2 = 0.0 - p = r > r0 ? p0_outer : p0_inner - - return prim2cons(SVector(rho, v1, v2, p), equations) + # Set up polar coordinates + inicenter = SVector(0.0, 0.0) + x_norm = x[1] - inicenter[1] + y_norm = x[2] - inicenter[2] + r = sqrt(x_norm^2 + y_norm^2) + + # Setup based on http://flash.uchicago.edu/site/flashcode/user_support/flash_ug_devel/node184.html#SECTION010114000000000000000 + r0 = 0.21875 # = 3.5 * smallest dx (for domain length=4 and max-ref=6) + # r0 = 0.5 # = more reasonable setup + E = 1.0 + p0_inner = 3 * (equations.gamma - 1) * E / (3 * pi * r0^2) + p0_outer = 1.0e-5 # = true Sedov setup + # p0_outer = 1.0e-3 # = more reasonable setup + + # Calculate primitive variables + rho = 1.0 + v1 = 0.0 + v2 = 0.0 + p = r > r0 ? p0_outer : p0_inner + + return prim2cons(SVector(rho, v1, v2, p), equations) end initial_condition = initial_condition_sedov_blast_wave surface_flux = flux_lax_friedrichs -volume_flux = flux_chandrashekar +volume_flux = flux_chandrashekar basis = LobattoLegendreBasis(3) limiter_idp = SubcellLimiterIDP(equations, basis; - local_minmax_variables_cons=[1], - spec_entropy=true, - smoothness_indicator=false, - bar_states=true) + local_minmax_variables_cons = [1], + spec_entropy = true, + smoothness_indicator = false, + bar_states = true) volume_integral = VolumeIntegralSubcellLimiting(limiter_idp; - volume_flux_dg=volume_flux, - volume_flux_fv=surface_flux) + volume_flux_dg = volume_flux, + volume_flux_fv = surface_flux) solver = DGSEM(basis, surface_flux, volume_integral) coordinates_min = (-2.0, -2.0) -coordinates_max = ( 2.0, 2.0) +coordinates_max = (2.0, 2.0) mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=3, - n_cells_max=100_000) - + initial_refinement_level = 3, + n_cells_max = 100_000) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver) - ############################################################################### # ODE solvers, callbacks etc. @@ -70,18 +68,19 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 1000 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=1000, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 1000, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) -stepsize_callback = StepsizeCallback(cfl=0.9) +stepsize_callback = StepsizeCallback(cfl = 0.9) -limiting_analysis_callback = LimitingAnalysisCallback(output_directory="out", interval=1) +limiting_analysis_callback = LimitingAnalysisCallback(output_directory = "out", + interval = 1) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, @@ -91,9 +90,9 @@ callbacks = CallbackSet(summary_callback, ############################################################################### # run the simulation -stage_callbacks = (SubcellLimiterIDPCorrection(), BoundsCheckCallback(save_errors=false)) +stage_callbacks = (SubcellLimiterIDPCorrection(), BoundsCheckCallback(save_errors = false)) -sol = Trixi.solve(ode, Trixi.SimpleSSPRK33(stage_callbacks=stage_callbacks); - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = Trixi.solve(ode, Trixi.SimpleSSPRK33(stage_callbacks = stage_callbacks); + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/tree_2d_dgsem/elixir_euler_shockcapturing.jl b/examples/tree_2d_dgsem/elixir_euler_shockcapturing.jl index f0a7ed0b953..40f19cbd4e2 100644 --- a/examples/tree_2d_dgsem/elixir_euler_shockcapturing.jl +++ b/examples/tree_2d_dgsem/elixir_euler_shockcapturing.jl @@ -10,28 +10,26 @@ equations = CompressibleEulerEquations2D(1.4) initial_condition = initial_condition_weak_blast_wave surface_flux = flux_lax_friedrichs -volume_flux = flux_shima_etal +volume_flux = flux_shima_etal basis = LobattoLegendreBasis(3) indicator_sc = IndicatorHennemannGassner(equations, basis, - alpha_max=0.5, - alpha_min=0.001, - alpha_smooth=true, - variable=density_pressure) + alpha_max = 0.5, + alpha_min = 0.001, + alpha_smooth = true, + variable = density_pressure) volume_integral = VolumeIntegralShockCapturingHG(indicator_sc; - volume_flux_dg=volume_flux, - volume_flux_fv=surface_flux) + volume_flux_dg = volume_flux, + volume_flux_fv = surface_flux) solver = DGSEM(basis, surface_flux, volume_integral) coordinates_min = (-2.0, -2.0) -coordinates_max = ( 2.0, 2.0) +coordinates_max = (2.0, 2.0) mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=5, - n_cells_max=10_000) - + initial_refinement_level = 5, + n_cells_max = 10_000) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver) - ############################################################################### # ODE solvers, callbacks etc. @@ -41,26 +39,25 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=100, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 100, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) -stepsize_callback = StepsizeCallback(cfl=1.0) +stepsize_callback = StepsizeCallback(cfl = 1.0) callbacks = CallbackSet(summary_callback, stepsize_callback, save_solution, analysis_callback, alive_callback) - ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/tree_2d_dgsem/elixir_euler_shockcapturing_subcell.jl b/examples/tree_2d_dgsem/elixir_euler_shockcapturing_subcell.jl index 810c37ff5bd..4e64cb3a91c 100644 --- a/examples/tree_2d_dgsem/elixir_euler_shockcapturing_subcell.jl +++ b/examples/tree_2d_dgsem/elixir_euler_shockcapturing_subcell.jl @@ -16,46 +16,45 @@ A medium blast wave (modified to lower density and higher pressure) taken from [arXiv: 2008.12044](https://arxiv.org/abs/2008.12044) """ function initial_condition_blast_wave(x, t, equations::CompressibleEulerEquations2D) - # Modified From Hennemann & Gassner JCP paper 2020 (Sec. 6.3) -> modified to lower density, higher pressure - # Set up polar coordinates - inicenter = SVector(0.0, 0.0) - x_norm = x[1] - inicenter[1] - y_norm = x[2] - inicenter[2] - r = sqrt(x_norm^2 + y_norm^2) - phi = atan(y_norm, x_norm) - sin_phi, cos_phi = sincos(phi) - - # Calculate primitive variables "normal" medium blast wave - rho = r > 0.5 ? 0.1 : 0.2691 # rho = r > 0.5 ? 1 : 1.1691 - v1 = r > 0.5 ? 0.0 : 0.1882 * cos_phi - v2 = r > 0.5 ? 0.0 : 0.1882 * sin_phi - p = r > 0.5 ? 1.0E-1 : 1.245 # p = r > 0.5 ? 1.0E-3 : 1.245 - - return prim2cons(SVector(rho, v1, v2, p), equations) + # Modified From Hennemann & Gassner JCP paper 2020 (Sec. 6.3) -> modified to lower density, higher pressure + # Set up polar coordinates + inicenter = SVector(0.0, 0.0) + x_norm = x[1] - inicenter[1] + y_norm = x[2] - inicenter[2] + r = sqrt(x_norm^2 + y_norm^2) + phi = atan(y_norm, x_norm) + sin_phi, cos_phi = sincos(phi) + + # Calculate primitive variables "normal" medium blast wave + rho = r > 0.5 ? 0.1 : 0.2691 # rho = r > 0.5 ? 1 : 1.1691 + v1 = r > 0.5 ? 0.0 : 0.1882 * cos_phi + v2 = r > 0.5 ? 0.0 : 0.1882 * sin_phi + p = r > 0.5 ? 1.0E-1 : 1.245 # p = r > 0.5 ? 1.0E-3 : 1.245 + + return prim2cons(SVector(rho, v1, v2, p), equations) end initial_condition = initial_condition_blast_wave surface_flux = flux_lax_friedrichs -volume_flux = flux_ranocha +volume_flux = flux_ranocha basis = LobattoLegendreBasis(3) limiter_idp = SubcellLimiterIDP(equations, basis; - positivity_variables_cons=[1], - positivity_correction_factor=0.5, - bar_states=false) + positivity_variables_cons = [1], + positivity_correction_factor = 0.5, + bar_states = false) volume_integral = VolumeIntegralSubcellLimiting(limiter_idp; - volume_flux_dg=volume_flux, - volume_flux_fv=surface_flux) + volume_flux_dg = volume_flux, + volume_flux_fv = surface_flux) solver = DGSEM(basis, surface_flux, volume_integral) coordinates_min = (-2.0, -2.0) -coordinates_max = ( 2.0, 2.0) +coordinates_max = (2.0, 2.0) mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=5, - n_cells_max=100_000) + initial_refinement_level = 5, + n_cells_max = 100_000) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver) - ############################################################################### # ODE solvers, callbacks etc. @@ -65,29 +64,28 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=100, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 100, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) -stepsize_callback = StepsizeCallback(cfl=0.6) +stepsize_callback = StepsizeCallback(cfl = 0.6) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, save_solution, stepsize_callback) - ############################################################################### # run the simulation -stage_callbacks = (SubcellLimiterIDPCorrection(), BoundsCheckCallback(save_errors=false)) +stage_callbacks = (SubcellLimiterIDPCorrection(), BoundsCheckCallback(save_errors = false)) -sol = Trixi.solve(ode, Trixi.SimpleSSPRK33(stage_callbacks=stage_callbacks); - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = Trixi.solve(ode, Trixi.SimpleSSPRK33(stage_callbacks = stage_callbacks); + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/tree_2d_dgsem/elixir_euler_source_terms.jl b/examples/tree_2d_dgsem/elixir_euler_source_terms.jl index 36d93147289..ec230145537 100644 --- a/examples/tree_2d_dgsem/elixir_euler_source_terms.jl +++ b/examples/tree_2d_dgsem/elixir_euler_source_terms.jl @@ -8,18 +8,16 @@ using Trixi equations = CompressibleEulerEquations2D(1.4) initial_condition = initial_condition_convergence_test -solver = DGSEM(polydeg=3, surface_flux=flux_lax_friedrichs) +solver = DGSEM(polydeg = 3, surface_flux = flux_lax_friedrichs) coordinates_min = (0.0, 0.0) coordinates_max = (2.0, 2.0) mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=4, - n_cells_max=10_000) - + initial_refinement_level = 4, + n_cells_max = 10_000) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver, - source_terms=source_terms_convergence_test) - + source_terms = source_terms_convergence_test) ############################################################################### # ODE solvers, callbacks etc. @@ -30,16 +28,16 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=100, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 100, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) -stepsize_callback = StepsizeCallback(cfl=1.0) +stepsize_callback = StepsizeCallback(cfl = 1.0) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, @@ -49,7 +47,7 @@ callbacks = CallbackSet(summary_callback, ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/tree_2d_dgsem/elixir_euler_source_terms_amr_refine_coarsen.jl b/examples/tree_2d_dgsem/elixir_euler_source_terms_amr_refine_coarsen.jl index 231486b11c9..28ab4cec1d3 100644 --- a/examples/tree_2d_dgsem/elixir_euler_source_terms_amr_refine_coarsen.jl +++ b/examples/tree_2d_dgsem/elixir_euler_source_terms_amr_refine_coarsen.jl @@ -10,60 +10,57 @@ module TrixiExtensionEulerAMR using Trixi -struct IndicatorRefineCoarsen{Cache<:NamedTuple} <: Trixi.AbstractIndicator - cache::Cache +struct IndicatorRefineCoarsen{Cache <: NamedTuple} <: Trixi.AbstractIndicator + cache::Cache end function IndicatorRefineCoarsen(semi) - basis = semi.solver.basis - alpha = Vector{real(basis)}() - cache = (; semi.mesh, alpha) + basis = semi.solver.basis + alpha = Vector{real(basis)}() + cache = (; semi.mesh, alpha) - return IndicatorRefineCoarsen{typeof(cache)}(cache) + return IndicatorRefineCoarsen{typeof(cache)}(cache) end -function (indicator::IndicatorRefineCoarsen)(u::AbstractArray{<:Any,4}, +function (indicator::IndicatorRefineCoarsen)(u::AbstractArray{<:Any, 4}, mesh, equations, dg, cache; t, kwargs...) - alpha = indicator.cache.alpha - resize!(alpha, nelements(dg, cache)) - - if t >= 0.7 && t < 1.0 - # Refine to max level - alpha .= 1.0 - elseif t >= 1.0 - # Coarsen to base level - alpha .= -1.0 - else - alpha .= 0.0 - end - - return alpha + alpha = indicator.cache.alpha + resize!(alpha, nelements(dg, cache)) + + if t >= 0.7 && t < 1.0 + # Refine to max level + alpha .= 1.0 + elseif t >= 1.0 + # Coarsen to base level + alpha .= -1.0 + else + alpha .= 0.0 + end + + return alpha end end # module TrixiExtensionEulerAMR import .TrixiExtensionEulerAMR - ############################################################################### # semidiscretization of the compressible Euler equations equations = CompressibleEulerEquations2D(1.4) initial_condition = initial_condition_convergence_test -solver = DGSEM(polydeg=3, surface_flux=flux_lax_friedrichs) +solver = DGSEM(polydeg = 3, surface_flux = flux_lax_friedrichs) coordinates_min = (0.0, 0.0) coordinates_max = (2.0, 2.0) mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=3, - n_cells_max=10_000) - + initial_refinement_level = 3, + n_cells_max = 10_000) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver, - source_terms=source_terms_convergence_test) - + source_terms = source_terms_convergence_test) ############################################################################### # ODE solvers, callbacks etc. @@ -74,25 +71,26 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=100, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 100, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) -amr_controller = ControllerThreeLevel(semi, TrixiExtensionEulerAMR.IndicatorRefineCoarsen(semi), - base_level=3, max_level=6, - med_threshold=0.1, max_threshold=0.6) +amr_controller = ControllerThreeLevel(semi, + TrixiExtensionEulerAMR.IndicatorRefineCoarsen(semi), + base_level = 3, max_level = 6, + med_threshold = 0.1, max_threshold = 0.6) amr_callback = AMRCallback(semi, amr_controller, - interval=5, - adapt_initial_condition=true, - adapt_initial_condition_only_refine=true) + interval = 5, + adapt_initial_condition = true, + adapt_initial_condition_only_refine = true) -stepsize_callback = StepsizeCallback(cfl=1.0) +stepsize_callback = StepsizeCallback(cfl = 1.0) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, @@ -102,7 +100,7 @@ callbacks = CallbackSet(summary_callback, ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/tree_2d_dgsem/elixir_euler_source_terms_nonperiodic.jl b/examples/tree_2d_dgsem/elixir_euler_source_terms_nonperiodic.jl index 9826a53d3d5..05ed7ba78cc 100644 --- a/examples/tree_2d_dgsem/elixir_euler_source_terms_nonperiodic.jl +++ b/examples/tree_2d_dgsem/elixir_euler_source_terms_nonperiodic.jl @@ -12,26 +12,23 @@ initial_condition = initial_condition_convergence_test # you can either use a single function to impose the BCs weakly in all # 2*ndims == 4 directions or you can pass a tuple containing BCs for each direction boundary_condition = BoundaryConditionDirichlet(initial_condition) -boundary_conditions = (x_neg=boundary_condition, - x_pos=boundary_condition, - y_neg=boundary_condition, - y_pos=boundary_condition,) - -solver = DGSEM(polydeg=3, surface_flux=flux_lax_friedrichs) +boundary_conditions = (x_neg = boundary_condition, + x_pos = boundary_condition, + y_neg = boundary_condition, + y_pos = boundary_condition) +solver = DGSEM(polydeg = 3, surface_flux = flux_lax_friedrichs) coordinates_min = (0.0, 0.0) coordinates_max = (2.0, 2.0) mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=4, - n_cells_max=10_000, - periodicity=false) - + initial_refinement_level = 4, + n_cells_max = 10_000, + periodicity = false) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver, - source_terms=source_terms_convergence_test, - boundary_conditions=boundary_conditions) - + source_terms = source_terms_convergence_test, + boundary_conditions = boundary_conditions) ############################################################################### # ODE solvers, callbacks etc. @@ -42,19 +39,19 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_restart = SaveRestartCallback(interval=100, - save_final_restart=true) +save_restart = SaveRestartCallback(interval = 100, + save_final_restart = true) -save_solution = SaveSolutionCallback(interval=100, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 100, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) -stepsize_callback = StepsizeCallback(cfl=1.0) +stepsize_callback = StepsizeCallback(cfl = 1.0) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, @@ -63,7 +60,7 @@ callbacks = CallbackSet(summary_callback, ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/tree_2d_dgsem/elixir_euler_source_terms_sc_subcell.jl b/examples/tree_2d_dgsem/elixir_euler_source_terms_sc_subcell.jl index 5c92414e66a..6d5281fcbc0 100644 --- a/examples/tree_2d_dgsem/elixir_euler_source_terms_sc_subcell.jl +++ b/examples/tree_2d_dgsem/elixir_euler_source_terms_sc_subcell.jl @@ -14,25 +14,24 @@ volume_flux = flux_ranocha polydeg = 3 basis = LobattoLegendreBasis(polydeg) limiter_idp = SubcellLimiterIDP(equations, basis; - local_minmax_variables_cons=[1], - positivity_variables_cons=[1], - positivity_variables_nonlinear=(pressure,), - bar_states=true, - smoothness_indicator=true) + local_minmax_variables_cons = [1], + positivity_variables_cons = [1], + positivity_variables_nonlinear = (pressure,), + bar_states = true, + smoothness_indicator = true) volume_integral = VolumeIntegralSubcellLimiting(limiter_idp; - volume_flux_dg=volume_flux, - volume_flux_fv=surface_flux) + volume_flux_dg = volume_flux, + volume_flux_fv = surface_flux) solver = DGSEM(basis, surface_flux, volume_integral) coordinates_min = (0.0, 0.0) coordinates_max = (2.0, 2.0) mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=4, - n_cells_max=10_000) + initial_refinement_level = 4, + n_cells_max = 10_000) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver, - source_terms=source_terms_convergence_test) - + source_terms = source_terms_convergence_test) ############################################################################### # ODE solvers, callbacks etc. @@ -43,16 +42,16 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=100, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 100, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) -stepsize_callback = StepsizeCallback(cfl=0.6) +stepsize_callback = StepsizeCallback(cfl = 0.6) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, @@ -61,9 +60,9 @@ callbacks = CallbackSet(summary_callback, ############################################################################### # run the simulation -stage_callbacks = (SubcellLimiterIDPCorrection(), BoundsCheckCallback(save_errors=false)) +stage_callbacks = (SubcellLimiterIDPCorrection(), BoundsCheckCallback(save_errors = false)) -sol = Trixi.solve(ode, Trixi.SimpleSSPRK33(stage_callbacks=stage_callbacks); - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = Trixi.solve(ode, Trixi.SimpleSSPRK33(stage_callbacks = stage_callbacks); + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/tree_2d_dgsem/elixir_euler_vortex.jl b/examples/tree_2d_dgsem/elixir_euler_vortex.jl index 14e46ce7540..c87d6f49ba8 100644 --- a/examples/tree_2d_dgsem/elixir_euler_vortex.jl +++ b/examples/tree_2d_dgsem/elixir_euler_vortex.jl @@ -17,46 +17,45 @@ The classical isentropic vortex test case of [NASA/CR-97-206253](https://ntrs.nasa.gov/citations/19980007543) """ function initial_condition_isentropic_vortex(x, t, equations::CompressibleEulerEquations2D) - # needs appropriate mesh size, e.g. [-10,-10]x[10,10] - # for error convergence: make sure that the end time is such that the vortex is back at the initial state!! - # for the current velocity and domain size: t_end should be a multiple of 20s - # initial center of the vortex - inicenter = SVector(0.0, 0.0) - # size and strength of the vortex - iniamplitude = 5.0 - # base flow - rho = 1.0 - v1 = 1.0 - v2 = 1.0 - vel = SVector(v1, v2) - p = 25.0 - rt = p / rho # ideal gas equation - t_loc = 0.0 - cent = inicenter + vel*t_loc # advection of center - # ATTENTION: handle periodic BC, but only for v1 = v2 = 1.0 (!!!!) - cent = x - cent # distance to center point - # cent = cross(iniaxis, cent) # distance to axis, tangent vector, length r - # cross product with iniaxis = [0, 0, 1] - cent = SVector(-cent[2], cent[1]) - r2 = cent[1]^2 + cent[2]^2 - du = iniamplitude / (2*π) * exp(0.5 * (1 - r2)) # vel. perturbation - dtemp = -(equations.gamma - 1) / (2 * equations.gamma * rt) * du^2 # isentropic - rho = rho * (1 + dtemp)^(1 / (equations.gamma - 1)) - vel = vel + du * cent - v1, v2 = vel - p = p * (1 + dtemp)^(equations.gamma / (equations.gamma - 1)) - prim = SVector(rho, v1, v2, p) - return prim2cons(prim, equations) + # needs appropriate mesh size, e.g. [-10,-10]x[10,10] + # for error convergence: make sure that the end time is such that the vortex is back at the initial state!! + # for the current velocity and domain size: t_end should be a multiple of 20s + # initial center of the vortex + inicenter = SVector(0.0, 0.0) + # size and strength of the vortex + iniamplitude = 5.0 + # base flow + rho = 1.0 + v1 = 1.0 + v2 = 1.0 + vel = SVector(v1, v2) + p = 25.0 + rt = p / rho # ideal gas equation + t_loc = 0.0 + cent = inicenter + vel * t_loc # advection of center + # ATTENTION: handle periodic BC, but only for v1 = v2 = 1.0 (!!!!) + cent = x - cent # distance to center point + # cent = cross(iniaxis, cent) # distance to axis, tangent vector, length r + # cross product with iniaxis = [0, 0, 1] + cent = SVector(-cent[2], cent[1]) + r2 = cent[1]^2 + cent[2]^2 + du = iniamplitude / (2 * π) * exp(0.5 * (1 - r2)) # vel. perturbation + dtemp = -(equations.gamma - 1) / (2 * equations.gamma * rt) * du^2 # isentropic + rho = rho * (1 + dtemp)^(1 / (equations.gamma - 1)) + vel = vel + du * cent + v1, v2 = vel + p = p * (1 + dtemp)^(equations.gamma / (equations.gamma - 1)) + prim = SVector(rho, v1, v2, p) + return prim2cons(prim, equations) end initial_condition = initial_condition_isentropic_vortex -solver = DGSEM(polydeg=3, surface_flux=flux_lax_friedrichs) +solver = DGSEM(polydeg = 3, surface_flux = flux_lax_friedrichs) coordinates_min = (-10.0, -10.0) -coordinates_max = ( 10.0, 10.0) +coordinates_max = (10.0, 10.0) mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=4, - n_cells_max=10_000) - + initial_refinement_level = 4, + n_cells_max = 10_000) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver) @@ -69,30 +68,31 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval, save_analysis=true, - extra_analysis_errors=(:conservation_error,), - extra_analysis_integrals=(entropy, energy_total, - energy_kinetic, energy_internal)) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval, + save_analysis = true, + extra_analysis_errors = (:conservation_error,), + extra_analysis_integrals = (entropy, energy_total, + energy_kinetic, + energy_internal)) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=100, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 100, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) -stepsize_callback = StepsizeCallback(cfl=1.1) +stepsize_callback = StepsizeCallback(cfl = 1.1) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, save_solution, stepsize_callback) - ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/tree_2d_dgsem/elixir_euler_vortex_amr.jl b/examples/tree_2d_dgsem/elixir_euler_vortex_amr.jl index 6f6eb25efa4..e9831c95526 100644 --- a/examples/tree_2d_dgsem/elixir_euler_vortex_amr.jl +++ b/examples/tree_2d_dgsem/elixir_euler_vortex_amr.jl @@ -7,55 +7,54 @@ module TrixiExtension using Trixi -struct IndicatorVortex{Cache<:NamedTuple} <: Trixi.AbstractIndicator - cache::Cache +struct IndicatorVortex{Cache <: NamedTuple} <: Trixi.AbstractIndicator + cache::Cache end function IndicatorVortex(semi) - basis = semi.solver.basis - alpha = Vector{real(basis)}() - A = Array{real(basis), 2} - indicator_threaded = [A(undef, nnodes(basis), nnodes(basis)) - for _ in 1:Threads.nthreads()] - cache = (; semi.mesh, alpha, indicator_threaded) - - return IndicatorVortex{typeof(cache)}(cache) + basis = semi.solver.basis + alpha = Vector{real(basis)}() + A = Array{real(basis), 2} + indicator_threaded = [A(undef, nnodes(basis), nnodes(basis)) + for _ in 1:Threads.nthreads()] + cache = (; semi.mesh, alpha, indicator_threaded) + + return IndicatorVortex{typeof(cache)}(cache) end -function (indicator_vortex::IndicatorVortex)(u::AbstractArray{<:Any,4}, +function (indicator_vortex::IndicatorVortex)(u::AbstractArray{<:Any, 4}, mesh, equations, dg, cache; t, kwargs...) - mesh = indicator_vortex.cache.mesh - alpha = indicator_vortex.cache.alpha - indicator_threaded = indicator_vortex.cache.indicator_threaded - resize!(alpha, nelements(dg, cache)) - - - # get analytical vortex center (based on assumption that center=[0.0,0.0] - # at t=0.0 and that we stop after one period) - domain_length = mesh.tree.length_level_0 - if t < 0.5 * domain_length - center = (t, t) - else - center = (t-domain_length, t-domain_length) - end - - Threads.@threads for element in eachelement(dg, cache) - cell_id = cache.elements.cell_ids[element] - coordinates = (mesh.tree.coordinates[1, cell_id], mesh.tree.coordinates[2, cell_id]) - # use the negative radius as indicator since the AMR controller increases - # the level with increasing value of the indicator and we want to use - # high levels near the vortex center - alpha[element] = -periodic_distance_2d(coordinates, center, domain_length) - end - - return alpha + mesh = indicator_vortex.cache.mesh + alpha = indicator_vortex.cache.alpha + indicator_threaded = indicator_vortex.cache.indicator_threaded + resize!(alpha, nelements(dg, cache)) + + # get analytical vortex center (based on assumption that center=[0.0,0.0] + # at t=0.0 and that we stop after one period) + domain_length = mesh.tree.length_level_0 + if t < 0.5 * domain_length + center = (t, t) + else + center = (t - domain_length, t - domain_length) + end + + Threads.@threads for element in eachelement(dg, cache) + cell_id = cache.elements.cell_ids[element] + coordinates = (mesh.tree.coordinates[1, cell_id], mesh.tree.coordinates[2, cell_id]) + # use the negative radius as indicator since the AMR controller increases + # the level with increasing value of the indicator and we want to use + # high levels near the vortex center + alpha[element] = -periodic_distance_2d(coordinates, center, domain_length) + end + + return alpha end function periodic_distance_2d(coordinates, center, domain_length) - dx = @. abs(coordinates - center) - dx_periodic = @. min(dx, domain_length - dx) - return sqrt(sum(abs2, dx_periodic)) + dx = @. abs(coordinates - center) + dx_periodic = @. min(dx, domain_length - dx) + return sqrt(sum(abs2, dx_periodic)) end end # module TrixiExtension @@ -77,48 +76,47 @@ The classical isentropic vortex test case of [NASA/CR-97-206253](https://ntrs.nasa.gov/citations/19980007543) """ function initial_condition_isentropic_vortex(x, t, equations::CompressibleEulerEquations2D) - # needs appropriate mesh size, e.g. [-10,-10]x[10,10] - # for error convergence: make sure that the end time is such that the vortex is back at the initial state!! - # for the current velocity and domain size: t_end should be a multiple of 20s - # initial center of the vortex - inicenter = SVector(0.0, 0.0) - # size and strength of the vortex - iniamplitude = 5.0 - # base flow - rho = 1.0 - v1 = 1.0 - v2 = 1.0 - vel = SVector(v1, v2) - p = 25.0 - rt = p / rho # ideal gas equation - t_loc = 0.0 - cent = inicenter + vel*t_loc # advection of center - # ATTENTION: handle periodic BC, but only for v1 = v2 = 1.0 (!!!!) - - cent = x - cent # distance to center point - - # cent = cross(iniaxis, cent) # distance to axis, tangent vector, length r - # cross product with iniaxis = [0, 0, 1] - cent = SVector(-cent[2], cent[1]) - r2 = cent[1]^2 + cent[2]^2 - du = iniamplitude / (2*π) * exp(0.5 * (1 - r2)) # vel. perturbation - dtemp = -(equations.gamma - 1) / (2 * equations.gamma * rt) * du^2 # isentropic - rho = rho * (1 + dtemp)^(1 / (equations.gamma - 1)) - vel = vel + du * cent - v1, v2 = vel - p = p * (1 + dtemp)^(equations.gamma / (equations.gamma - 1)) - prim = SVector(rho, v1, v2, p) - return prim2cons(prim, equations) + # needs appropriate mesh size, e.g. [-10,-10]x[10,10] + # for error convergence: make sure that the end time is such that the vortex is back at the initial state!! + # for the current velocity and domain size: t_end should be a multiple of 20s + # initial center of the vortex + inicenter = SVector(0.0, 0.0) + # size and strength of the vortex + iniamplitude = 5.0 + # base flow + rho = 1.0 + v1 = 1.0 + v2 = 1.0 + vel = SVector(v1, v2) + p = 25.0 + rt = p / rho # ideal gas equation + t_loc = 0.0 + cent = inicenter + vel * t_loc # advection of center + # ATTENTION: handle periodic BC, but only for v1 = v2 = 1.0 (!!!!) + + cent = x - cent # distance to center point + + # cent = cross(iniaxis, cent) # distance to axis, tangent vector, length r + # cross product with iniaxis = [0, 0, 1] + cent = SVector(-cent[2], cent[1]) + r2 = cent[1]^2 + cent[2]^2 + du = iniamplitude / (2 * π) * exp(0.5 * (1 - r2)) # vel. perturbation + dtemp = -(equations.gamma - 1) / (2 * equations.gamma * rt) * du^2 # isentropic + rho = rho * (1 + dtemp)^(1 / (equations.gamma - 1)) + vel = vel + du * cent + v1, v2 = vel + p = p * (1 + dtemp)^(equations.gamma / (equations.gamma - 1)) + prim = SVector(rho, v1, v2, p) + return prim2cons(prim, equations) end initial_condition = initial_condition_isentropic_vortex -solver = DGSEM(polydeg=3, surface_flux=flux_lax_friedrichs) +solver = DGSEM(polydeg = 3, surface_flux = flux_lax_friedrichs) coordinates_min = (-10.0, -10.0) -coordinates_max = ( 10.0, 10.0) +coordinates_max = (10.0, 10.0) mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=3, - n_cells_max=10_000) - + initial_refinement_level = 3, + n_cells_max = 10_000) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver) @@ -132,39 +130,40 @@ summary_callback = SummaryCallback() analysis_interval = 200 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval, save_analysis=true, - extra_analysis_errors=(:conservation_error,), - extra_analysis_integrals=(entropy, energy_total, - energy_kinetic, energy_internal)) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval, + save_analysis = true, + extra_analysis_errors = (:conservation_error,), + extra_analysis_integrals = (entropy, energy_total, + energy_kinetic, + energy_internal)) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=50, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 50, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) amr_controller = ControllerThreeLevel(semi, TrixiExtension.IndicatorVortex(semi), - base_level=3, - med_level=4, med_threshold=-3.0, - max_level=5, max_threshold=-2.0) + base_level = 3, + med_level = 4, med_threshold = -3.0, + max_level = 5, max_threshold = -2.0) amr_callback = AMRCallback(semi, amr_controller, - interval=5, - adapt_initial_condition=true, - adapt_initial_condition_only_refine=true) + interval = 5, + adapt_initial_condition = true, + adapt_initial_condition_only_refine = true) -stepsize_callback = StepsizeCallback(cfl=1.1) +stepsize_callback = StepsizeCallback(cfl = 1.1) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, save_solution, amr_callback, stepsize_callback) - ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/tree_2d_dgsem/elixir_euler_vortex_mortar.jl b/examples/tree_2d_dgsem/elixir_euler_vortex_mortar.jl index 637133b9b2f..858799d2d3d 100644 --- a/examples/tree_2d_dgsem/elixir_euler_vortex_mortar.jl +++ b/examples/tree_2d_dgsem/elixir_euler_vortex_mortar.jl @@ -17,49 +17,48 @@ The classical isentropic vortex test case of [NASA/CR-97-206253](https://ntrs.nasa.gov/citations/19980007543) """ function initial_condition_isentropic_vortex(x, t, equations::CompressibleEulerEquations2D) - # needs appropriate mesh size, e.g. [-10,-10]x[10,10] - # for error convergence: make sure that the end time is such that the vortex is back at the initial state!! - # for the current velocity and domain size: t_end should be a multiple of 20s - # initial center of the vortex - inicenter = SVector(0.0, 0.0) - # size and strength of the vortex - iniamplitude = 5.0 - # base flow - rho = 1.0 - v1 = 1.0 - v2 = 1.0 - vel = SVector(v1, v2) - p = 25.0 - rt = p / rho # ideal gas equation - t_loc = 0.0 - cent = inicenter + vel*t_loc # advection of center - # ATTENTION: handle periodic BC, but only for v1 = v2 = 1.0 (!!!!) - cent = x - cent # distance to center point - # cent = cross(iniaxis, cent) # distance to axis, tangent vector, length r - # cross product with iniaxis = [0, 0, 1] - cent = SVector(-cent[2], cent[1]) - r2 = cent[1]^2 + cent[2]^2 - du = iniamplitude / (2*π) * exp(0.5 * (1 - r2)) # vel. perturbation - dtemp = -(equations.gamma - 1) / (2 * equations.gamma * rt) * du^2 # isentropic - rho = rho * (1 + dtemp)^(1 / (equations.gamma - 1)) - vel = vel + du * cent - v1, v2 = vel - p = p * (1 + dtemp)^(equations.gamma / (equations.gamma - 1)) - prim = SVector(rho, v1, v2, p) - return prim2cons(prim, equations) + # needs appropriate mesh size, e.g. [-10,-10]x[10,10] + # for error convergence: make sure that the end time is such that the vortex is back at the initial state!! + # for the current velocity and domain size: t_end should be a multiple of 20s + # initial center of the vortex + inicenter = SVector(0.0, 0.0) + # size and strength of the vortex + iniamplitude = 5.0 + # base flow + rho = 1.0 + v1 = 1.0 + v2 = 1.0 + vel = SVector(v1, v2) + p = 25.0 + rt = p / rho # ideal gas equation + t_loc = 0.0 + cent = inicenter + vel * t_loc # advection of center + # ATTENTION: handle periodic BC, but only for v1 = v2 = 1.0 (!!!!) + cent = x - cent # distance to center point + # cent = cross(iniaxis, cent) # distance to axis, tangent vector, length r + # cross product with iniaxis = [0, 0, 1] + cent = SVector(-cent[2], cent[1]) + r2 = cent[1]^2 + cent[2]^2 + du = iniamplitude / (2 * π) * exp(0.5 * (1 - r2)) # vel. perturbation + dtemp = -(equations.gamma - 1) / (2 * equations.gamma * rt) * du^2 # isentropic + rho = rho * (1 + dtemp)^(1 / (equations.gamma - 1)) + vel = vel + du * cent + v1, v2 = vel + p = p * (1 + dtemp)^(equations.gamma / (equations.gamma - 1)) + prim = SVector(rho, v1, v2, p) + return prim2cons(prim, equations) end initial_condition = initial_condition_isentropic_vortex -solver = DGSEM(polydeg=3, surface_flux=flux_lax_friedrichs) +solver = DGSEM(polydeg = 3, surface_flux = flux_lax_friedrichs) coordinates_min = (-10.0, -10.0) -coordinates_max = ( 10.0, 10.0) -refinement_patches = ( - (type="box", coordinates_min=(0.0, -10.0), coordinates_max=(10.0, 10.0)), -) +coordinates_max = (10.0, 10.0) +refinement_patches = ((type = "box", coordinates_min = (0.0, -10.0), + coordinates_max = (10.0, 10.0)),) mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=4, - refinement_patches=refinement_patches, - n_cells_max=10_000,) + initial_refinement_level = 4, + refinement_patches = refinement_patches, + n_cells_max = 10_000) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver) @@ -72,30 +71,31 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval, save_analysis=true, - extra_analysis_errors=(:conservation_error,), - extra_analysis_integrals=(entropy, energy_total, - energy_kinetic, energy_internal)) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval, + save_analysis = true, + extra_analysis_errors = (:conservation_error,), + extra_analysis_integrals = (entropy, energy_total, + energy_kinetic, + energy_internal)) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=100, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 100, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) -stepsize_callback = StepsizeCallback(cfl=1.4) +stepsize_callback = StepsizeCallback(cfl = 1.4) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, save_solution, stepsize_callback) - ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/tree_2d_dgsem/elixir_euler_vortex_mortar_shockcapturing.jl b/examples/tree_2d_dgsem/elixir_euler_vortex_mortar_shockcapturing.jl index dc6a326c5d5..026f6d1462c 100644 --- a/examples/tree_2d_dgsem/elixir_euler_vortex_mortar_shockcapturing.jl +++ b/examples/tree_2d_dgsem/elixir_euler_vortex_mortar_shockcapturing.jl @@ -17,36 +17,36 @@ The classical isentropic vortex test case of [NASA/CR-97-206253](https://ntrs.nasa.gov/citations/19980007543) """ function initial_condition_isentropic_vortex(x, t, equations::CompressibleEulerEquations2D) - # needs appropriate mesh size, e.g. [-10,-10]x[10,10] - # for error convergence: make sure that the end time is such that the vortex is back at the initial state!! - # for the current velocity and domain size: t_end should be a multiple of 20s - # initial center of the vortex - inicenter = SVector(0.0, 0.0) - # size and strength of the vortex - iniamplitude = 5.0 - # base flow - rho = 1.0 - v1 = 1.0 - v2 = 1.0 - vel = SVector(v1, v2) - p = 25.0 - rt = p / rho # ideal gas equation - t_loc = 0.0 - cent = inicenter + vel*t_loc # advection of center - # ATTENTION: handle periodic BC, but only for v1 = v2 = 1.0 (!!!!) - cent = x - cent # distance to center point - # cent = cross(iniaxis, cent) # distance to axis, tangent vector, length r - # cross product with iniaxis = [0, 0, 1] - cent = SVector(-cent[2], cent[1]) - r2 = cent[1]^2 + cent[2]^2 - du = iniamplitude / (2*π) * exp(0.5 * (1 - r2)) # vel. perturbation - dtemp = -(equations.gamma - 1) / (2 * equations.gamma * rt) * du^2 # isentropic - rho = rho * (1 + dtemp)^(1 / (equations.gamma - 1)) - vel = vel + du * cent - v1, v2 = vel - p = p * (1 + dtemp)^(equations.gamma / (equations.gamma - 1)) - prim = SVector(rho, v1, v2, p) - return prim2cons(prim, equations) + # needs appropriate mesh size, e.g. [-10,-10]x[10,10] + # for error convergence: make sure that the end time is such that the vortex is back at the initial state!! + # for the current velocity and domain size: t_end should be a multiple of 20s + # initial center of the vortex + inicenter = SVector(0.0, 0.0) + # size and strength of the vortex + iniamplitude = 5.0 + # base flow + rho = 1.0 + v1 = 1.0 + v2 = 1.0 + vel = SVector(v1, v2) + p = 25.0 + rt = p / rho # ideal gas equation + t_loc = 0.0 + cent = inicenter + vel * t_loc # advection of center + # ATTENTION: handle periodic BC, but only for v1 = v2 = 1.0 (!!!!) + cent = x - cent # distance to center point + # cent = cross(iniaxis, cent) # distance to axis, tangent vector, length r + # cross product with iniaxis = [0, 0, 1] + cent = SVector(-cent[2], cent[1]) + r2 = cent[1]^2 + cent[2]^2 + du = iniamplitude / (2 * π) * exp(0.5 * (1 - r2)) # vel. perturbation + dtemp = -(equations.gamma - 1) / (2 * equations.gamma * rt) * du^2 # isentropic + rho = rho * (1 + dtemp)^(1 / (equations.gamma - 1)) + vel = vel + du * cent + v1, v2 = vel + p = p * (1 + dtemp)^(equations.gamma / (equations.gamma - 1)) + prim = SVector(rho, v1, v2, p) + return prim2cons(prim, equations) end initial_condition = initial_condition_isentropic_vortex @@ -56,24 +56,23 @@ volume_flux = flux_shima_etal polydeg = 3 basis = LobattoLegendreBasis(polydeg) indicator_sc = IndicatorHennemannGassner(equations, basis, - alpha_max=0.5, - alpha_min=0.001, - alpha_smooth=true, - variable=density_pressure) + alpha_max = 0.5, + alpha_min = 0.001, + alpha_smooth = true, + variable = density_pressure) volume_integral = VolumeIntegralShockCapturingHG(indicator_sc; - volume_flux_dg=volume_flux, - volume_flux_fv=surface_flux) + volume_flux_dg = volume_flux, + volume_flux_fv = surface_flux) solver = DGSEM(basis, surface_flux, volume_integral) coordinates_min = (-10.0, -10.0) -coordinates_max = ( 10.0, 10.0) -refinement_patches = ( - (type="box", coordinates_min=(0.0, -10.0), coordinates_max=(10.0, 10.0)), -) +coordinates_max = (10.0, 10.0) +refinement_patches = ((type = "box", coordinates_min = (0.0, -10.0), + coordinates_max = (10.0, 10.0)),) mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=4, - refinement_patches=refinement_patches, - n_cells_max=10_000,) + initial_refinement_level = 4, + refinement_patches = refinement_patches, + n_cells_max = 10_000) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver) @@ -86,30 +85,31 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval, save_analysis=true, - extra_analysis_errors=(:conservation_error,), - extra_analysis_integrals=(entropy, energy_total, - energy_kinetic, energy_internal)) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval, + save_analysis = true, + extra_analysis_errors = (:conservation_error,), + extra_analysis_integrals = (entropy, energy_total, + energy_kinetic, + energy_internal)) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=100, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 100, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) -stepsize_callback = StepsizeCallback(cfl=0.7) +stepsize_callback = StepsizeCallback(cfl = 0.7) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, save_solution, stepsize_callback) - ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/tree_2d_dgsem/elixir_euler_vortex_mortar_split.jl b/examples/tree_2d_dgsem/elixir_euler_vortex_mortar_split.jl index 99036c36451..d719e01fd7c 100644 --- a/examples/tree_2d_dgsem/elixir_euler_vortex_mortar_split.jl +++ b/examples/tree_2d_dgsem/elixir_euler_vortex_mortar_split.jl @@ -17,52 +17,51 @@ The classical isentropic vortex test case of [NASA/CR-97-206253](https://ntrs.nasa.gov/citations/19980007543) """ function initial_condition_isentropic_vortex(x, t, equations::CompressibleEulerEquations2D) - # needs appropriate mesh size, e.g. [-10,-10]x[10,10] - # for error convergence: make sure that the end time is such that the vortex is back at the initial state!! - # for the current velocity and domain size: t_end should be a multiple of 20s - # initial center of the vortex - inicenter = SVector(0.0, 0.0) - # size and strength of the vortex - iniamplitude = 5.0 - # base flow - rho = 1.0 - v1 = 1.0 - v2 = 1.0 - vel = SVector(v1, v2) - p = 25.0 - rt = p / rho # ideal gas equation - t_loc = 0.0 - cent = inicenter + vel*t_loc # advection of center - # ATTENTION: handle periodic BC, but only for v1 = v2 = 1.0 (!!!!) - cent = x - cent # distance to center point - # cent = cross(iniaxis, cent) # distance to axis, tangent vector, length r - # cross product with iniaxis = [0, 0, 1] - cent = SVector(-cent[2], cent[1]) - r2 = cent[1]^2 + cent[2]^2 - du = iniamplitude / (2*π) * exp(0.5 * (1 - r2)) # vel. perturbation - dtemp = -(equations.gamma - 1) / (2 * equations.gamma * rt) * du^2 # isentropic - rho = rho * (1 + dtemp)^(1 / (equations.gamma - 1)) - vel = vel + du * cent - v1, v2 = vel - p = p * (1 + dtemp)^(equations.gamma / (equations.gamma - 1)) - prim = SVector(rho, v1, v2, p) - return prim2cons(prim, equations) + # needs appropriate mesh size, e.g. [-10,-10]x[10,10] + # for error convergence: make sure that the end time is such that the vortex is back at the initial state!! + # for the current velocity and domain size: t_end should be a multiple of 20s + # initial center of the vortex + inicenter = SVector(0.0, 0.0) + # size and strength of the vortex + iniamplitude = 5.0 + # base flow + rho = 1.0 + v1 = 1.0 + v2 = 1.0 + vel = SVector(v1, v2) + p = 25.0 + rt = p / rho # ideal gas equation + t_loc = 0.0 + cent = inicenter + vel * t_loc # advection of center + # ATTENTION: handle periodic BC, but only for v1 = v2 = 1.0 (!!!!) + cent = x - cent # distance to center point + # cent = cross(iniaxis, cent) # distance to axis, tangent vector, length r + # cross product with iniaxis = [0, 0, 1] + cent = SVector(-cent[2], cent[1]) + r2 = cent[1]^2 + cent[2]^2 + du = iniamplitude / (2 * π) * exp(0.5 * (1 - r2)) # vel. perturbation + dtemp = -(equations.gamma - 1) / (2 * equations.gamma * rt) * du^2 # isentropic + rho = rho * (1 + dtemp)^(1 / (equations.gamma - 1)) + vel = vel + du * cent + v1, v2 = vel + p = p * (1 + dtemp)^(equations.gamma / (equations.gamma - 1)) + prim = SVector(rho, v1, v2, p) + return prim2cons(prim, equations) end initial_condition = initial_condition_isentropic_vortex volume_flux = flux_shima_etal -solver = DGSEM(polydeg=3, surface_flux=flux_lax_friedrichs, - volume_integral=VolumeIntegralFluxDifferencing(volume_flux)) +solver = DGSEM(polydeg = 3, surface_flux = flux_lax_friedrichs, + volume_integral = VolumeIntegralFluxDifferencing(volume_flux)) coordinates_min = (-10.0, -10.0) -coordinates_max = ( 10.0, 10.0) -refinement_patches = ( - (type="box", coordinates_min=(0.0, -10.0), coordinates_max=(10.0, 10.0)), -) +coordinates_max = (10.0, 10.0) +refinement_patches = ((type = "box", coordinates_min = (0.0, -10.0), + coordinates_max = (10.0, 10.0)),) mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=4, - refinement_patches=refinement_patches, - n_cells_max=10_000,) + initial_refinement_level = 4, + refinement_patches = refinement_patches, + n_cells_max = 10_000) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver) @@ -75,30 +74,31 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval, save_analysis=true, - extra_analysis_errors=(:conservation_error,), - extra_analysis_integrals=(entropy, energy_total, - energy_kinetic, energy_internal)) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval, + save_analysis = true, + extra_analysis_errors = (:conservation_error,), + extra_analysis_integrals = (entropy, energy_total, + energy_kinetic, + energy_internal)) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=100, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 100, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) -stepsize_callback = StepsizeCallback(cfl=1.4) +stepsize_callback = StepsizeCallback(cfl = 1.4) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, save_solution, stepsize_callback) - ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/tree_2d_dgsem/elixir_euler_vortex_shockcapturing.jl b/examples/tree_2d_dgsem/elixir_euler_vortex_shockcapturing.jl index 65a497374ed..99e4b090633 100644 --- a/examples/tree_2d_dgsem/elixir_euler_vortex_shockcapturing.jl +++ b/examples/tree_2d_dgsem/elixir_euler_vortex_shockcapturing.jl @@ -17,36 +17,36 @@ The classical isentropic vortex test case of [NASA/CR-97-206253](https://ntrs.nasa.gov/citations/19980007543) """ function initial_condition_isentropic_vortex(x, t, equations::CompressibleEulerEquations2D) - # needs appropriate mesh size, e.g. [-10,-10]x[10,10] - # for error convergence: make sure that the end time is such that the vortex is back at the initial state!! - # for the current velocity and domain size: t_end should be a multiple of 20s - # initial center of the vortex - inicenter = SVector(0.0, 0.0) - # size and strength of the vortex - iniamplitude = 5.0 - # base flow - rho = 1.0 - v1 = 1.0 - v2 = 1.0 - vel = SVector(v1, v2) - p = 25.0 - rt = p / rho # ideal gas equation - t_loc = 0.0 - cent = inicenter + vel*t_loc # advection of center - # ATTENTION: handle periodic BC, but only for v1 = v2 = 1.0 (!!!!) - cent = x - cent # distance to center point - # cent = cross(iniaxis, cent) # distance to axis, tangent vector, length r - # cross product with iniaxis = [0, 0, 1] - cent = SVector(-cent[2], cent[1]) - r2 = cent[1]^2 + cent[2]^2 - du = iniamplitude / (2*π) * exp(0.5 * (1 - r2)) # vel. perturbation - dtemp = -(equations.gamma - 1) / (2 * equations.gamma * rt) * du^2 # isentropic - rho = rho * (1 + dtemp)^(1 / (equations.gamma - 1)) - vel = vel + du * cent - v1, v2 = vel - p = p * (1 + dtemp)^(equations.gamma / (equations.gamma - 1)) - prim = SVector(rho, v1, v2, p) - return prim2cons(prim, equations) + # needs appropriate mesh size, e.g. [-10,-10]x[10,10] + # for error convergence: make sure that the end time is such that the vortex is back at the initial state!! + # for the current velocity and domain size: t_end should be a multiple of 20s + # initial center of the vortex + inicenter = SVector(0.0, 0.0) + # size and strength of the vortex + iniamplitude = 5.0 + # base flow + rho = 1.0 + v1 = 1.0 + v2 = 1.0 + vel = SVector(v1, v2) + p = 25.0 + rt = p / rho # ideal gas equation + t_loc = 0.0 + cent = inicenter + vel * t_loc # advection of center + # ATTENTION: handle periodic BC, but only for v1 = v2 = 1.0 (!!!!) + cent = x - cent # distance to center point + # cent = cross(iniaxis, cent) # distance to axis, tangent vector, length r + # cross product with iniaxis = [0, 0, 1] + cent = SVector(-cent[2], cent[1]) + r2 = cent[1]^2 + cent[2]^2 + du = iniamplitude / (2 * π) * exp(0.5 * (1 - r2)) # vel. perturbation + dtemp = -(equations.gamma - 1) / (2 * equations.gamma * rt) * du^2 # isentropic + rho = rho * (1 + dtemp)^(1 / (equations.gamma - 1)) + vel = vel + du * cent + v1, v2 = vel + p = p * (1 + dtemp)^(equations.gamma / (equations.gamma - 1)) + prim = SVector(rho, v1, v2, p) + return prim2cons(prim, equations) end initial_condition = initial_condition_isentropic_vortex @@ -56,20 +56,20 @@ volume_flux = flux_shima_etal polydeg = 3 basis = LobattoLegendreBasis(polydeg) indicator_sc = IndicatorHennemannGassner(equations, basis, - alpha_max=0.5, - alpha_min=0.001, - alpha_smooth=true, - variable=density_pressure) + alpha_max = 0.5, + alpha_min = 0.001, + alpha_smooth = true, + variable = density_pressure) volume_integral = VolumeIntegralShockCapturingHG(indicator_sc; - volume_flux_dg=volume_flux, - volume_flux_fv=surface_flux) + volume_flux_dg = volume_flux, + volume_flux_fv = surface_flux) solver = DGSEM(basis, surface_flux, volume_integral) coordinates_min = (-10.0, -10.0) -coordinates_max = ( 10.0, 10.0) +coordinates_max = (10.0, 10.0) mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=4, - n_cells_max=10_000,) + initial_refinement_level = 4, + n_cells_max = 10_000) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver) @@ -82,22 +82,24 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval, save_analysis=true, - extra_analysis_errors=(:conservation_error,), - extra_analysis_integrals=(entropy, energy_total, - energy_kinetic, energy_internal)) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval, + save_analysis = true, + extra_analysis_errors = (:conservation_error,), + extra_analysis_integrals = (entropy, energy_total, + energy_kinetic, + energy_internal)) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_restart = SaveRestartCallback(interval=100, - save_final_restart=true) +save_restart = SaveRestartCallback(interval = 100, + save_final_restart = true) -save_solution = SaveSolutionCallback(interval=100, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 100, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) -stepsize_callback = StepsizeCallback(cfl=0.7) +stepsize_callback = StepsizeCallback(cfl = 0.7) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, @@ -107,7 +109,7 @@ callbacks = CallbackSet(summary_callback, ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/tree_2d_dgsem/elixir_euleracoustics_co-rotating_vortex_pair.jl b/examples/tree_2d_dgsem/elixir_euleracoustics_co-rotating_vortex_pair.jl index 38b48b5d537..ea81bd049e4 100644 --- a/examples/tree_2d_dgsem/elixir_euleracoustics_co-rotating_vortex_pair.jl +++ b/examples/tree_2d_dgsem/elixir_euleracoustics_co-rotating_vortex_pair.jl @@ -19,203 +19,199 @@ module VortexPairSetup using LinearAlgebra: norm using Trixi - # Parameters that describe the co-rotating vortex pair -struct VortexPair{RealT<:Real} - r0::RealT # Distance between origin and each vortex center - rc::RealT # Vortex core radius - c0::RealT # Speed of sound - circulation::RealT # Circulation of the vortices - rho0::RealT # Density +struct VortexPair{RealT <: Real} + r0::RealT # Distance between origin and each vortex center + rc::RealT # Vortex core radius + c0::RealT # Speed of sound + circulation::RealT # Circulation of the vortices + rho0::RealT # Density end - # Analytical flow solution, used for the initial condition of the flow simulation function velocity(x, t, vortex_pair::VortexPair) - @unpack r0, rc, circulation = vortex_pair + @unpack r0, rc, circulation = vortex_pair - omega = circulation / (4 * pi * r0^2) - si, co = sincos(omega * t) - b = SVector(r0 * co, r0 * si) # vortex centers are b and -b - z_plus = x - b - z_minus = x + b + omega = circulation / (4 * pi * r0^2) + si, co = sincos(omega * t) + b = SVector(r0 * co, r0 * si) # vortex centers are b and -b + z_plus = x - b + z_minus = x + b - # Transform to polar coordinates - r_plus = norm(z_plus) - r_minus = norm(z_minus) - theta_plus = atan(z_plus[2], z_plus[1]) - theta_minus = atan(z_minus[2], z_minus[1]) + # Transform to polar coordinates + r_plus = norm(z_plus) + r_minus = norm(z_minus) + theta_plus = atan(z_plus[2], z_plus[1]) + theta_minus = atan(z_minus[2], z_minus[1]) - si_plus, co_plus = sincos(theta_plus) - si_minus, co_minus = sincos(theta_minus) + si_plus, co_plus = sincos(theta_plus) + si_minus, co_minus = sincos(theta_minus) - v1 = -circulation/(2 * pi) * ( r_plus /(rc^2 + r_plus^2) * si_plus + - r_minus/(rc^2 + r_minus^2) * si_minus) - v2 = circulation/(2 * pi) * ( r_plus /(rc^2 + r_plus^2) * co_plus + - r_minus/(rc^2 + r_minus^2) * co_minus ) + v1 = -circulation / (2 * pi) * (r_plus / (rc^2 + r_plus^2) * si_plus + + r_minus / (rc^2 + r_minus^2) * si_minus) + v2 = circulation / (2 * pi) * (r_plus / (rc^2 + r_plus^2) * co_plus + + r_minus / (rc^2 + r_minus^2) * co_minus) - return SVector(v1, v2) + return SVector(v1, v2) end - # Initial condition of the flow simulation. Uses constant density rho0 and analytical velocities. # The pressure is calculated using the given speed of sound c0 and Bernoulli's principle -struct InitialCondition{RealT<:Real} - vortex_pair::VortexPair{RealT} +struct InitialCondition{RealT <: Real} + vortex_pair::VortexPair{RealT} end -function (initial_condition::InitialCondition)(x, t, equations::CompressibleEulerEquations2D) - @unpack vortex_pair = initial_condition - @unpack rho0, c0 = vortex_pair - gamma = equations.gamma +function (initial_condition::InitialCondition)(x, t, + equations::CompressibleEulerEquations2D) + @unpack vortex_pair = initial_condition + @unpack rho0, c0 = vortex_pair + gamma = equations.gamma - v = velocity(x, t, vortex_pair) - p0 = rho0 * c0^2 / gamma - p = p0 - 0.5 * (gamma-1)/gamma * sum(v.^2) # Bernoulli's principle + v = velocity(x, t, vortex_pair) + p0 = rho0 * c0^2 / gamma + p = p0 - 0.5 * (gamma - 1) / gamma * sum(v .^ 2) # Bernoulli's principle - prim = SVector(rho0, v[1], v[2], p) - return prim2cons(prim, equations) + prim = SVector(rho0, v[1], v[2], p) + return prim2cons(prim, equations) end - # For both the flow and acoustics solvers, a sponge layer is used to dampen the density # and pressure towards the freestream values (for the flow solver) and the perturbed pressure # to zero (for the acoustics solver). -struct SpongeLayer{RealT<:Real, uEltype<:Real, N, SourceTerms} - sponge_layer_min::NTuple{4, RealT} # (-x,+x,-y,+y) min coordinates of sponge layer per direction - sponge_layer_max::NTuple{4, RealT} # (-x,+x,-y,+y) max coordinates of sponge layer per direction - reference_values::NTuple{N, uEltype} # reference values for variables affected by sponge layer - source_terms::SourceTerms # source terms to be used outside the sponge zone +struct SpongeLayer{RealT <: Real, uEltype <: Real, N, SourceTerms} + sponge_layer_min::NTuple{4, RealT} # (-x,+x,-y,+y) min coordinates of sponge layer per direction + sponge_layer_max::NTuple{4, RealT} # (-x,+x,-y,+y) max coordinates of sponge layer per direction + reference_values::NTuple{N, uEltype} # reference values for variables affected by sponge layer + source_terms::SourceTerms # source terms to be used outside the sponge zone end -function SpongeLayer(; sponge_layer_min, sponge_layer_max, reference_values, source_terms=nothing) - return SpongeLayer(sponge_layer_min, sponge_layer_max, reference_values, source_terms) +function SpongeLayer(; sponge_layer_min, sponge_layer_max, reference_values, + source_terms = nothing) + return SpongeLayer(sponge_layer_min, sponge_layer_max, reference_values, source_terms) end function (sponge_layer::SpongeLayer)(u, x, t, equations) - @unpack sponge_layer_min, sponge_layer_max, reference_values, source_terms = sponge_layer - - if lies_in_sponge_layer(x, sponge_layer_min, sponge_layer_max) - return source_term_sponge_layer(u, x, t, equations, sponge_layer_min, sponge_layer_max, - reference_values) - elseif source_terms !== nothing - return source_terms(u, x, t, equations) - else - return SVector(ntuple(v -> zero(eltype(u)), Val(nvariables(equations)))) - end + @unpack sponge_layer_min, sponge_layer_max, reference_values, source_terms = sponge_layer + + if lies_in_sponge_layer(x, sponge_layer_min, sponge_layer_max) + return source_term_sponge_layer(u, x, t, equations, sponge_layer_min, + sponge_layer_max, + reference_values) + elseif source_terms !== nothing + return source_terms(u, x, t, equations) + else + return SVector(ntuple(v -> zero(eltype(u)), Val(nvariables(equations)))) + end end function lies_in_sponge_layer(x, sponge_layer_min, sponge_layer_max) - return (sponge_layer_min[1] <= x[1] <= sponge_layer_max[1]) || # -x direction - (sponge_layer_min[2] <= x[1] <= sponge_layer_max[2]) || # +x direction - (sponge_layer_min[3] <= x[2] <= sponge_layer_max[3]) || # -y direction - (sponge_layer_min[4] <= x[2] <= sponge_layer_max[4]) # +y direction + return (sponge_layer_min[1] <= x[1] <= sponge_layer_max[1]) || # -x direction + (sponge_layer_min[2] <= x[1] <= sponge_layer_max[2]) || # +x direction + (sponge_layer_min[3] <= x[2] <= sponge_layer_max[3]) || # -y direction + (sponge_layer_min[4] <= x[2] <= sponge_layer_max[4]) # +y direction end function source_term_sponge_layer(u, x, t, equations::AcousticPerturbationEquations2D, sponge_layer_min::NTuple{4}, sponge_layer_max::NTuple{4}, reference_values) - # Perturbed pressure source is -alpha^2 * (u - reference_value) where alpha in [0,1] is a damping - # factor depending on the position inside the sponge layer + # Perturbed pressure source is -alpha^2 * (u - reference_value) where alpha in [0,1] is a damping + # factor depending on the position inside the sponge layer - # Calculate the damping factors for each direction (=0 if x is not in the corresponding sponge - # zone) and take the maximum. This ensures proper damping if x lies in a corner where the sponge - # zones for two directions overlap - alphas = ntuple(i -> calc_damping_factor(x, i, sponge_layer_min, sponge_layer_max), - Val(2*ndims(equations))) - alpha_square = maximum(alphas)^2 + # Calculate the damping factors for each direction (=0 if x is not in the corresponding sponge + # zone) and take the maximum. This ensures proper damping if x lies in a corner where the sponge + # zones for two directions overlap + alphas = ntuple(i -> calc_damping_factor(x, i, sponge_layer_min, sponge_layer_max), + Val(2 * ndims(equations))) + alpha_square = maximum(alphas)^2 - return SVector(0, 0, -alpha_square*(u[3] - reference_values[1]/u[6]^2), 0, 0, 0, 0) + return SVector(0, 0, -alpha_square * (u[3] - reference_values[1] / u[6]^2), 0, 0, 0, 0) end function source_term_sponge_layer(u, x, t, equations::CompressibleEulerEquations2D, sponge_layer_min::NTuple{4}, sponge_layer_max::NTuple{4}, reference_values) - # Calculate the damping factors for each direction (=0 if x is not in the corresponding sponge - # zone) and take the maximum. This ensures proper damping if x lies in a corner where the sponge - # zones for two directions overlap - alphas = ntuple(i -> calc_damping_factor(x, i, sponge_layer_min, sponge_layer_max), - Val(2*ndims(equations))) - alpha_square = maximum(alphas)^2 - - u_prim = cons2prim(u, equations) - s = SVector(-alpha_square*(u_prim[1] - reference_values[1]), 0, 0, - -alpha_square*(u_prim[4] - reference_values[2])) - - return prim2cons(s, equations) + # Calculate the damping factors for each direction (=0 if x is not in the corresponding sponge + # zone) and take the maximum. This ensures proper damping if x lies in a corner where the sponge + # zones for two directions overlap + alphas = ntuple(i -> calc_damping_factor(x, i, sponge_layer_min, sponge_layer_max), + Val(2 * ndims(equations))) + alpha_square = maximum(alphas)^2 + + u_prim = cons2prim(u, equations) + s = SVector(-alpha_square * (u_prim[1] - reference_values[1]), 0, 0, + -alpha_square * (u_prim[4] - reference_values[2])) + + return prim2cons(s, equations) end function calc_damping_factor(x, direction, sponge_layer_min, sponge_layer_max) - # Damping factor alpha grows linearly from 0 to 1 depending on how deep x lies in the sponge layer - # If x does not lie in the sponge layer, this returns 0 - - # Get the coordinate that determines how deep we are in the sponge zone - if direction in (1, 2) - pos = x[1] - else - pos = x[2] - end - - # Determine where the sponge layer begins/ends to allow calculating the damping factor - if iseven(direction) - sponge_begin = sponge_layer_min[direction] - sponge_end = sponge_layer_max[direction] - else - sponge_begin = sponge_layer_max[direction] - sponge_end = sponge_layer_min[direction] - end - - alpha = (pos - sponge_begin) / (sponge_end - sponge_begin) - - # alpha lies in [0, 1] if and only if x lies in the sponge zone - if 0 <= alpha <= 1 - return alpha - else - return zero(alpha) - end + # Damping factor alpha grows linearly from 0 to 1 depending on how deep x lies in the sponge layer + # If x does not lie in the sponge layer, this returns 0 + + # Get the coordinate that determines how deep we are in the sponge zone + if direction in (1, 2) + pos = x[1] + else + pos = x[2] + end + + # Determine where the sponge layer begins/ends to allow calculating the damping factor + if iseven(direction) + sponge_begin = sponge_layer_min[direction] + sponge_end = sponge_layer_max[direction] + else + sponge_begin = sponge_layer_max[direction] + sponge_end = sponge_layer_min[direction] + end + + alpha = (pos - sponge_begin) / (sponge_end - sponge_begin) + + # alpha lies in [0, 1] if and only if x lies in the sponge zone + if 0 <= alpha <= 1 + return alpha + else + return zero(alpha) + end end - # Boundary condition for the flow problem: The sponge layer dampens density and pressure towards the # freestream values. The freestream values (converted into conservative variables) are therefore # used as a Dirichlet boundary struct BoundaryCondition{uEltype} - rho::uEltype - rho_e::uEltype + rho::uEltype + rho_e::uEltype end function (bc::BoundaryCondition)(u_inner, orientation, direction, x, t, surface_flux_function, equations::CompressibleEulerEquations2D) - u_boundary = SVector(bc.rho, zero(bc.rho), zero(bc.rho), bc.rho_e) + u_boundary = SVector(bc.rho, zero(bc.rho), zero(bc.rho), bc.rho_e) - # Calculate boundary flux - if iseven(direction) # u_inner is "left" of boundary, u_boundary is "right" of boundary - flux = surface_flux_function(u_inner, u_boundary, orientation, equations) - else # u_boundary is "left" of boundary, u_inner is "right" of boundary - flux = surface_flux_function(u_boundary, u_inner, orientation, equations) - end + # Calculate boundary flux + if iseven(direction) # u_inner is "left" of boundary, u_boundary is "right" of boundary + flux = surface_flux_function(u_inner, u_boundary, orientation, equations) + else # u_boundary is "left" of boundary, u_inner is "right" of boundary + flux = surface_flux_function(u_boundary, u_inner, orientation, equations) + end - return flux + return flux end end # module - import .VortexPairSetup - ############################################################################### # shared parameters, mesh and solver for both semidiscretizations # Parameters of the vortex pair -Mach = 1/9 +Mach = 1 / 9 c0 = 1.0 r0 = 1.0 circulation = 4 * pi * r0 * c0 * Mach rho = 1.0 -rc = 2/9 * r0 * 1.0 +rc = 2 / 9 * r0 * 1.0 T_r = 8 * pi^2 * r0^2 / circulation # Rotational period of the vortex pair T_a = T_r / 2 # Acoustic period of the vortex pair @@ -223,24 +219,22 @@ T_a = T_r / 2 # Acoustic period of the vortex pair vortex_pair = VortexPairSetup.VortexPair(r0, rc, c0, circulation, rho) # Shared mesh for both semidiscretizations -coordinates_min = (-135*r0, -135*r0) # minimum coordinates (min(x), min(y)) -coordinates_max = ( 135*r0, 135*r0) # maximum coordinates (max(x), max(y)) -refinement_patches = ( - (type="sphere", center=(0.0, 0.0), radius=85.0*r0), - (type="sphere", center=(0.0, 0.0), radius=20.0*r0), - (type="sphere", center=(0.0, 0.0), radius=10.0*r0), - (type="sphere", center=(0.0, 0.0), radius=5.0*r0) -) -initial_refinement_level=7 -n_cells_max=500_000 +coordinates_min = (-135 * r0, -135 * r0) # minimum coordinates (min(x), min(y)) +coordinates_max = (135 * r0, 135 * r0) # maximum coordinates (max(x), max(y)) +refinement_patches = ((type = "sphere", center = (0.0, 0.0), radius = 85.0 * r0), + (type = "sphere", center = (0.0, 0.0), radius = 20.0 * r0), + (type = "sphere", center = (0.0, 0.0), radius = 10.0 * r0), + (type = "sphere", center = (0.0, 0.0), radius = 5.0 * r0)) +initial_refinement_level = 7 +n_cells_max = 500_000 mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=initial_refinement_level, - refinement_patches=refinement_patches, - n_cells_max=n_cells_max, # set maximum capacity of tree data structure - periodicity=false) + initial_refinement_level = initial_refinement_level, + refinement_patches = refinement_patches, + n_cells_max = n_cells_max, # set maximum capacity of tree data structure + periodicity = false) # Create DG solver with polynomial degree = 3 and (local) Lax-Friedrichs/Rusanov flux as surface flux -solver = DGSEM(polydeg=3, surface_flux=flux_lax_friedrichs) +solver = DGSEM(polydeg = 3, surface_flux = flux_lax_friedrichs) ############################################################################### # semidiscretization Euler equations @@ -250,24 +244,37 @@ equations_euler = CompressibleEulerEquations2D(gamma) initial_condition_euler = VortexPairSetup.InitialCondition(vortex_pair) -sponge_layer_euler = VortexPairSetup.SpongeLayer(sponge_layer_min=(-135*r0, 115*r0, -135*r0, 115*r0), - sponge_layer_max=(-115*r0, 135*r0, -115*r0, 135*r0), - reference_values=(rho, rho * c0^2 / gamma)) # (rho0, p0) +sponge_layer_euler = VortexPairSetup.SpongeLayer(sponge_layer_min = (-135 * r0, 115 * r0, + -135 * r0, 115 * r0), + sponge_layer_max = (-115 * r0, 135 * r0, + -115 * r0, 135 * r0), + reference_values = (rho, + rho * c0^2 / gamma)) # (rho0, p0) -boundary_condition_euler = VortexPairSetup.BoundaryCondition(rho, (rho * c0^2 / gamma) / (gamma-1)) +boundary_condition_euler = VortexPairSetup.BoundaryCondition(rho, + (rho * c0^2 / gamma) / + (gamma - 1)) -semi_euler = SemidiscretizationHyperbolic(mesh, equations_euler, initial_condition_euler, solver, - boundary_conditions=boundary_condition_euler, - source_terms=sponge_layer_euler) +semi_euler = SemidiscretizationHyperbolic(mesh, equations_euler, initial_condition_euler, + solver, + boundary_conditions = boundary_condition_euler, + source_terms = sponge_layer_euler) ############################################################################### # semidiscretization acoustic perturbation equations -equations_acoustics = AcousticPerturbationEquations2D(v_mean_global=(13.0, 26.0), c_mean_global=39.0, - rho_mean_global=52.0) # global mean values will be overwritten - -sponge_layer_acoustics = VortexPairSetup.SpongeLayer(sponge_layer_min=(-135*r0, 100*r0, -135*r0, 100*r0), - sponge_layer_max=(-100*r0, 135*r0, -100*r0, 135*r0), - reference_values=(0.0,)) +equations_acoustics = AcousticPerturbationEquations2D(v_mean_global = (13.0, 26.0), + c_mean_global = 39.0, + rho_mean_global = 52.0) # global mean values will be overwritten + +sponge_layer_acoustics = VortexPairSetup.SpongeLayer(sponge_layer_min = (-135 * r0, + 100 * r0, + -135 * r0, + 100 * r0), + sponge_layer_max = (-100 * r0, + 135 * r0, + -100 * r0, + 135 * r0), + reference_values = (0.0,)) """ boundary_condition_zero(u_inner, orientation, direction, x, t, surface_flux_function, @@ -276,24 +283,27 @@ sponge_layer_acoustics = VortexPairSetup.SpongeLayer(sponge_layer_min=(-135*r0, Boundary condition that uses a boundary state where the state variables are zero and the mean variables are the same as in `u_inner`. """ -function boundary_condition_zero(u_inner, orientation, direction, x, t, surface_flux_function, +function boundary_condition_zero(u_inner, orientation, direction, x, t, + surface_flux_function, equations::AcousticPerturbationEquations2D) - value = zero(eltype(u_inner)) - u_boundary = SVector(value, value, value, cons2mean(u_inner, equations)...) + value = zero(eltype(u_inner)) + u_boundary = SVector(value, value, value, cons2mean(u_inner, equations)...) - # Calculate boundary flux - if iseven(direction) # u_inner is "left" of boundary, u_boundary is "right" of boundary - flux = surface_flux_function(u_inner, u_boundary, orientation, equations) - else # u_boundary is "left" of boundary, u_inner is "right" of boundary - flux = surface_flux_function(u_boundary, u_inner, orientation, equations) - end + # Calculate boundary flux + if iseven(direction) # u_inner is "left" of boundary, u_boundary is "right" of boundary + flux = surface_flux_function(u_inner, u_boundary, orientation, equations) + else # u_boundary is "left" of boundary, u_inner is "right" of boundary + flux = surface_flux_function(u_boundary, u_inner, orientation, equations) + end - return flux + return flux end -semi_acoustics = SemidiscretizationHyperbolic(mesh, equations_acoustics, initial_condition_constant, - solver, boundary_conditions=boundary_condition_zero, - source_terms=sponge_layer_acoustics) +semi_acoustics = SemidiscretizationHyperbolic(mesh, equations_acoustics, + initial_condition_constant, + solver, + boundary_conditions = boundary_condition_zero, + source_terms = sponge_layer_acoustics) ############################################################################### # ODE solvers, callbacks etc. for averaging the flow field @@ -307,12 +317,12 @@ ode_averaging = semidiscretize(semi_euler, tspan1) summary_callback = SummaryCallback() analysis_interval = 5000 -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) tspan_averaging = (50.0, 400.0) averaging_callback = AveragingCallback(semi_euler, tspan_averaging) -stepsize_callback = StepsizeCallback(cfl=0.8) +stepsize_callback = StepsizeCallback(cfl = 0.8) callbacks_averaging = CallbackSet(summary_callback, alive_callback, averaging_callback, stepsize_callback) @@ -321,14 +331,13 @@ callbacks_averaging = CallbackSet(summary_callback, alive_callback, averaging_ca # run simulation for averaging the flow field # OrdinaryDiffEq's `solve` method evolves the solution in time and executes the passed callbacks -sol_averaging = solve(ode_averaging, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks_averaging); +sol_averaging = solve(ode_averaging, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks_averaging); # Print the timer summary summary_callback() - ############################################################################### # set up coupled semidiscretization @@ -337,13 +346,13 @@ source_region(x) = sum(abs2, x) < 6.0^2 # calculate sources within radius 6 arou weights(x) = sum(abs2, x) < 5.0^2 ? 1.0 : cospi(0.5 * (norm(x) - 5.0)) semi = SemidiscretizationEulerAcoustics(semi_acoustics, semi_euler, - source_region=source_region, weights=weights) + source_region = source_region, weights = weights) ############################################################################### # ODE solvers, callbacks etc. for the coupled simulation # Create ODE problem -tspan = (0.0, 7.0*T_a) +tspan = (0.0, 7.0 * T_a) ode = semidiscretize(semi, tspan) # We need an additional ODE for the pure flow problem ode_euler = semidiscretize(semi.semi_euler, tspan) @@ -351,28 +360,30 @@ ode_euler = semidiscretize(semi.semi_euler, tspan) # Set up coupling callback cfl_acoustics = 0.8 cfl_euler = 0.8 -euler_acoustics_coupling = EulerAcousticsCouplingCallback( - ode_euler, "out/averaging.h5", CarpenterKennedy2N54(williamson_condition=false), - cfl_acoustics, cfl_euler, callback=SaveRestartCallback(interval=2300, output_directory="out/euler/")) +euler_acoustics_coupling = EulerAcousticsCouplingCallback(ode_euler, "out/averaging.h5", + CarpenterKennedy2N54(williamson_condition = false), + cfl_acoustics, cfl_euler, + callback = SaveRestartCallback(interval = 2300, + output_directory = "out/euler/")) # At the beginning of the main loop, the SummaryCallback prints a summary of the simulation setup # and resets the timers summary_callback = SummaryCallback() analysis_interval = 5000 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) output_directory = "out/" -save_solution = SaveSolutionCallback(interval=2300, output_directory=output_directory) -save_restart = SaveRestartCallback(interval=2300, output_directory=output_directory) +save_solution = SaveSolutionCallback(interval = 2300, output_directory = output_directory) +save_restart = SaveRestartCallback(interval = 2300, output_directory = output_directory) callbacks = CallbackSet(summary_callback, alive_callback, analysis_callback, save_solution, save_restart, euler_acoustics_coupling) -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); # Print the timer summary -summary_callback() \ No newline at end of file +summary_callback() diff --git a/examples/tree_2d_dgsem/elixir_eulermulti_convergence_ec.jl b/examples/tree_2d_dgsem/elixir_eulermulti_convergence_ec.jl index d423b800fd0..bc4859e5760 100644 --- a/examples/tree_2d_dgsem/elixir_eulermulti_convergence_ec.jl +++ b/examples/tree_2d_dgsem/elixir_eulermulti_convergence_ec.jl @@ -4,25 +4,23 @@ using Trixi ############################################################################### # semidiscretization of the compressible Euler multicomponent equations -equations = CompressibleEulerMulticomponentEquations2D(gammas = (1.4, 1.4), +equations = CompressibleEulerMulticomponentEquations2D(gammas = (1.4, 1.4), gas_constants = (0.4, 0.4)) initial_condition = initial_condition_convergence_test volume_flux = flux_ranocha -solver = DGSEM(polydeg=3, surface_flux=flux_ranocha, - volume_integral=VolumeIntegralFluxDifferencing(volume_flux)) +solver = DGSEM(polydeg = 3, surface_flux = flux_ranocha, + volume_integral = VolumeIntegralFluxDifferencing(volume_flux)) coordinates_min = (-1.0, -1.0) -coordinates_max = ( 1.0, 1.0) +coordinates_max = (1.0, 1.0) mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=3, - n_cells_max=30_000) - + initial_refinement_level = 3, + n_cells_max = 30_000) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver, - source_terms=source_terms_convergence_test) - + source_terms = source_terms_convergence_test) ############################################################################### # ODE solvers, callbacks etc. @@ -33,27 +31,26 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=100, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 100, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) -stepsize_callback = StepsizeCallback(cfl=0.5) +stepsize_callback = StepsizeCallback(cfl = 0.5) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, save_solution, stepsize_callback) - ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/tree_2d_dgsem/elixir_eulermulti_convergence_es.jl b/examples/tree_2d_dgsem/elixir_eulermulti_convergence_es.jl index 62c5bab51ea..771343937a4 100644 --- a/examples/tree_2d_dgsem/elixir_eulermulti_convergence_es.jl +++ b/examples/tree_2d_dgsem/elixir_eulermulti_convergence_es.jl @@ -4,25 +4,23 @@ using Trixi ############################################################################### # semidiscretization of the compressible Euler multicomponent equations -equations = CompressibleEulerMulticomponentEquations2D(gammas = (1.4, 1.4), +equations = CompressibleEulerMulticomponentEquations2D(gammas = (1.4, 1.4), gas_constants = (0.4, 0.4)) initial_condition = initial_condition_convergence_test volume_flux = flux_ranocha -solver = DGSEM(polydeg=3, surface_flux=flux_lax_friedrichs, - volume_integral=VolumeIntegralFluxDifferencing(volume_flux)) +solver = DGSEM(polydeg = 3, surface_flux = flux_lax_friedrichs, + volume_integral = VolumeIntegralFluxDifferencing(volume_flux)) coordinates_min = (-1.0, -1.0) -coordinates_max = ( 1.0, 1.0) +coordinates_max = (1.0, 1.0) mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=4, - n_cells_max=30_000) - + initial_refinement_level = 4, + n_cells_max = 30_000) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver, - source_terms=source_terms_convergence_test) - + source_terms = source_terms_convergence_test) ############################################################################### # ODE solvers, callbacks etc. @@ -33,27 +31,26 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=100, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 100, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) -stepsize_callback = StepsizeCallback(cfl=0.5) +stepsize_callback = StepsizeCallback(cfl = 0.5) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, save_solution, stepsize_callback) - ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/tree_2d_dgsem/elixir_eulermulti_ec.jl b/examples/tree_2d_dgsem/elixir_eulermulti_ec.jl index 0715dfe35d6..d912a280e49 100644 --- a/examples/tree_2d_dgsem/elixir_eulermulti_ec.jl +++ b/examples/tree_2d_dgsem/elixir_eulermulti_ec.jl @@ -4,26 +4,23 @@ using Trixi ############################################################################### # semidiscretization of the compressible Euler multicomponent equations -equations = CompressibleEulerMulticomponentEquations2D(gammas = 1.4, +equations = CompressibleEulerMulticomponentEquations2D(gammas = 1.4, gas_constants = 0.4) - initial_condition = initial_condition_weak_blast_wave volume_flux = flux_ranocha -solver = DGSEM(polydeg=3, surface_flux=flux_ranocha, - volume_integral=VolumeIntegralFluxDifferencing(volume_flux)) +solver = DGSEM(polydeg = 3, surface_flux = flux_ranocha, + volume_integral = VolumeIntegralFluxDifferencing(volume_flux)) coordinates_min = (-2.0, -2.0) -coordinates_max = ( 2.0, 2.0) +coordinates_max = (2.0, 2.0) mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=5, - n_cells_max=10_000) - + initial_refinement_level = 5, + n_cells_max = 10_000) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver) - ############################################################################### # ODE solvers, callbacks etc. @@ -34,28 +31,27 @@ summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval, - extra_analysis_integrals=(Trixi.density,)) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval, + extra_analysis_integrals = (Trixi.density,)) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=100, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 100, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) -stepsize_callback = StepsizeCallback(cfl=1.0) +stepsize_callback = StepsizeCallback(cfl = 1.0) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, save_solution, stepsize_callback) - ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/tree_2d_dgsem/elixir_eulermulti_es.jl b/examples/tree_2d_dgsem/elixir_eulermulti_es.jl index a3e5580b572..470e533ab8d 100644 --- a/examples/tree_2d_dgsem/elixir_eulermulti_es.jl +++ b/examples/tree_2d_dgsem/elixir_eulermulti_es.jl @@ -4,25 +4,23 @@ using Trixi ############################################################################### # semidiscretization of the compressible Euler multicomponent equations -equations = CompressibleEulerMulticomponentEquations2D(gammas = (1.4, 1.4, 1.4, 1.4), +equations = CompressibleEulerMulticomponentEquations2D(gammas = (1.4, 1.4, 1.4, 1.4), gas_constants = (0.4, 0.4, 0.4, 0.4)) initial_condition = initial_condition_weak_blast_wave volume_flux = flux_ranocha -solver = DGSEM(polydeg=3, surface_flux=flux_lax_friedrichs, - volume_integral=VolumeIntegralFluxDifferencing(volume_flux)) +solver = DGSEM(polydeg = 3, surface_flux = flux_lax_friedrichs, + volume_integral = VolumeIntegralFluxDifferencing(volume_flux)) coordinates_min = (-2.0, -2.0) -coordinates_max = ( 2.0, 2.0) +coordinates_max = (2.0, 2.0) mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=5, - n_cells_max=10_000) - + initial_refinement_level = 5, + n_cells_max = 10_000) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver) - ############################################################################### # ODE solvers, callbacks etc. @@ -32,30 +30,29 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_restart = SaveRestartCallback(interval=100, - save_final_restart=true) +save_restart = SaveRestartCallback(interval = 100, + save_final_restart = true) -save_solution = SaveSolutionCallback(interval=100, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 100, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) -stepsize_callback = StepsizeCallback(cfl=1.0) +stepsize_callback = StepsizeCallback(cfl = 1.0) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, save_restart, save_solution, stepsize_callback) - ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/tree_2d_dgsem/elixir_eulermulti_shock_bubble.jl b/examples/tree_2d_dgsem/elixir_eulermulti_shock_bubble.jl index 38510446cb1..f5ef51c108a 100644 --- a/examples/tree_2d_dgsem/elixir_eulermulti_shock_bubble.jl +++ b/examples/tree_2d_dgsem/elixir_eulermulti_shock_bubble.jl @@ -5,7 +5,7 @@ using Trixi # semidiscretization of the compressible Euler multicomponent equations # 1) Dry Air 2) Helium + 28% Air -equations = CompressibleEulerMulticomponentEquations2D(gammas = (1.4, 1.648), +equations = CompressibleEulerMulticomponentEquations2D(gammas = (1.4, 1.648), gas_constants = (0.287, 1.578)) """ @@ -16,124 +16,126 @@ A shock-bubble testcase for multicomponent Euler equations Formulation of Entropy-Stable schemes for the multicomponent compressible Euler equations [arXiv: 1904.00972](https://arxiv.org/abs/1904.00972) """ -function initial_condition_shock_bubble(x, t, equations::CompressibleEulerMulticomponentEquations2D{5, 2}) - # bubble test case, see Gouasmi et al. https://arxiv.org/pdf/1904.00972 - # other reference: https://www.researchgate.net/profile/Pep_Mulet/publication/222675930_A_flux-split_algorithm_applied_to_conservative_models_for_multicomponent_compressible_flows/links/568da54508aeaa1481ae7af0.pdf - # typical domain is rectangular, we change it to a square, as Trixi can only do squares - @unpack gas_constants = equations - - # Positivity Preserving Parameter, can be set to zero if scheme is positivity preserving - delta = 0.03 - - # Region I - rho1_1 = delta - rho2_1 = 1.225 * gas_constants[1]/gas_constants[2] - delta - v1_1 = zero(delta) - v2_1 = zero(delta) - p_1 = 101325 - - # Region II - rho1_2 = 1.225-delta - rho2_2 = delta - v1_2 = zero(delta) - v2_2 = zero(delta) - p_2 = 101325 - - # Region III - rho1_3 = 1.6861 - delta - rho2_3 = delta - v1_3 = -113.5243 - v2_3 = zero(delta) - p_3 = 159060 - - # Set up Region I & II: - inicenter = SVector(zero(delta), zero(delta)) - x_norm = x[1] - inicenter[1] - y_norm = x[2] - inicenter[2] - r = sqrt(x_norm^2 + y_norm^2) - - if (x[1] > 0.50) - # Set up Region III - rho1 = rho1_3 - rho2 = rho2_3 - v1 = v1_3 - v2 = v2_3 - p = p_3 - elseif (r < 0.25) - # Set up Region I - rho1 = rho1_1 - rho2 = rho2_1 - v1 = v1_1 - v2 = v2_1 - p = p_1 - else - # Set up Region II - rho1 = rho1_2 - rho2 = rho2_2 - v1 = v1_2 - v2 = v2_2 - p = p_2 - end - - return prim2cons(SVector(v1, v2, p, rho1, rho2), equations) +function initial_condition_shock_bubble(x, t, + equations::CompressibleEulerMulticomponentEquations2D{ + 5, + 2 + }) + # bubble test case, see Gouasmi et al. https://arxiv.org/pdf/1904.00972 + # other reference: https://www.researchgate.net/profile/Pep_Mulet/publication/222675930_A_flux-split_algorithm_applied_to_conservative_models_for_multicomponent_compressible_flows/links/568da54508aeaa1481ae7af0.pdf + # typical domain is rectangular, we change it to a square, as Trixi can only do squares + @unpack gas_constants = equations + + # Positivity Preserving Parameter, can be set to zero if scheme is positivity preserving + delta = 0.03 + + # Region I + rho1_1 = delta + rho2_1 = 1.225 * gas_constants[1] / gas_constants[2] - delta + v1_1 = zero(delta) + v2_1 = zero(delta) + p_1 = 101325 + + # Region II + rho1_2 = 1.225 - delta + rho2_2 = delta + v1_2 = zero(delta) + v2_2 = zero(delta) + p_2 = 101325 + + # Region III + rho1_3 = 1.6861 - delta + rho2_3 = delta + v1_3 = -113.5243 + v2_3 = zero(delta) + p_3 = 159060 + + # Set up Region I & II: + inicenter = SVector(zero(delta), zero(delta)) + x_norm = x[1] - inicenter[1] + y_norm = x[2] - inicenter[2] + r = sqrt(x_norm^2 + y_norm^2) + + if (x[1] > 0.50) + # Set up Region III + rho1 = rho1_3 + rho2 = rho2_3 + v1 = v1_3 + v2 = v2_3 + p = p_3 + elseif (r < 0.25) + # Set up Region I + rho1 = rho1_1 + rho2 = rho2_1 + v1 = v1_1 + v2 = v2_1 + p = p_1 + else + # Set up Region II + rho1 = rho1_2 + rho2 = rho2_2 + v1 = v1_2 + v2 = v2_2 + p = p_2 + end + + return prim2cons(SVector(v1, v2, p, rho1, rho2), equations) end initial_condition = initial_condition_shock_bubble -surface_flux = flux_lax_friedrichs -volume_flux = flux_ranocha -basis = LobattoLegendreBasis(3) -indicator_sc = IndicatorHennemannGassner(equations, basis, - alpha_max=0.5, - alpha_min=0.001, - alpha_smooth=true, - variable=density_pressure) -volume_integral = VolumeIntegralShockCapturingHG(indicator_sc; - volume_flux_dg=volume_flux, - volume_flux_fv=surface_flux) -solver = DGSEM(basis, surface_flux, volume_integral) - -coordinates_min = (-2.25, -2.225) -coordinates_max = ( 2.20, 2.225) -mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=3, - n_cells_max=1_000_000) - -semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver) - +surface_flux = flux_lax_friedrichs +volume_flux = flux_ranocha +basis = LobattoLegendreBasis(3) +indicator_sc = IndicatorHennemannGassner(equations, basis, + alpha_max = 0.5, + alpha_min = 0.001, + alpha_smooth = true, + variable = density_pressure) +volume_integral = VolumeIntegralShockCapturingHG(indicator_sc; + volume_flux_dg = volume_flux, + volume_flux_fv = surface_flux) +solver = DGSEM(basis, surface_flux, volume_integral) + +coordinates_min = (-2.25, -2.225) +coordinates_max = (2.20, 2.225) +mesh = TreeMesh(coordinates_min, coordinates_max, + initial_refinement_level = 3, + n_cells_max = 1_000_000) + +semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver) ############################################################################### # ODE solvers, callbacks etc. -tspan = (0.0, 0.01) -ode = semidiscretize(semi, tspan) - -summary_callback = SummaryCallback() +tspan = (0.0, 0.01) +ode = semidiscretize(semi, tspan) -analysis_interval = 300 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval, - extra_analysis_integrals=(Trixi.density,)) +summary_callback = SummaryCallback() -alive_callback = AliveCallback(analysis_interval=analysis_interval) +analysis_interval = 300 +analysis_callback = AnalysisCallback(semi, interval = analysis_interval, + extra_analysis_integrals = (Trixi.density,)) -save_solution = SaveSolutionCallback(interval=300, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -stepsize_callback = StepsizeCallback(cfl=0.3) +save_solution = SaveSolutionCallback(interval = 300, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) -callbacks = CallbackSet(summary_callback, - analysis_callback, - alive_callback, - save_solution, - stepsize_callback) +stepsize_callback = StepsizeCallback(cfl = 0.3) +callbacks = CallbackSet(summary_callback, + analysis_callback, + alive_callback, + save_solution, + stepsize_callback) ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, - callback=callbacks, - maxiters=1e5); -summary_callback() # print the timer summary \ No newline at end of file +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, + callback = callbacks, + maxiters = 1e5); +summary_callback() # print the timer summary diff --git a/examples/tree_2d_dgsem/elixir_eulermulti_shock_bubble_shockcapturing_subcell_minmax.jl b/examples/tree_2d_dgsem/elixir_eulermulti_shock_bubble_shockcapturing_subcell_minmax.jl index 1c6cbef533e..4a8a70b5663 100644 --- a/examples/tree_2d_dgsem/elixir_eulermulti_shock_bubble_shockcapturing_subcell_minmax.jl +++ b/examples/tree_2d_dgsem/elixir_eulermulti_shock_bubble_shockcapturing_subcell_minmax.jl @@ -5,7 +5,7 @@ using Trixi # semidiscretization of the compressible Euler multicomponent equations # 1) Dry Air 2) Helium + 28% Air -equations = CompressibleEulerMulticomponentEquations2D(gammas = (1.4, 1.648), +equations = CompressibleEulerMulticomponentEquations2D(gammas = (1.4, 1.648), gas_constants = (0.287, 1.578)) """ @@ -16,126 +16,130 @@ A shock-bubble testcase for multicomponent Euler equations Formulation of Entropy-Stable schemes for the multicomponent compressible Euler equations [arXiv: 1904.00972](https://arxiv.org/abs/1904.00972) """ -function initial_condition_shock_bubble(x, t, equations::CompressibleEulerMulticomponentEquations2D{5, 2}) - # bubble test case, see Gouasmi et al. https://arxiv.org/pdf/1904.00972 - # other reference: https://www.researchgate.net/profile/Pep_Mulet/publication/222675930_A_flux-split_algorithm_applied_to_conservative_models_for_multicomponent_compressible_flows/links/568da54508aeaa1481ae7af0.pdf - # typical domain is rectangular, we change it to a square, as Trixi can only do squares - @unpack gas_constants = equations - - # Positivity Preserving Parameter, can be set to zero if scheme is positivity preserving - delta = 0.03 - - # Region I - rho1_1 = delta - rho2_1 = 1.225 * gas_constants[1]/gas_constants[2] - delta - v1_1 = zero(delta) - v2_1 = zero(delta) - p_1 = 101325 - - # Region II - rho1_2 = 1.225-delta - rho2_2 = delta - v1_2 = zero(delta) - v2_2 = zero(delta) - p_2 = 101325 - - # Region III - rho1_3 = 1.6861 - delta - rho2_3 = delta - v1_3 = -113.5243 - v2_3 = zero(delta) - p_3 = 159060 - - # Set up Region I & II: - inicenter = SVector(zero(delta), zero(delta)) - x_norm = x[1] - inicenter[1] - y_norm = x[2] - inicenter[2] - r = sqrt(x_norm^2 + y_norm^2) - - if (x[1] > 0.50) - # Set up Region III - rho1 = rho1_3 - rho2 = rho2_3 - v1 = v1_3 - v2 = v2_3 - p = p_3 - elseif (r < 0.25) - # Set up Region I - rho1 = rho1_1 - rho2 = rho2_1 - v1 = v1_1 - v2 = v2_1 - p = p_1 - else - # Set up Region II - rho1 = rho1_2 - rho2 = rho2_2 - v1 = v1_2 - v2 = v2_2 - p = p_2 - end - - return prim2cons(SVector(v1, v2, p, rho1, rho2), equations) +function initial_condition_shock_bubble(x, t, + equations::CompressibleEulerMulticomponentEquations2D{ + 5, + 2 + }) + # bubble test case, see Gouasmi et al. https://arxiv.org/pdf/1904.00972 + # other reference: https://www.researchgate.net/profile/Pep_Mulet/publication/222675930_A_flux-split_algorithm_applied_to_conservative_models_for_multicomponent_compressible_flows/links/568da54508aeaa1481ae7af0.pdf + # typical domain is rectangular, we change it to a square, as Trixi can only do squares + @unpack gas_constants = equations + + # Positivity Preserving Parameter, can be set to zero if scheme is positivity preserving + delta = 0.03 + + # Region I + rho1_1 = delta + rho2_1 = 1.225 * gas_constants[1] / gas_constants[2] - delta + v1_1 = zero(delta) + v2_1 = zero(delta) + p_1 = 101325 + + # Region II + rho1_2 = 1.225 - delta + rho2_2 = delta + v1_2 = zero(delta) + v2_2 = zero(delta) + p_2 = 101325 + + # Region III + rho1_3 = 1.6861 - delta + rho2_3 = delta + v1_3 = -113.5243 + v2_3 = zero(delta) + p_3 = 159060 + + # Set up Region I & II: + inicenter = SVector(zero(delta), zero(delta)) + x_norm = x[1] - inicenter[1] + y_norm = x[2] - inicenter[2] + r = sqrt(x_norm^2 + y_norm^2) + + if (x[1] > 0.50) + # Set up Region III + rho1 = rho1_3 + rho2 = rho2_3 + v1 = v1_3 + v2 = v2_3 + p = p_3 + elseif (r < 0.25) + # Set up Region I + rho1 = rho1_1 + rho2 = rho2_1 + v1 = v1_1 + v2 = v2_1 + p = p_1 + else + # Set up Region II + rho1 = rho1_2 + rho2 = rho2_2 + v1 = v1_2 + v2 = v2_2 + p = p_2 + end + + return prim2cons(SVector(v1, v2, p, rho1, rho2), equations) end initial_condition = initial_condition_shock_bubble -surface_flux = flux_lax_friedrichs -volume_flux = flux_ranocha -basis = LobattoLegendreBasis(3) +surface_flux = flux_lax_friedrichs +volume_flux = flux_ranocha +basis = LobattoLegendreBasis(3) limiter_idp = SubcellLimiterIDP(equations, basis; - local_minmax_variables_cons=[(i+3 for i in eachcomponent(equations))...], - spec_entropy=false, - bar_states=true) + local_minmax_variables_cons = [ + (i + 3 for i in eachcomponent(equations))..., + ], + spec_entropy = false, + bar_states = true) volume_integral = VolumeIntegralSubcellLimiting(limiter_idp; - volume_flux_dg=volume_flux, - volume_flux_fv=surface_flux) + volume_flux_dg = volume_flux, + volume_flux_fv = surface_flux) solver = DGSEM(basis, surface_flux, volume_integral) -coordinates_min = (-2.25, -2.225) -coordinates_max = ( 2.20, 2.225) -mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=3, - n_cells_max=1_000_000) - -semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver) +coordinates_min = (-2.25, -2.225) +coordinates_max = (2.20, 2.225) +mesh = TreeMesh(coordinates_min, coordinates_max, + initial_refinement_level = 3, + n_cells_max = 1_000_000) +semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver) ############################################################################### # ODE solvers, callbacks etc. -tspan = (0.0, 0.01) -ode = semidiscretize(semi, tspan) - -summary_callback = SummaryCallback() +tspan = (0.0, 0.01) +ode = semidiscretize(semi, tspan) -analysis_interval = 300 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval, - extra_analysis_integrals=(Trixi.density,)) +summary_callback = SummaryCallback() -alive_callback = AliveCallback(analysis_interval=analysis_interval) +analysis_interval = 300 +analysis_callback = AnalysisCallback(semi, interval = analysis_interval, + extra_analysis_integrals = (Trixi.density,)) -save_solution = SaveSolutionCallback(interval=600, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -stepsize_callback = StepsizeCallback(cfl=0.9) +save_solution = SaveSolutionCallback(interval = 600, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) -callbacks = CallbackSet(summary_callback, - analysis_callback, - alive_callback, - save_solution, - stepsize_callback) +stepsize_callback = StepsizeCallback(cfl = 0.9) +callbacks = CallbackSet(summary_callback, + analysis_callback, + alive_callback, + save_solution, + stepsize_callback) ############################################################################### # run the simulation -stage_callbacks = (SubcellLimiterIDPCorrection(), BoundsCheckCallback(save_errors=false)) +stage_callbacks = (SubcellLimiterIDPCorrection(), BoundsCheckCallback(save_errors = false)) -sol = Trixi.solve(ode, Trixi.SimpleSSPRK33(stage_callbacks=stage_callbacks); - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); -summary_callback() # print the timer summary \ No newline at end of file +sol = Trixi.solve(ode, Trixi.SimpleSSPRK33(stage_callbacks = stage_callbacks); + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); +summary_callback() # print the timer summary diff --git a/examples/tree_2d_dgsem/elixir_eulermulti_shock_bubble_shockcapturing_subcell_positivity.jl b/examples/tree_2d_dgsem/elixir_eulermulti_shock_bubble_shockcapturing_subcell_positivity.jl index f817a91a58f..5f6cdb1e9c0 100644 --- a/examples/tree_2d_dgsem/elixir_eulermulti_shock_bubble_shockcapturing_subcell_positivity.jl +++ b/examples/tree_2d_dgsem/elixir_eulermulti_shock_bubble_shockcapturing_subcell_positivity.jl @@ -5,7 +5,7 @@ using Trixi # semidiscretization of the compressible Euler multicomponent equations # 1) Dry Air 2) Helium + 28% Air -equations = CompressibleEulerMulticomponentEquations2D(gammas = (1.4, 1.648), +equations = CompressibleEulerMulticomponentEquations2D(gammas = (1.4, 1.648), gas_constants = (0.287, 1.578)) """ @@ -16,131 +16,136 @@ A shock-bubble testcase for multicomponent Euler equations Formulation of Entropy-Stable schemes for the multicomponent compressible Euler equations [arXiv: 1904.00972](https://arxiv.org/abs/1904.00972) """ -function initial_condition_shock_bubble(x, t, equations::CompressibleEulerMulticomponentEquations2D{5, 2}) - # bubble test case, see Gouasmi et al. https://arxiv.org/pdf/1904.00972 - # other reference: https://www.researchgate.net/profile/Pep_Mulet/publication/222675930_A_flux-split_algorithm_applied_to_conservative_models_for_multicomponent_compressible_flows/links/568da54508aeaa1481ae7af0.pdf - # typical domain is rectangular, we change it to a square, as Trixi can only do squares - @unpack gas_constants = equations - - # Positivity Preserving Parameter, can be set to zero if scheme is positivity preserving - delta = 0.03 - - # Region I - rho1_1 = delta - rho2_1 = 1.225 * gas_constants[1]/gas_constants[2] - delta - v1_1 = zero(delta) - v2_1 = zero(delta) - p_1 = 101325 - - # Region II - rho1_2 = 1.225-delta - rho2_2 = delta - v1_2 = zero(delta) - v2_2 = zero(delta) - p_2 = 101325 - - # Region III - rho1_3 = 1.6861 - delta - rho2_3 = delta - v1_3 = -113.5243 - v2_3 = zero(delta) - p_3 = 159060 - - # Set up Region I & II: - inicenter = SVector(zero(delta), zero(delta)) - x_norm = x[1] - inicenter[1] - y_norm = x[2] - inicenter[2] - r = sqrt(x_norm^2 + y_norm^2) - - if (x[1] > 0.50) - # Set up Region III - rho1 = rho1_3 - rho2 = rho2_3 - v1 = v1_3 - v2 = v2_3 - p = p_3 - elseif (r < 0.25) - # Set up Region I - rho1 = rho1_1 - rho2 = rho2_1 - v1 = v1_1 - v2 = v2_1 - p = p_1 - else - # Set up Region II - rho1 = rho1_2 - rho2 = rho2_2 - v1 = v1_2 - v2 = v2_2 - p = p_2 - end - - return prim2cons(SVector(v1, v2, p, rho1, rho2), equations) +function initial_condition_shock_bubble(x, t, + equations::CompressibleEulerMulticomponentEquations2D{ + 5, + 2 + }) + # bubble test case, see Gouasmi et al. https://arxiv.org/pdf/1904.00972 + # other reference: https://www.researchgate.net/profile/Pep_Mulet/publication/222675930_A_flux-split_algorithm_applied_to_conservative_models_for_multicomponent_compressible_flows/links/568da54508aeaa1481ae7af0.pdf + # typical domain is rectangular, we change it to a square, as Trixi can only do squares + @unpack gas_constants = equations + + # Positivity Preserving Parameter, can be set to zero if scheme is positivity preserving + delta = 0.03 + + # Region I + rho1_1 = delta + rho2_1 = 1.225 * gas_constants[1] / gas_constants[2] - delta + v1_1 = zero(delta) + v2_1 = zero(delta) + p_1 = 101325 + + # Region II + rho1_2 = 1.225 - delta + rho2_2 = delta + v1_2 = zero(delta) + v2_2 = zero(delta) + p_2 = 101325 + + # Region III + rho1_3 = 1.6861 - delta + rho2_3 = delta + v1_3 = -113.5243 + v2_3 = zero(delta) + p_3 = 159060 + + # Set up Region I & II: + inicenter = SVector(zero(delta), zero(delta)) + x_norm = x[1] - inicenter[1] + y_norm = x[2] - inicenter[2] + r = sqrt(x_norm^2 + y_norm^2) + + if (x[1] > 0.50) + # Set up Region III + rho1 = rho1_3 + rho2 = rho2_3 + v1 = v1_3 + v2 = v2_3 + p = p_3 + elseif (r < 0.25) + # Set up Region I + rho1 = rho1_1 + rho2 = rho2_1 + v1 = v1_1 + v2 = v2_1 + p = p_1 + else + # Set up Region II + rho1 = rho1_2 + rho2 = rho2_2 + v1 = v1_2 + v2 = v2_2 + p = p_2 + end + + return prim2cons(SVector(v1, v2, p, rho1, rho2), equations) end initial_condition = initial_condition_shock_bubble -surface_flux = flux_lax_friedrichs -volume_flux = flux_ranocha -basis = LobattoLegendreBasis(3) +surface_flux = flux_lax_friedrichs +volume_flux = flux_ranocha +basis = LobattoLegendreBasis(3) limiter_idp = SubcellLimiterIDP(equations, basis; - positivity_variables_cons=[(i+3 for i in eachcomponent(equations))...], - positivity_variables_nonlinear=(), - positivity_correction_factor=0.1, - spec_entropy=false, - bar_states=false) + positivity_variables_cons = [ + (i + 3 for i in eachcomponent(equations))..., + ], + positivity_variables_nonlinear = (), + positivity_correction_factor = 0.1, + spec_entropy = false, + bar_states = false) volume_integral = VolumeIntegralSubcellLimiting(limiter_idp; - volume_flux_dg=volume_flux, - volume_flux_fv=surface_flux) + volume_flux_dg = volume_flux, + volume_flux_fv = surface_flux) solver = DGSEM(basis, surface_flux, volume_integral) -coordinates_min = (-2.25, -2.225) -coordinates_max = ( 2.20, 2.225) -mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=3, - n_cells_max=1_000_000) - -semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver) +coordinates_min = (-2.25, -2.225) +coordinates_max = (2.20, 2.225) +mesh = TreeMesh(coordinates_min, coordinates_max, + initial_refinement_level = 3, + n_cells_max = 1_000_000) +semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver) ############################################################################### # ODE solvers, callbacks etc. -tspan = (0.0, 0.01) -ode = semidiscretize(semi, tspan) - -summary_callback = SummaryCallback() +tspan = (0.0, 0.01) +ode = semidiscretize(semi, tspan) -analysis_interval = 300 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval, - extra_analysis_integrals=(Trixi.density,)) +summary_callback = SummaryCallback() -alive_callback = AliveCallback(analysis_interval=analysis_interval) +analysis_interval = 300 +analysis_callback = AnalysisCallback(semi, interval = analysis_interval, + extra_analysis_integrals = (Trixi.density,)) -save_solution = SaveSolutionCallback(interval=300, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -stepsize_callback = StepsizeCallback(cfl=0.9) +save_solution = SaveSolutionCallback(interval = 300, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) -callbacks = CallbackSet(summary_callback, - analysis_callback, - alive_callback, - save_solution, - stepsize_callback) +stepsize_callback = StepsizeCallback(cfl = 0.9) +callbacks = CallbackSet(summary_callback, + analysis_callback, + alive_callback, + save_solution, + stepsize_callback) ############################################################################### # run the simulation output_directory = "out" stage_callbacks = (SubcellLimiterIDPCorrection(), - BoundsCheckCallback(save_errors=true, interval=100, output_directory=output_directory)) + BoundsCheckCallback(save_errors = true, interval = 100, + output_directory = output_directory)) -sol = Trixi.solve(ode, Trixi.SimpleSSPRK33(stage_callbacks=stage_callbacks); - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); -summary_callback() # print the timer summary \ No newline at end of file +sol = Trixi.solve(ode, Trixi.SimpleSSPRK33(stage_callbacks = stage_callbacks); + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); +summary_callback() # print the timer summary diff --git a/examples/tree_2d_dgsem/elixir_hypdiff_godunov.jl b/examples/tree_2d_dgsem/elixir_hypdiff_godunov.jl index abf9735fd28..1700957d900 100644 --- a/examples/tree_2d_dgsem/elixir_hypdiff_godunov.jl +++ b/examples/tree_2d_dgsem/elixir_hypdiff_godunov.jl @@ -8,51 +8,50 @@ using Trixi equations = HyperbolicDiffusionEquations2D() function initial_condition_poisson_periodic(x, t, equations::HyperbolicDiffusionEquations2D) - # elliptic equation: -νΔϕ = f - # depending on initial constant state, c, for phi this converges to the solution ϕ + c - if iszero(t) - phi = 0.0 - q1 = 0.0 - q2 = 0.0 - else - phi = sin(2.0*pi*x[1])*sin(2.0*pi*x[2]) - q1 = 2*pi*cos(2.0*pi*x[1])*sin(2.0*pi*x[2]) - q2 = 2*pi*sin(2.0*pi*x[1])*cos(2.0*pi*x[2]) - end - return SVector(phi, q1, q2) + # elliptic equation: -νΔϕ = f + # depending on initial constant state, c, for phi this converges to the solution ϕ + c + if iszero(t) + phi = 0.0 + q1 = 0.0 + q2 = 0.0 + else + phi = sin(2.0 * pi * x[1]) * sin(2.0 * pi * x[2]) + q1 = 2 * pi * cos(2.0 * pi * x[1]) * sin(2.0 * pi * x[2]) + q2 = 2 * pi * sin(2.0 * pi * x[1]) * cos(2.0 * pi * x[2]) + end + return SVector(phi, q1, q2) end initial_condition = initial_condition_poisson_periodic -@inline function source_terms_poisson_periodic(u, x, t, equations::HyperbolicDiffusionEquations2D) - # elliptic equation: -νΔϕ = f - # analytical solution: phi = sin(2πx)*sin(2πy) and f = -8νπ^2 sin(2πx)*sin(2πy) - @unpack inv_Tr = equations - C = -8 * equations.nu * pi^2 - - x1, x2 = x - tmp1 = sinpi(2 * x1) - tmp2 = sinpi(2 * x2) - du1 = -C*tmp1*tmp2 - du2 = -inv_Tr * u[2] - du3 = -inv_Tr * u[3] - - return SVector(du1, du2, du3) +@inline function source_terms_poisson_periodic(u, x, t, + equations::HyperbolicDiffusionEquations2D) + # elliptic equation: -νΔϕ = f + # analytical solution: phi = sin(2πx)*sin(2πy) and f = -8νπ^2 sin(2πx)*sin(2πy) + @unpack inv_Tr = equations + C = -8 * equations.nu * pi^2 + + x1, x2 = x + tmp1 = sinpi(2 * x1) + tmp2 = sinpi(2 * x2) + du1 = -C * tmp1 * tmp2 + du2 = -inv_Tr * u[2] + du3 = -inv_Tr * u[3] + + return SVector(du1, du2, du3) end volume_flux = flux_central -solver = DGSEM(polydeg=4, surface_flux=flux_godunov, - volume_integral=VolumeIntegralFluxDifferencing(volume_flux)) +solver = DGSEM(polydeg = 4, surface_flux = flux_godunov, + volume_integral = VolumeIntegralFluxDifferencing(volume_flux)) coordinates_min = (0.0, 0.0) coordinates_max = (1.0, 1.0) mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=3, - n_cells_max=30_000) - + initial_refinement_level = 3, + n_cells_max = 30_000) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver, - source_terms=source_terms_poisson_periodic) - + source_terms = source_terms_poisson_periodic) ############################################################################### # ODE solvers, callbacks etc. @@ -63,30 +62,29 @@ ode = semidiscretize(semi, tspan); summary_callback = SummaryCallback() resid_tol = 5.0e-12 -steady_state_callback = SteadyStateCallback(abstol=resid_tol, reltol=0.0) +steady_state_callback = SteadyStateCallback(abstol = resid_tol, reltol = 0.0) analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=100, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 100, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) -stepsize_callback = StepsizeCallback(cfl=1.0) +stepsize_callback = StepsizeCallback(cfl = 1.0) callbacks = CallbackSet(summary_callback, steady_state_callback, analysis_callback, alive_callback, save_solution, stepsize_callback) - ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/tree_2d_dgsem/elixir_hypdiff_harmonic_nonperiodic.jl b/examples/tree_2d_dgsem/elixir_hypdiff_harmonic_nonperiodic.jl index c144ef47a63..e70b91906b1 100644 --- a/examples/tree_2d_dgsem/elixir_hypdiff_harmonic_nonperiodic.jl +++ b/examples/tree_2d_dgsem/elixir_hypdiff_harmonic_nonperiodic.jl @@ -7,44 +7,43 @@ using Trixi equations = HyperbolicDiffusionEquations2D() -@inline function initial_condition_harmonic_nonperiodic(x, t, equations::HyperbolicDiffusionEquations2D) - # elliptic equation: -ν Δϕ = 0 in Ω, u = g on ∂Ω - if t == 0.0 - phi = 1.0 - q1 = 1.0 - q2 = 1.0 - else - C = inv(sinh(pi)) - sinpi_x1, cospi_x1 = sincos(pi*x[1]) - sinpi_x2, cospi_x2 = sincos(pi*x[2]) - sinh_pix1 = sinh(pi*x[1]) - cosh_pix1 = cosh(pi*x[1]) - sinh_pix2 = sinh(pi*x[2]) - cosh_pix2 = cosh(pi*x[2]) - phi = C * (sinh_pix1 * sinpi_x2 + sinh_pix2 * sinpi_x1) - q1 = C * pi * (cosh_pix1 * sinpi_x2 + sinh_pix2 * cospi_x1) - q2 = C * pi * (sinh_pix1 * cospi_x2 + cosh_pix2 * sinpi_x1) - end - return SVector(phi, q1, q2) +@inline function initial_condition_harmonic_nonperiodic(x, t, + equations::HyperbolicDiffusionEquations2D) + # elliptic equation: -ν Δϕ = 0 in Ω, u = g on ∂Ω + if t == 0.0 + phi = 1.0 + q1 = 1.0 + q2 = 1.0 + else + C = inv(sinh(pi)) + sinpi_x1, cospi_x1 = sincos(pi * x[1]) + sinpi_x2, cospi_x2 = sincos(pi * x[2]) + sinh_pix1 = sinh(pi * x[1]) + cosh_pix1 = cosh(pi * x[1]) + sinh_pix2 = sinh(pi * x[2]) + cosh_pix2 = cosh(pi * x[2]) + phi = C * (sinh_pix1 * sinpi_x2 + sinh_pix2 * sinpi_x1) + q1 = C * pi * (cosh_pix1 * sinpi_x2 + sinh_pix2 * cospi_x1) + q2 = C * pi * (sinh_pix1 * cospi_x2 + cosh_pix2 * sinpi_x1) + end + return SVector(phi, q1, q2) end initial_condition = initial_condition_harmonic_nonperiodic boundary_conditions = BoundaryConditionDirichlet(initial_condition) -solver = DGSEM(polydeg=4, surface_flux=flux_godunov) +solver = DGSEM(polydeg = 4, surface_flux = flux_godunov) coordinates_min = (0.0, 0.0) coordinates_max = (1.0, 1.0) mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=3, - n_cells_max=30_000, - periodicity=false) - + initial_refinement_level = 3, + n_cells_max = 30_000, + periodicity = false) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver, - boundary_conditions=boundary_conditions, - source_terms=source_terms_harmonic) - + boundary_conditions = boundary_conditions, + source_terms = source_terms_harmonic) ############################################################################### # ODE solvers, callbacks etc. @@ -55,30 +54,29 @@ ode = semidiscretize(semi, tspan); summary_callback = SummaryCallback() resid_tol = 5.0e-12 -steady_state_callback = SteadyStateCallback(abstol=resid_tol, reltol=0.0) +steady_state_callback = SteadyStateCallback(abstol = resid_tol, reltol = 0.0) analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=100, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 100, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) -stepsize_callback = StepsizeCallback(cfl=1.0) +stepsize_callback = StepsizeCallback(cfl = 1.0) callbacks = CallbackSet(summary_callback, steady_state_callback, analysis_callback, alive_callback, save_solution, stepsize_callback) - ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/tree_2d_dgsem/elixir_hypdiff_lax_friedrichs.jl b/examples/tree_2d_dgsem/elixir_hypdiff_lax_friedrichs.jl index d0d706981a2..a1a0397a46c 100644 --- a/examples/tree_2d_dgsem/elixir_hypdiff_lax_friedrichs.jl +++ b/examples/tree_2d_dgsem/elixir_hypdiff_lax_friedrichs.jl @@ -8,49 +8,48 @@ using Trixi equations = HyperbolicDiffusionEquations2D() function initial_condition_poisson_periodic(x, t, equations::HyperbolicDiffusionEquations2D) - # elliptic equation: -νΔϕ = f - # depending on initial constant state, c, for phi this converges to the solution ϕ + c - if iszero(t) - phi = 0.0 - q1 = 0.0 - q2 = 0.0 - else - phi = sin(2.0*pi*x[1])*sin(2.0*pi*x[2]) - q1 = 2*pi*cos(2.0*pi*x[1])*sin(2.0*pi*x[2]) - q2 = 2*pi*sin(2.0*pi*x[1])*cos(2.0*pi*x[2]) - end - return SVector(phi, q1, q2) + # elliptic equation: -νΔϕ = f + # depending on initial constant state, c, for phi this converges to the solution ϕ + c + if iszero(t) + phi = 0.0 + q1 = 0.0 + q2 = 0.0 + else + phi = sin(2.0 * pi * x[1]) * sin(2.0 * pi * x[2]) + q1 = 2 * pi * cos(2.0 * pi * x[1]) * sin(2.0 * pi * x[2]) + q2 = 2 * pi * sin(2.0 * pi * x[1]) * cos(2.0 * pi * x[2]) + end + return SVector(phi, q1, q2) end initial_condition = initial_condition_poisson_periodic -@inline function source_terms_poisson_periodic(u, x, t, equations::HyperbolicDiffusionEquations2D) - # elliptic equation: -νΔϕ = f - # analytical solution: phi = sin(2πx)*sin(2πy) and f = -8νπ^2 sin(2πx)*sin(2πy) - @unpack inv_Tr = equations - C = -8 * equations.nu * pi^2 - - x1, x2 = x - tmp1 = sinpi(2 * x1) - tmp2 = sinpi(2 * x2) - du1 = -C*tmp1*tmp2 - du2 = -inv_Tr * u[2] - du3 = -inv_Tr * u[3] - - return SVector(du1, du2, du3) +@inline function source_terms_poisson_periodic(u, x, t, + equations::HyperbolicDiffusionEquations2D) + # elliptic equation: -νΔϕ = f + # analytical solution: phi = sin(2πx)*sin(2πy) and f = -8νπ^2 sin(2πx)*sin(2πy) + @unpack inv_Tr = equations + C = -8 * equations.nu * pi^2 + + x1, x2 = x + tmp1 = sinpi(2 * x1) + tmp2 = sinpi(2 * x2) + du1 = -C * tmp1 * tmp2 + du2 = -inv_Tr * u[2] + du3 = -inv_Tr * u[3] + + return SVector(du1, du2, du3) end -solver = DGSEM(polydeg=3, surface_flux=flux_lax_friedrichs) +solver = DGSEM(polydeg = 3, surface_flux = flux_lax_friedrichs) coordinates_min = (0.0, 0.0) coordinates_max = (1.0, 1.0) mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=3, - n_cells_max=30_000) - + initial_refinement_level = 3, + n_cells_max = 30_000) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver, - source_terms=source_terms_poisson_periodic) - + source_terms = source_terms_poisson_periodic) ############################################################################### # ODE solvers, callbacks etc. @@ -61,31 +60,30 @@ ode = semidiscretize(semi, tspan); summary_callback = SummaryCallback() resid_tol = 5.0e-12 -steady_state_callback = SteadyStateCallback(abstol=resid_tol, reltol=0.0) +steady_state_callback = SteadyStateCallback(abstol = resid_tol, reltol = 0.0) analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval, - extra_analysis_integrals=(entropy, energy_total)) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval, + extra_analysis_integrals = (entropy, energy_total)) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=100, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 100, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) -stepsize_callback = StepsizeCallback(cfl=1.2) +stepsize_callback = StepsizeCallback(cfl = 1.2) callbacks = CallbackSet(summary_callback, steady_state_callback, analysis_callback, alive_callback, save_solution, stepsize_callback) - ############################################################################### # run the simulation sol = Trixi.solve(ode, Trixi.HypDiffN3Erk3Sstar52(), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/tree_2d_dgsem/elixir_hypdiff_nonperiodic.jl b/examples/tree_2d_dgsem/elixir_hypdiff_nonperiodic.jl index fc825660f1e..1396481a3f1 100644 --- a/examples/tree_2d_dgsem/elixir_hypdiff_nonperiodic.jl +++ b/examples/tree_2d_dgsem/elixir_hypdiff_nonperiodic.jl @@ -9,25 +9,23 @@ equations = HyperbolicDiffusionEquations2D() initial_condition = initial_condition_poisson_nonperiodic # 1 => -x, 2 => +x, 3 => -y, 4 => +y as usual for orientations -boundary_conditions = (x_neg=boundary_condition_poisson_nonperiodic, - x_pos=boundary_condition_poisson_nonperiodic, - y_neg=boundary_condition_periodic, - y_pos=boundary_condition_periodic) +boundary_conditions = (x_neg = boundary_condition_poisson_nonperiodic, + x_pos = boundary_condition_poisson_nonperiodic, + y_neg = boundary_condition_periodic, + y_pos = boundary_condition_periodic) -solver = DGSEM(polydeg=4, surface_flux=flux_lax_friedrichs) +solver = DGSEM(polydeg = 4, surface_flux = flux_lax_friedrichs) coordinates_min = (0.0, 0.0) coordinates_max = (1.0, 1.0) mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=3, - n_cells_max=30_000, - periodicity=(false, true)) - + initial_refinement_level = 3, + n_cells_max = 30_000, + periodicity = (false, true)) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver, - boundary_conditions=boundary_conditions, - source_terms=source_terms_poisson_nonperiodic) - + boundary_conditions = boundary_conditions, + source_terms = source_terms_poisson_nonperiodic) ############################################################################### # ODE solvers, callbacks etc. @@ -38,30 +36,29 @@ ode = semidiscretize(semi, tspan); summary_callback = SummaryCallback() resid_tol = 5.0e-12 -steady_state_callback = SteadyStateCallback(abstol=resid_tol, reltol=0.0) +steady_state_callback = SteadyStateCallback(abstol = resid_tol, reltol = 0.0) analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=100, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 100, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) -stepsize_callback = StepsizeCallback(cfl=1.0) +stepsize_callback = StepsizeCallback(cfl = 1.0) callbacks = CallbackSet(summary_callback, steady_state_callback, analysis_callback, alive_callback, save_solution, stepsize_callback) - ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/tree_2d_dgsem/elixir_kpp.jl b/examples/tree_2d_dgsem/elixir_kpp.jl index f3cbc1cb664..b48bde0d155 100644 --- a/examples/tree_2d_dgsem/elixir_kpp.jl +++ b/examples/tree_2d_dgsem/elixir_kpp.jl @@ -25,22 +25,25 @@ end @inline function Trixi.flux_ec(u_ll, u_rr, orientation::Integer, ::KPPEquation2D) # The tolerance of 1e-12 is based on experience and somewhat arbitrarily chosen if abs(u_ll[1] - u_rr[1]) < 1e-12 - return 0.5 * (flux(u_ll, orientation, KPPEquation2D()) + flux(u_rr, orientation, KPPEquation2D())) + return 0.5 * (flux(u_ll, orientation, KPPEquation2D()) + + flux(u_rr, orientation, KPPEquation2D())) else factor = 1.0 / (u_rr[1] - u_ll[1]) if orientation == 1 - return SVector(factor*(-cos(u_rr[1]) + cos(u_ll[1]))) + return SVector(factor * (-cos(u_rr[1]) + cos(u_ll[1]))) else - return SVector(factor*(sin(u_rr[1]) - sin(u_ll[1]))) + return SVector(factor * (sin(u_rr[1]) - sin(u_ll[1]))) end end end # Wavespeeds @inline wavespeed(::KPPEquation2D) = 1.0 -@inline Trixi.max_abs_speeds(u, equation::KPPEquation2D) = (wavespeed(equation), wavespeed(equation)) +@inline Trixi.max_abs_speeds(u, equation::KPPEquation2D) = (wavespeed(equation), + wavespeed(equation)) @inline Trixi.max_abs_speed_naive(u_ll, u_rr, orientation::Integer, equation::KPPEquation2D) = wavespeed(equation) -@inline Trixi.max_abs_speed_naive(u_ll, u_rr, normal_direction::AbstractVector, equation::KPPEquation2D) = wavespeed(equation) * norm(normal_direction) +@inline Trixi.max_abs_speed_naive(u_ll, u_rr, normal_direction::AbstractVector, equation::KPPEquation2D) = wavespeed(equation) * + norm(normal_direction) # Compute entropy: we use the square entropy @inline Trixi.entropy(u::Real, ::KPPEquation2D) = 0.5 * u^2 @@ -74,24 +77,25 @@ volume_flux = flux_ec polydeg = 3 basis = LobattoLegendreBasis(polydeg) shock_indicator = IndicatorHennemannGassner(equation, basis, - alpha_max=0.5, - alpha_min=0.001, - alpha_smooth=true, - variable=first) + alpha_max = 0.5, + alpha_min = 0.001, + alpha_smooth = true, + variable = first) volume_integral = VolumeIntegralShockCapturingHG(shock_indicator; - volume_flux_dg=volume_flux, - volume_flux_fv=surface_flux) -solver = DGSEM(polydeg=polydeg, surface_flux=surface_flux, volume_integral=volume_integral) + volume_flux_dg = volume_flux, + volume_flux_fv = surface_flux) +solver = DGSEM(polydeg = polydeg, surface_flux = surface_flux, + volume_integral = volume_integral) ############################################################################### # Set up the tree mesh (initially a Cartesian grid of [-2,2]^2) coordinates_min = (-2.0, -2.0) -coordinates_max = ( 2.0, 2.0) +coordinates_max = (2.0, 2.0) mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=6, - periodicity=true, - n_cells_max=500_000) + initial_refinement_level = 6, + periodicity = true, + n_cells_max = 500_000) ############################################################################### # Create the semi discretization object @@ -100,23 +104,24 @@ semi = SemidiscretizationHyperbolic(mesh, equation, initial_condition_kpp, solve ############################################################################### # Set up adaptive mesh refinement amr_indicator = IndicatorHennemannGassner(semi, - alpha_max=1.0, - alpha_min=0.0001, - alpha_smooth=false, - variable=first) + alpha_max = 1.0, + alpha_min = 0.0001, + alpha_smooth = false, + variable = first) max_refinement_level = 8 amr_controller = ControllerThreeLevelCombined(semi, amr_indicator, shock_indicator, - base_level=2, - med_level=0, med_threshold=0.0003, - max_level=max_refinement_level, max_threshold=0.003, - max_threshold_secondary=shock_indicator.alpha_max) + base_level = 2, + med_level = 0, med_threshold = 0.0003, + max_level = max_refinement_level, + max_threshold = 0.003, + max_threshold_secondary = shock_indicator.alpha_max) amr_callback = AMRCallback(semi, amr_controller, - interval=1, - adapt_initial_condition=true, - adapt_initial_condition_only_refine=true) + interval = 1, + adapt_initial_condition = true, + adapt_initial_condition_only_refine = true) ############################################################################### # ODE solvers, callbacks etc. @@ -125,14 +130,14 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() -analysis_callback = AnalysisCallback(semi, interval=200) +analysis_callback = AnalysisCallback(semi, interval = 200) -alive_callback = AliveCallback(analysis_interval=200) +alive_callback = AliveCallback(analysis_interval = 200) -save_solution = SaveSolutionCallback(interval=200, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2cons) +save_solution = SaveSolutionCallback(interval = 200, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2cons) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, @@ -140,6 +145,6 @@ callbacks = CallbackSet(summary_callback, ############################################################################### # run the simulation -sol = solve(ode, SSPRK43(); ode_default_options()..., callback=callbacks) +sol = solve(ode, SSPRK43(); ode_default_options()..., callback = callbacks) summary_callback() # Print the timer summary diff --git a/examples/tree_2d_dgsem/elixir_lbm_constant.jl b/examples/tree_2d_dgsem/elixir_lbm_constant.jl index 40b16f41ef6..5a4f3074e4e 100644 --- a/examples/tree_2d_dgsem/elixir_lbm_constant.jl +++ b/examples/tree_2d_dgsem/elixir_lbm_constant.jl @@ -5,22 +5,20 @@ using Trixi ############################################################################### # semidiscretization of the Lattice-Boltzmann equations for the D2Q9 scheme -equations = LatticeBoltzmannEquations2D(Ma=0.1, Re=Inf) +equations = LatticeBoltzmannEquations2D(Ma = 0.1, Re = Inf) initial_condition = initial_condition_constant -solver = DGSEM(polydeg=3, surface_flux=flux_godunov) +solver = DGSEM(polydeg = 3, surface_flux = flux_godunov) coordinates_min = (-1.0, -1.0) -coordinates_max = ( 1.0, 1.0) +coordinates_max = (1.0, 1.0) mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=4, - n_cells_max=10_000,) - + initial_refinement_level = 4, + n_cells_max = 10_000) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver) - ############################################################################### # ODE solvers, callbacks etc. @@ -30,19 +28,19 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_restart = SaveRestartCallback(interval=100, - save_final_restart=true) +save_restart = SaveRestartCallback(interval = 100, + save_final_restart = true) -save_solution = SaveSolutionCallback(interval=100, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2macroscopic) +save_solution = SaveSolutionCallback(interval = 100, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2macroscopic) -stepsize_callback = StepsizeCallback(cfl=1.0) +stepsize_callback = StepsizeCallback(cfl = 1.0) collision_callback = LBMCollisionCallback() @@ -52,11 +50,10 @@ callbacks = CallbackSet(summary_callback, stepsize_callback, collision_callback) - ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/tree_2d_dgsem/elixir_lbm_couette.jl b/examples/tree_2d_dgsem/elixir_lbm_couette.jl index 6a33b2fb0ee..1ba040405d1 100644 --- a/examples/tree_2d_dgsem/elixir_lbm_couette.jl +++ b/examples/tree_2d_dgsem/elixir_lbm_couette.jl @@ -5,7 +5,7 @@ using Trixi ############################################################################### # semidiscretization of the Lattice-Boltzmann equations for the D2Q9 scheme -equations = LatticeBoltzmannEquations2D(Ma=0.05, Re=2000) +equations = LatticeBoltzmannEquations2D(Ma = 0.05, Re = 2000) """ initial_condition_couette_unsteady(x, t, equations::LatticeBoltzmannEquations2D) @@ -16,19 +16,20 @@ incompressible Navier-Stokes equations. To be used in combination with this setup will converge to the state set in [`initial_condition_couette_steady`](@ref). """ function initial_condition_couette_unsteady(x, t, equations::LatticeBoltzmannEquations2D) - @unpack L, u0, rho0, nu = equations + @unpack L, u0, rho0, nu = equations - x1, x2 = x - v1 = u0*x2/L - for m in 1:100 - lambda_m = m * pi / L - v1 += 2 * u0 * (-1)^m/(lambda_m * L) * exp(-nu * lambda_m^2 * t) * sin(lambda_m * x2) - end + x1, x2 = x + v1 = u0 * x2 / L + for m in 1:100 + lambda_m = m * pi / L + v1 += 2 * u0 * (-1)^m / (lambda_m * L) * exp(-nu * lambda_m^2 * t) * + sin(lambda_m * x2) + end - rho = 1 - v2 = 0 + rho = 1 + v2 = 0 - return equilibrium_distribution(rho, v1, v2, equations) + return equilibrium_distribution(rho, v1, v2, equations) end initial_condition = initial_condition_couette_unsteady @@ -44,53 +45,49 @@ Moving *upper* wall boundary condition for a Couette flow setup. To be used in c function boundary_condition_couette(u_inner, orientation, direction, x, t, surface_flux_function, equations::LatticeBoltzmannEquations2D) - return boundary_condition_moving_wall_ypos(u_inner, orientation, direction, x, t, - surface_flux_function, equations) + return boundary_condition_moving_wall_ypos(u_inner, orientation, direction, x, t, + surface_flux_function, equations) end function boundary_condition_moving_wall_ypos(u_inner, orientation, direction, x, t, surface_flux_function, equations::LatticeBoltzmannEquations2D) - @assert direction == 4 "moving wall assumed in +y direction" + @assert direction==4 "moving wall assumed in +y direction" - @unpack rho0, u0, weights, c_s = equations - cs_squared = c_s^2 + @unpack rho0, u0, weights, c_s = equations + cs_squared = c_s^2 - pdf1 = u_inner[3] + 2 * weights[1] * rho0 * u0 / cs_squared - pdf2 = u_inner[2] # outgoing - pdf3 = u_inner[1] + 2 * weights[3] * rho0 * (-u0) / cs_squared - pdf4 = u_inner[2] - pdf5 = u_inner[5] # outgoing - pdf6 = u_inner[6] # outgoing - pdf7 = u_inner[5] + 2 * weights[7] * rho0 * (-u0) / cs_squared - pdf8 = u_inner[6] + 2 * weights[8] * rho0 * u0 / cs_squared - pdf9 = u_inner[9] + pdf1 = u_inner[3] + 2 * weights[1] * rho0 * u0 / cs_squared + pdf2 = u_inner[2] # outgoing + pdf3 = u_inner[1] + 2 * weights[3] * rho0 * (-u0) / cs_squared + pdf4 = u_inner[2] + pdf5 = u_inner[5] # outgoing + pdf6 = u_inner[6] # outgoing + pdf7 = u_inner[5] + 2 * weights[7] * rho0 * (-u0) / cs_squared + pdf8 = u_inner[6] + 2 * weights[8] * rho0 * u0 / cs_squared + pdf9 = u_inner[9] - u_boundary = SVector(pdf1, pdf2, pdf3, pdf4, pdf5, pdf6, pdf7, pdf8, pdf9) + u_boundary = SVector(pdf1, pdf2, pdf3, pdf4, pdf5, pdf6, pdf7, pdf8, pdf9) - # Calculate boundary flux (u_inner is "left" of boundary, u_boundary is "right" of boundary) - return surface_flux_function(u_inner, u_boundary, orientation, equations) + # Calculate boundary flux (u_inner is "left" of boundary, u_boundary is "right" of boundary) + return surface_flux_function(u_inner, u_boundary, orientation, equations) end -boundary_conditions = ( - x_neg=boundary_condition_periodic, - x_pos=boundary_condition_periodic, - y_neg=boundary_condition_noslip_wall, - y_pos=boundary_condition_couette, - ) +boundary_conditions = (x_neg = boundary_condition_periodic, + x_pos = boundary_condition_periodic, + y_neg = boundary_condition_noslip_wall, + y_pos = boundary_condition_couette) -solver = DGSEM(polydeg=3, surface_flux=flux_godunov) +solver = DGSEM(polydeg = 3, surface_flux = flux_godunov) coordinates_min = (0.0, 0.0) coordinates_max = (1.0, 1.0) mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=3, - periodicity=(true, false), - n_cells_max=10_000,) - + initial_refinement_level = 3, + periodicity = (true, false), + n_cells_max = 10_000) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver, - boundary_conditions=boundary_conditions) - + boundary_conditions = boundary_conditions) ############################################################################### # ODE solvers, callbacks etc. @@ -101,26 +98,29 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 1000 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) # Custom solution variables: normalize velocities by reference speed `u0` @inline function macroscopic_normalized(u, equations::LatticeBoltzmannEquations2D) - macroscopic = cons2macroscopic(u, equations) - rho, v1, v2, p = macroscopic + macroscopic = cons2macroscopic(u, equations) + rho, v1, v2, p = macroscopic - # Use `typeof(macroscopic)` to avoid having to explicitly add `using StaticArrays` - convert(typeof(macroscopic), (rho, v1/equations.u0, v2/equations.u0, p)) + # Use `typeof(macroscopic)` to avoid having to explicitly add `using StaticArrays` + convert(typeof(macroscopic), (rho, v1 / equations.u0, v2 / equations.u0, p)) +end +function Trixi.varnames(::typeof(macroscopic_normalized), + equations::LatticeBoltzmannEquations2D) + ("rho", "v1_normalized", "v2_normalized", "p") end -Trixi.varnames(::typeof(macroscopic_normalized), equations::LatticeBoltzmannEquations2D) = ("rho", "v1_normalized", "v2_normalized", "p") -save_solution = SaveSolutionCallback(interval=1000, - save_initial_solution=true, - save_final_solution=true, - solution_variables=macroscopic_normalized) +save_solution = SaveSolutionCallback(interval = 1000, + save_initial_solution = true, + save_final_solution = true, + solution_variables = macroscopic_normalized) -stepsize_callback = StepsizeCallback(cfl=1.0) +stepsize_callback = StepsizeCallback(cfl = 1.0) collision_callback = LBMCollisionCallback() @@ -130,11 +130,10 @@ callbacks = CallbackSet(summary_callback, stepsize_callback, collision_callback) - ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/tree_2d_dgsem/elixir_lbm_lid_driven_cavity.jl b/examples/tree_2d_dgsem/elixir_lbm_lid_driven_cavity.jl index a34e784e7ac..d00926cafad 100644 --- a/examples/tree_2d_dgsem/elixir_lbm_lid_driven_cavity.jl +++ b/examples/tree_2d_dgsem/elixir_lbm_lid_driven_cavity.jl @@ -5,7 +5,7 @@ using Trixi ############################################################################### # semidiscretization of the Lattice-Boltzmann equations for the D2Q9 scheme -equations = LatticeBoltzmannEquations2D(Ma=0.1, Re=1000) +equations = LatticeBoltzmannEquations2D(Ma = 0.1, Re = 1000) """ initial_condition_lid_driven_cavity(x, t, equations::LatticeBoltzmannEquations2D) @@ -14,13 +14,13 @@ Initial state for a lid-driven cavity flow setup. To be used in combination with [`boundary_condition_lid_driven_cavity`](@ref) and [`boundary_condition_noslip_wall`](@ref). """ function initial_condition_lid_driven_cavity(x, t, equations::LatticeBoltzmannEquations2D) - @unpack L, u0, nu = equations + @unpack L, u0, nu = equations - rho = 1 - v1 = 0 - v2 = 0 + rho = 1 + v1 = 0 + v2 = 0 - return equilibrium_distribution(rho, v1, v2, equations) + return equilibrium_distribution(rho, v1, v2, equations) end initial_condition = initial_condition_lid_driven_cavity @@ -35,53 +35,49 @@ no-slip wall. To be used in combination with [`initial_condition_lid_driven_cavi function boundary_condition_lid_driven_cavity(u_inner, orientation, direction, x, t, surface_flux_function, equations::LatticeBoltzmannEquations2D) - return boundary_condition_moving_wall_ypos(u_inner, orientation, direction, x, t, - surface_flux_function, equations) + return boundary_condition_moving_wall_ypos(u_inner, orientation, direction, x, t, + surface_flux_function, equations) end function boundary_condition_moving_wall_ypos(u_inner, orientation, direction, x, t, surface_flux_function, equations::LatticeBoltzmannEquations2D) - @assert direction == 4 "moving wall assumed in +y direction" + @assert direction==4 "moving wall assumed in +y direction" - @unpack rho0, u0, weights, c_s = equations - cs_squared = c_s^2 + @unpack rho0, u0, weights, c_s = equations + cs_squared = c_s^2 - pdf1 = u_inner[3] + 2 * weights[1] * rho0 * u0 / cs_squared - pdf2 = u_inner[2] # outgoing - pdf3 = u_inner[1] + 2 * weights[3] * rho0 * (-u0) / cs_squared - pdf4 = u_inner[2] - pdf5 = u_inner[5] # outgoing - pdf6 = u_inner[6] # outgoing - pdf7 = u_inner[5] + 2 * weights[7] * rho0 * (-u0) / cs_squared - pdf8 = u_inner[6] + 2 * weights[8] * rho0 * u0 / cs_squared - pdf9 = u_inner[9] + pdf1 = u_inner[3] + 2 * weights[1] * rho0 * u0 / cs_squared + pdf2 = u_inner[2] # outgoing + pdf3 = u_inner[1] + 2 * weights[3] * rho0 * (-u0) / cs_squared + pdf4 = u_inner[2] + pdf5 = u_inner[5] # outgoing + pdf6 = u_inner[6] # outgoing + pdf7 = u_inner[5] + 2 * weights[7] * rho0 * (-u0) / cs_squared + pdf8 = u_inner[6] + 2 * weights[8] * rho0 * u0 / cs_squared + pdf9 = u_inner[9] - u_boundary = SVector(pdf1, pdf2, pdf3, pdf4, pdf5, pdf6, pdf7, pdf8, pdf9) + u_boundary = SVector(pdf1, pdf2, pdf3, pdf4, pdf5, pdf6, pdf7, pdf8, pdf9) - # Calculate boundary flux (u_inner is "left" of boundary, u_boundary is "right" of boundary) - return surface_flux_function(u_inner, u_boundary, orientation, equations) + # Calculate boundary flux (u_inner is "left" of boundary, u_boundary is "right" of boundary) + return surface_flux_function(u_inner, u_boundary, orientation, equations) end -boundary_conditions = ( - x_neg=boundary_condition_noslip_wall, - x_pos=boundary_condition_noslip_wall, - y_neg=boundary_condition_noslip_wall, - y_pos=boundary_condition_lid_driven_cavity, - ) +boundary_conditions = (x_neg = boundary_condition_noslip_wall, + x_pos = boundary_condition_noslip_wall, + y_neg = boundary_condition_noslip_wall, + y_pos = boundary_condition_lid_driven_cavity) -solver = DGSEM(polydeg=5, surface_flux=flux_godunov) +solver = DGSEM(polydeg = 5, surface_flux = flux_godunov) coordinates_min = (0.0, 0.0) coordinates_max = (1.0, 1.0) mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=4, - periodicity=false, - n_cells_max=10_000,) - + initial_refinement_level = 4, + periodicity = false, + n_cells_max = 10_000) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver, - boundary_conditions=boundary_conditions) - + boundary_conditions = boundary_conditions) ############################################################################### # ODE solvers, callbacks etc. @@ -92,16 +88,16 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 1000 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=1000, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2macroscopic) +save_solution = SaveSolutionCallback(interval = 1000, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2macroscopic) -stepsize_callback = StepsizeCallback(cfl=1.0) +stepsize_callback = StepsizeCallback(cfl = 1.0) collision_callback = LBMCollisionCallback() @@ -111,11 +107,10 @@ callbacks = CallbackSet(summary_callback, stepsize_callback, collision_callback) - ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/tree_2d_dgsem/elixir_linearizedeuler_convergence.jl b/examples/tree_2d_dgsem/elixir_linearizedeuler_convergence.jl index 14459fa4cb8..93272833b74 100644 --- a/examples/tree_2d_dgsem/elixir_linearizedeuler_convergence.jl +++ b/examples/tree_2d_dgsem/elixir_linearizedeuler_convergence.jl @@ -4,25 +4,25 @@ using Trixi ############################################################################### # semidiscretization of the linearized Euler equations -equations = LinearizedEulerEquations2D(v_mean_global=(0.0, 0.0), c_mean_global=1.0, rho_mean_global=1.0) +equations = LinearizedEulerEquations2D(v_mean_global = (0.0, 0.0), c_mean_global = 1.0, + rho_mean_global = 1.0) initial_condition = initial_condition_convergence_test # Create DG solver with polynomial degree = 3 and (local) Lax-Friedrichs/Rusanov flux as surface flux -solver = DGSEM(polydeg=3, surface_flux=flux_lax_friedrichs) +solver = DGSEM(polydeg = 3, surface_flux = flux_lax_friedrichs) coordinates_min = (-1.0, -1.0) # minimum coordinates (min(x), min(y)) -coordinates_max = ( 1.0, 1.0) # maximum coordinates (max(x), max(y)) +coordinates_max = (1.0, 1.0) # maximum coordinates (max(x), max(y)) # Create a uniformly refined mesh with periodic boundaries mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=4, - n_cells_max=30_000) + initial_refinement_level = 4, + n_cells_max = 30_000) # A semidiscretization collects data structures and functions for the spatial discretization semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver) - ############################################################################### # ODE solvers, callbacks etc. @@ -37,28 +37,29 @@ summary_callback = SummaryCallback() analysis_interval = 100 # The AnalysisCallback allows to analyse the solution in regular intervals and prints the results -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) # The SaveSolutionCallback allows to save the solution to a file in regular intervals -save_solution = SaveSolutionCallback(interval=analysis_interval, solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = analysis_interval, + solution_variables = cons2prim) # The AliveCallback prints short status information in regular intervals -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) # The StepsizeCallback handles the re-calculation of the maximum Δt after each time step -stepsize_callback = StepsizeCallback(cfl=0.8) +stepsize_callback = StepsizeCallback(cfl = 0.8) # Create a CallbackSet to collect all callbacks such that they can be passed to the ODE solver -callbacks = CallbackSet(summary_callback, analysis_callback, save_solution, alive_callback, stepsize_callback) - +callbacks = CallbackSet(summary_callback, analysis_callback, save_solution, alive_callback, + stepsize_callback) ############################################################################### # run the simulation # OrdinaryDiffEq's `solve` method evolves the solution in time and executes the passed callbacks -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); # print the timer summary summary_callback() # print the timer summary diff --git a/examples/tree_2d_dgsem/elixir_linearizedeuler_gauss_wall.jl b/examples/tree_2d_dgsem/elixir_linearizedeuler_gauss_wall.jl index 14fe201a291..fad03fab6ef 100644 --- a/examples/tree_2d_dgsem/elixir_linearizedeuler_gauss_wall.jl +++ b/examples/tree_2d_dgsem/elixir_linearizedeuler_gauss_wall.jl @@ -5,33 +5,32 @@ using Trixi ############################################################################### # semidiscretization of the linearized Euler equations -equations = LinearizedEulerEquations2D(v_mean_global=(0.5, 0.0), c_mean_global=1.0, - rho_mean_global=1.0) +equations = LinearizedEulerEquations2D(v_mean_global = (0.5, 0.0), c_mean_global = 1.0, + rho_mean_global = 1.0) # Create DG solver with polynomial degree = 5 and upwind flux as surface flux -solver = DGSEM(polydeg=5, surface_flux=flux_godunov) +solver = DGSEM(polydeg = 5, surface_flux = flux_godunov) coordinates_min = (-100.0, 0.0) # minimum coordinates (min(x), min(y)) coordinates_max = (100.0, 200.0) # maximum coordinates (max(x), max(y)) # Create a uniformly refined mesh with periodic boundaries mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=4, - n_cells_max=100_000, - periodicity=false) + initial_refinement_level = 4, + n_cells_max = 100_000, + periodicity = false) function initial_condition_gauss_wall(x, t, equations::LinearizedEulerEquations2D) - v1_prime = 0.0 - v2_prime = 0.0 - rho_prime = p_prime = exp(-log(2) * (x[1]^2 + (x[2] - 25)^2) / 25) - return SVector(rho_prime, v1_prime, v2_prime, p_prime) + v1_prime = 0.0 + v2_prime = 0.0 + rho_prime = p_prime = exp(-log(2) * (x[1]^2 + (x[2] - 25)^2) / 25) + return SVector(rho_prime, v1_prime, v2_prime, p_prime) end initial_condition = initial_condition_gauss_wall # A semidiscretization collects data structures and functions for the spatial discretization semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver, - boundary_conditions=boundary_condition_wall) - + boundary_conditions = boundary_condition_wall) ############################################################################### # ODE solvers, callbacks etc. @@ -45,24 +44,25 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() # The AnalysisCallback allows to analyse the solution in regular intervals and prints the results -analysis_callback = AnalysisCallback(semi, interval=100) +analysis_callback = AnalysisCallback(semi, interval = 100) # The SaveSolutionCallback allows to save the solution to a file in regular intervals -save_solution = SaveSolutionCallback(interval=100) +save_solution = SaveSolutionCallback(interval = 100) # The StepsizeCallback handles the re-calculation of the maximum Δt after each time step -stepsize_callback = StepsizeCallback(cfl=0.7) +stepsize_callback = StepsizeCallback(cfl = 0.7) # Create a CallbackSet to collect all callbacks such that they can be passed to the ODE solver -callbacks = CallbackSet(summary_callback, analysis_callback, save_solution, stepsize_callback) +callbacks = CallbackSet(summary_callback, analysis_callback, save_solution, + stepsize_callback) ############################################################################### # run the simulation # OrdinaryDiffEq's `solve` method evolves the solution in time and executes the passed callbacks -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks) +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks) # Print the timer summary summary_callback() diff --git a/examples/tree_2d_dgsem/elixir_mhd_alfven_wave.jl b/examples/tree_2d_dgsem/elixir_mhd_alfven_wave.jl index d9e59160e7d..377a07e947e 100644 --- a/examples/tree_2d_dgsem/elixir_mhd_alfven_wave.jl +++ b/examples/tree_2d_dgsem/elixir_mhd_alfven_wave.jl @@ -4,25 +4,24 @@ using Trixi ############################################################################### # semidiscretization of the compressible ideal GLM-MHD equations -gamma = 5/3 +gamma = 5 / 3 equations = IdealGlmMhdEquations2D(gamma) initial_condition = initial_condition_convergence_test volume_flux = (flux_central, flux_nonconservative_powell) -solver = DGSEM(polydeg=3, surface_flux=(flux_lax_friedrichs, flux_nonconservative_powell), - volume_integral=VolumeIntegralFluxDifferencing(volume_flux)) +solver = DGSEM(polydeg = 3, + surface_flux = (flux_lax_friedrichs, flux_nonconservative_powell), + volume_integral = VolumeIntegralFluxDifferencing(volume_flux)) coordinates_min = (0.0, 0.0) coordinates_max = (sqrt(2.0), sqrt(2.0)) mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=4, - n_cells_max=10_000) - + initial_refinement_level = 4, + n_cells_max = 10_000) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver) - ############################################################################### # ODE solvers, callbacks etc. @@ -32,22 +31,25 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval, save_analysis=true, - extra_analysis_integrals=(entropy, energy_total, - energy_kinetic, energy_internal, - energy_magnetic, cross_helicity)) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval, + save_analysis = true, + extra_analysis_integrals = (entropy, energy_total, + energy_kinetic, + energy_internal, + energy_magnetic, + cross_helicity)) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=10, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 10, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) cfl = 1.5 -stepsize_callback = StepsizeCallback(cfl=cfl) +stepsize_callback = StepsizeCallback(cfl = cfl) -glm_speed_callback = GlmSpeedCallback(glm_scale=0.5, cfl=cfl) +glm_speed_callback = GlmSpeedCallback(glm_scale = 0.5, cfl = cfl) callbacks = CallbackSet(summary_callback, analysis_callback, @@ -56,11 +58,10 @@ callbacks = CallbackSet(summary_callback, stepsize_callback, glm_speed_callback) - ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/tree_2d_dgsem/elixir_mhd_alfven_wave_mortar.jl b/examples/tree_2d_dgsem/elixir_mhd_alfven_wave_mortar.jl index 11dfeacde6a..229360f266e 100644 --- a/examples/tree_2d_dgsem/elixir_mhd_alfven_wave_mortar.jl +++ b/examples/tree_2d_dgsem/elixir_mhd_alfven_wave_mortar.jl @@ -4,25 +4,23 @@ using Trixi ############################################################################### # semidiscretization of the compressible ideal GLM-MHD equations -gamma = 5/3 +gamma = 5 / 3 equations = IdealGlmMhdEquations2D(gamma) initial_condition = initial_condition_convergence_test volume_flux = (flux_hindenlang_gassner, flux_nonconservative_powell) -solver = DGSEM(polydeg=3, surface_flux=(flux_hll, flux_nonconservative_powell), - volume_integral=VolumeIntegralFluxDifferencing(volume_flux)) +solver = DGSEM(polydeg = 3, surface_flux = (flux_hll, flux_nonconservative_powell), + volume_integral = VolumeIntegralFluxDifferencing(volume_flux)) coordinates_min = (0.0, 0.0) coordinates_max = (sqrt(2.0), sqrt(2.0)) -refinement_patches = ( - (type="box", coordinates_min=0.25 .* coordinates_max, - coordinates_max=0.75 .* coordinates_max), -) +refinement_patches = ((type = "box", coordinates_min = 0.25 .* coordinates_max, + coordinates_max = 0.75 .* coordinates_max),) mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=4, - refinement_patches=refinement_patches, - n_cells_max=10_000,) + initial_refinement_level = 4, + refinement_patches = refinement_patches, + n_cells_max = 10_000) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver) @@ -35,22 +33,25 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval, save_analysis=true, - extra_analysis_integrals=(entropy, energy_total, - energy_kinetic, energy_internal, - energy_magnetic, cross_helicity)) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval, + save_analysis = true, + extra_analysis_integrals = (entropy, energy_total, + energy_kinetic, + energy_internal, + energy_magnetic, + cross_helicity)) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=10, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 10, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) cfl = 1.0 -stepsize_callback = StepsizeCallback(cfl=cfl) +stepsize_callback = StepsizeCallback(cfl = cfl) -glm_speed_callback = GlmSpeedCallback(glm_scale=0.5, cfl=cfl) +glm_speed_callback = GlmSpeedCallback(glm_scale = 0.5, cfl = cfl) callbacks = CallbackSet(summary_callback, analysis_callback, @@ -62,7 +63,7 @@ callbacks = CallbackSet(summary_callback, ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/tree_2d_dgsem/elixir_mhd_blast_wave.jl b/examples/tree_2d_dgsem/elixir_mhd_blast_wave.jl index af05fffaf54..a0909ca7580 100644 --- a/examples/tree_2d_dgsem/elixir_mhd_blast_wave.jl +++ b/examples/tree_2d_dgsem/elixir_mhd_blast_wave.jl @@ -16,52 +16,50 @@ An MHD blast wave taken from [doi: 10.1365/s13291-018-0178-9](https://doi.org/10.1365/s13291-018-0178-9) """ function initial_condition_blast_wave(x, t, equations::IdealGlmMhdEquations2D) - # setup taken from Derigs et al. DMV article (2018) - # domain must be [-0.5, 0.5] x [-0.5, 0.5], γ = 1.4 - r = sqrt(x[1]^2 + x[2]^2) - f = (0.1 - r)/0.01 - if r <= 0.09 - p = 1000.0 - elseif r >= 0.1 - p = 0.1 - else - p = 0.1 + 999.9*f - end - rho = 1.0 - v1 = 0.0 - v2 = 0.0 - v3 = 0.0 - B1 = 100.0/sqrt(4.0*pi) - B2 = 0.0 - B3 = 0.0 - psi = 0.0 - return prim2cons(SVector(rho, v1, v2, v3, p, B1, B2, B3, psi), equations) + # setup taken from Derigs et al. DMV article (2018) + # domain must be [-0.5, 0.5] x [-0.5, 0.5], γ = 1.4 + r = sqrt(x[1]^2 + x[2]^2) + f = (0.1 - r) / 0.01 + if r <= 0.09 + p = 1000.0 + elseif r >= 0.1 + p = 0.1 + else + p = 0.1 + 999.9 * f + end + rho = 1.0 + v1 = 0.0 + v2 = 0.0 + v3 = 0.0 + B1 = 100.0 / sqrt(4.0 * pi) + B2 = 0.0 + B3 = 0.0 + psi = 0.0 + return prim2cons(SVector(rho, v1, v2, v3, p, B1, B2, B3, psi), equations) end initial_condition = initial_condition_blast_wave surface_flux = (flux_lax_friedrichs, flux_nonconservative_powell) -volume_flux = (flux_central, flux_nonconservative_powell) +volume_flux = (flux_central, flux_nonconservative_powell) basis = LobattoLegendreBasis(3) indicator_sc = IndicatorHennemannGassner(equations, basis, - alpha_max=0.5, - alpha_min=0.001, - alpha_smooth=true, - variable=density_pressure) + alpha_max = 0.5, + alpha_min = 0.001, + alpha_smooth = true, + variable = density_pressure) volume_integral = VolumeIntegralShockCapturingHG(indicator_sc; - volume_flux_dg=volume_flux, - volume_flux_fv=surface_flux) + volume_flux_dg = volume_flux, + volume_flux_fv = surface_flux) solver = DGSEM(basis, surface_flux, volume_integral) coordinates_min = (-0.5, -0.5) -coordinates_max = ( 0.5, 0.5) +coordinates_max = (0.5, 0.5) mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=4, - n_cells_max=10_000) - + initial_refinement_level = 4, + n_cells_max = 10_000) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver) - ############################################################################### # ODE solvers, callbacks etc. @@ -71,32 +69,32 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=100, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 100, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) amr_indicator = IndicatorHennemannGassner(semi, - alpha_max=0.5, - alpha_min=0.001, - alpha_smooth=false, - variable=density_pressure) + alpha_max = 0.5, + alpha_min = 0.001, + alpha_smooth = false, + variable = density_pressure) amr_controller = ControllerThreeLevel(semi, amr_indicator, - base_level=4, - max_level =6, max_threshold=0.01) + base_level = 4, + max_level = 6, max_threshold = 0.01) amr_callback = AMRCallback(semi, amr_controller, - interval=7, - adapt_initial_condition=true, - adapt_initial_condition_only_refine=true) + interval = 7, + adapt_initial_condition = true, + adapt_initial_condition_only_refine = true) cfl = 0.8 -stepsize_callback = StepsizeCallback(cfl=cfl) +stepsize_callback = StepsizeCallback(cfl = cfl) -glm_speed_callback = GlmSpeedCallback(glm_scale=0.5, cfl=cfl) +glm_speed_callback = GlmSpeedCallback(glm_scale = 0.5, cfl = cfl) callbacks = CallbackSet(summary_callback, analysis_callback, @@ -109,7 +107,7 @@ callbacks = CallbackSet(summary_callback, ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/tree_2d_dgsem/elixir_mhd_ec.jl b/examples/tree_2d_dgsem/elixir_mhd_ec.jl index 5873388f798..173d3ed448f 100644 --- a/examples/tree_2d_dgsem/elixir_mhd_ec.jl +++ b/examples/tree_2d_dgsem/elixir_mhd_ec.jl @@ -10,19 +10,18 @@ equations = IdealGlmMhdEquations2D(1.4) initial_condition = initial_condition_weak_blast_wave volume_flux = (flux_hindenlang_gassner, flux_nonconservative_powell) -solver = DGSEM(polydeg=3, surface_flux=(flux_hindenlang_gassner, flux_nonconservative_powell), - volume_integral=VolumeIntegralFluxDifferencing(volume_flux)) +solver = DGSEM(polydeg = 3, + surface_flux = (flux_hindenlang_gassner, flux_nonconservative_powell), + volume_integral = VolumeIntegralFluxDifferencing(volume_flux)) coordinates_min = (-2.0, -2.0) -coordinates_max = ( 2.0, 2.0) +coordinates_max = (2.0, 2.0) mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=4, - n_cells_max=10_000) - + initial_refinement_level = 4, + n_cells_max = 10_000) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver) - ############################################################################### # ODE solvers, callbacks etc. @@ -32,19 +31,19 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=10, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 10, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) cfl = 1.0 -stepsize_callback = StepsizeCallback(cfl=cfl) +stepsize_callback = StepsizeCallback(cfl = cfl) -glm_speed_callback = GlmSpeedCallback(glm_scale=0.5, cfl=cfl) +glm_speed_callback = GlmSpeedCallback(glm_scale = 0.5, cfl = cfl) callbacks = CallbackSet(summary_callback, analysis_callback, @@ -53,11 +52,10 @@ callbacks = CallbackSet(summary_callback, stepsize_callback, glm_speed_callback) - ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/tree_2d_dgsem/elixir_mhd_orszag_tang.jl b/examples/tree_2d_dgsem/elixir_mhd_orszag_tang.jl index 460b24e02b2..7f26f270d6e 100644 --- a/examples/tree_2d_dgsem/elixir_mhd_orszag_tang.jl +++ b/examples/tree_2d_dgsem/elixir_mhd_orszag_tang.jl @@ -4,7 +4,7 @@ using Trixi ############################################################################### # semidiscretization of the compressible ideal GLM-MHD equations -gamma = 5/3 +gamma = 5 / 3 equations = IdealGlmMhdEquations2D(gamma) """ @@ -16,44 +16,42 @@ The classical Orszag-Tang vortex test case. Here, the setup is taken from [doi: 10.1365/s13291-018-0178-9](https://doi.org/10.1365/s13291-018-0178-9) """ function initial_condition_orszag_tang(x, t, equations::IdealGlmMhdEquations2D) - # setup taken from Derigs et al. DMV article (2018) - # domain must be [0, 1] x [0, 1], γ = 5/3 - rho = 1.0 - v1 = -sin(2.0*pi*x[2]) - v2 = sin(2.0*pi*x[1]) - v3 = 0.0 - p = 1.0 / equations.gamma - B1 = -sin(2.0*pi*x[2]) / equations.gamma - B2 = sin(4.0*pi*x[1]) / equations.gamma - B3 = 0.0 - psi = 0.0 - return prim2cons(SVector(rho, v1, v2, v3, p, B1, B2, B3, psi), equations) + # setup taken from Derigs et al. DMV article (2018) + # domain must be [0, 1] x [0, 1], γ = 5/3 + rho = 1.0 + v1 = -sin(2.0 * pi * x[2]) + v2 = sin(2.0 * pi * x[1]) + v3 = 0.0 + p = 1.0 / equations.gamma + B1 = -sin(2.0 * pi * x[2]) / equations.gamma + B2 = sin(4.0 * pi * x[1]) / equations.gamma + B3 = 0.0 + psi = 0.0 + return prim2cons(SVector(rho, v1, v2, v3, p, B1, B2, B3, psi), equations) end initial_condition = initial_condition_orszag_tang surface_flux = (flux_lax_friedrichs, flux_nonconservative_powell) -volume_flux = (flux_central, flux_nonconservative_powell) +volume_flux = (flux_central, flux_nonconservative_powell) basis = LobattoLegendreBasis(3) indicator_sc = IndicatorHennemannGassner(equations, basis, - alpha_max=0.5, - alpha_min=0.001, - alpha_smooth=true, - variable=density_pressure) + alpha_max = 0.5, + alpha_min = 0.001, + alpha_smooth = true, + variable = density_pressure) volume_integral = VolumeIntegralShockCapturingHG(indicator_sc; - volume_flux_dg=volume_flux, - volume_flux_fv=surface_flux) + volume_flux_dg = volume_flux, + volume_flux_fv = surface_flux) solver = DGSEM(basis, surface_flux, volume_integral) coordinates_min = (0.0, 0.0) coordinates_max = (1.0, 1.0) mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=4, - n_cells_max=10_000) - + initial_refinement_level = 4, + n_cells_max = 10_000) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver) - ############################################################################### # ODE solvers, callbacks etc. @@ -63,32 +61,32 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=100, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 100, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) amr_indicator = IndicatorHennemannGassner(semi, - alpha_max=0.5, - alpha_min=0.001, - alpha_smooth=false, - variable=density_pressure) + alpha_max = 0.5, + alpha_min = 0.001, + alpha_smooth = false, + variable = density_pressure) amr_controller = ControllerThreeLevel(semi, amr_indicator, - base_level=4, - max_level =6, max_threshold=0.01) + base_level = 4, + max_level = 6, max_threshold = 0.01) amr_callback = AMRCallback(semi, amr_controller, - interval=6, - adapt_initial_condition=true, - adapt_initial_condition_only_refine=true) + interval = 6, + adapt_initial_condition = true, + adapt_initial_condition_only_refine = true) cfl = 1.25 -stepsize_callback = StepsizeCallback(cfl=cfl) +stepsize_callback = StepsizeCallback(cfl = cfl) -glm_speed_callback = GlmSpeedCallback(glm_scale=0.5, cfl=cfl) +glm_speed_callback = GlmSpeedCallback(glm_scale = 0.5, cfl = cfl) callbacks = CallbackSet(summary_callback, analysis_callback, @@ -101,7 +99,7 @@ callbacks = CallbackSet(summary_callback, ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/tree_2d_dgsem/elixir_mhd_rotor.jl b/examples/tree_2d_dgsem/elixir_mhd_rotor.jl index c6d880e9e9d..3109b1ce303 100644 --- a/examples/tree_2d_dgsem/elixir_mhd_rotor.jl +++ b/examples/tree_2d_dgsem/elixir_mhd_rotor.jl @@ -2,7 +2,6 @@ using OrdinaryDiffEq using Trixi - ############################################################################### # semidiscretization of the compressible ideal GLM-MHD equations equations = IdealGlmMhdEquations2D(1.4) @@ -16,59 +15,57 @@ The classical MHD rotor test case. Here, the setup is taken from [doi: 10.1365/s13291-018-0178-9](https://doi.org/10.1365/s13291-018-0178-9) """ function initial_condition_rotor(x, t, equations::IdealGlmMhdEquations2D) - # setup taken from Derigs et al. DMV article (2018) - # domain must be [0, 1] x [0, 1], γ = 1.4 - dx = x[1] - 0.5 - dy = x[2] - 0.5 - r = sqrt(dx^2 + dy^2) - f = (0.115 - r)/0.015 - if r <= 0.1 - rho = 10.0 - v1 = -20.0*dy - v2 = 20.0*dx - elseif r >= 0.115 - rho = 1.0 - v1 = 0.0 - v2 = 0.0 - else - rho = 1.0 + 9.0*f - v1 = -20.0*f*dy - v2 = 20.0*f*dx - end - v3 = 0.0 - p = 1.0 - B1 = 5.0/sqrt(4.0*pi) - B2 = 0.0 - B3 = 0.0 - psi = 0.0 - return prim2cons(SVector(rho, v1, v2, v3, p, B1, B2, B3, psi), equations) + # setup taken from Derigs et al. DMV article (2018) + # domain must be [0, 1] x [0, 1], γ = 1.4 + dx = x[1] - 0.5 + dy = x[2] - 0.5 + r = sqrt(dx^2 + dy^2) + f = (0.115 - r) / 0.015 + if r <= 0.1 + rho = 10.0 + v1 = -20.0 * dy + v2 = 20.0 * dx + elseif r >= 0.115 + rho = 1.0 + v1 = 0.0 + v2 = 0.0 + else + rho = 1.0 + 9.0 * f + v1 = -20.0 * f * dy + v2 = 20.0 * f * dx + end + v3 = 0.0 + p = 1.0 + B1 = 5.0 / sqrt(4.0 * pi) + B2 = 0.0 + B3 = 0.0 + psi = 0.0 + return prim2cons(SVector(rho, v1, v2, v3, p, B1, B2, B3, psi), equations) end initial_condition = initial_condition_rotor surface_flux = (flux_lax_friedrichs, flux_nonconservative_powell) -volume_flux = (flux_hindenlang_gassner, flux_nonconservative_powell) +volume_flux = (flux_hindenlang_gassner, flux_nonconservative_powell) polydeg = 4 basis = LobattoLegendreBasis(polydeg) indicator_sc = IndicatorHennemannGassner(equations, basis, - alpha_max=0.5, - alpha_min=0.001, - alpha_smooth=true, - variable=density_pressure) + alpha_max = 0.5, + alpha_min = 0.001, + alpha_smooth = true, + variable = density_pressure) volume_integral = VolumeIntegralShockCapturingHG(indicator_sc; - volume_flux_dg=volume_flux, - volume_flux_fv=surface_flux) + volume_flux_dg = volume_flux, + volume_flux_fv = surface_flux) solver = DGSEM(basis, surface_flux, volume_integral) coordinates_min = (0.0, 0.0) coordinates_max = (1.0, 1.0) mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=4, - n_cells_max=10_000) - + initial_refinement_level = 4, + n_cells_max = 10_000) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver) - ############################################################################### # ODE solvers, callbacks etc. @@ -78,32 +75,32 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=100, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 100, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) amr_indicator = IndicatorHennemannGassner(semi, - alpha_max=0.5, - alpha_min=0.001, - alpha_smooth=false, - variable=density_pressure) + alpha_max = 0.5, + alpha_min = 0.001, + alpha_smooth = false, + variable = density_pressure) amr_controller = ControllerThreeLevel(semi, amr_indicator, - base_level=4, - max_level =6, max_threshold=0.01) + base_level = 4, + max_level = 6, max_threshold = 0.01) amr_callback = AMRCallback(semi, amr_controller, - interval=6, - adapt_initial_condition=true, - adapt_initial_condition_only_refine=true) + interval = 6, + adapt_initial_condition = true, + adapt_initial_condition_only_refine = true) cfl = 0.35 -stepsize_callback = StepsizeCallback(cfl=cfl) +stepsize_callback = StepsizeCallback(cfl = cfl) -glm_speed_callback = GlmSpeedCallback(glm_scale=0.5, cfl=cfl) +glm_speed_callback = GlmSpeedCallback(glm_scale = 0.5, cfl = cfl) callbacks = CallbackSet(summary_callback, analysis_callback, @@ -116,7 +113,7 @@ callbacks = CallbackSet(summary_callback, ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/tree_2d_dgsem/elixir_mhd_shockcapturing_subcell.jl b/examples/tree_2d_dgsem/elixir_mhd_shockcapturing_subcell.jl index 2e6429ad9b0..84361ef4f87 100644 --- a/examples/tree_2d_dgsem/elixir_mhd_shockcapturing_subcell.jl +++ b/examples/tree_2d_dgsem/elixir_mhd_shockcapturing_subcell.jl @@ -17,59 +17,57 @@ An MHD blast wave modified from: This setup needs a positivity limiter for the density. """ function initial_condition_blast_wave(x, t, equations::IdealGlmMhdEquations2D) - # setup taken from Derigs et al. DMV article (2018) - # domain must be [-0.5, 0.5] x [-0.5, 0.5], γ = 1.4 - r = sqrt(x[1]^2 + x[2]^2) - - pmax = 10.0 - pmin = 0.01 - rhomax = 1.0 - rhomin = 0.01 - if r <= 0.09 - p = pmax - rho = rhomax - elseif r >= 0.1 - p = pmin - rho = rhomin - else - p = pmin + (0.1 - r) * (pmax - pmin) / 0.01 - rho = rhomin + (0.1 - r) * (rhomax - rhomin) / 0.01 - end - v1 = 0.0 - v2 = 0.0 - v3 = 0.0 - B1 = 1.0/sqrt(4.0*pi) - B2 = 0.0 - B3 = 0.0 - psi = 0.0 - return prim2cons(SVector(rho, v1, v2, v3, p, B1, B2, B3, psi), equations) + # setup taken from Derigs et al. DMV article (2018) + # domain must be [-0.5, 0.5] x [-0.5, 0.5], γ = 1.4 + r = sqrt(x[1]^2 + x[2]^2) + + pmax = 10.0 + pmin = 0.01 + rhomax = 1.0 + rhomin = 0.01 + if r <= 0.09 + p = pmax + rho = rhomax + elseif r >= 0.1 + p = pmin + rho = rhomin + else + p = pmin + (0.1 - r) * (pmax - pmin) / 0.01 + rho = rhomin + (0.1 - r) * (rhomax - rhomin) / 0.01 + end + v1 = 0.0 + v2 = 0.0 + v3 = 0.0 + B1 = 1.0 / sqrt(4.0 * pi) + B2 = 0.0 + B3 = 0.0 + psi = 0.0 + return prim2cons(SVector(rho, v1, v2, v3, p, B1, B2, B3, psi), equations) end initial_condition = initial_condition_blast_wave surface_flux = (flux_lax_friedrichs, flux_nonconservative_powell_local_symmetric) -volume_flux = (flux_derigs_etal, flux_nonconservative_powell_local_symmetric) +volume_flux = (flux_derigs_etal, flux_nonconservative_powell_local_symmetric) basis = LobattoLegendreBasis(3) limiter_idp = SubcellLimiterIDP(equations, basis; - positivity_variables_cons=[1], - positivity_variables_nonlinear=[pressure], - positivity_correction_factor=0.1, - bar_states=false) + positivity_variables_cons = [1], + positivity_variables_nonlinear = [pressure], + positivity_correction_factor = 0.1, + bar_states = false) volume_integral = VolumeIntegralSubcellLimiting(limiter_idp; - volume_flux_dg=volume_flux, - volume_flux_fv=surface_flux) + volume_flux_dg = volume_flux, + volume_flux_fv = surface_flux) solver = DGSEM(basis, surface_flux, volume_integral) coordinates_min = (-0.5, -0.5) -coordinates_max = ( 0.5, 0.5) +coordinates_max = (0.5, 0.5) mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=4, - n_cells_max=10_000) - + initial_refinement_level = 4, + n_cells_max = 10_000) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver) - ############################################################################### # ODE solvers, callbacks etc. @@ -79,19 +77,19 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=100, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 100, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) cfl = 0.4 -stepsize_callback = StepsizeCallback(cfl=cfl) +stepsize_callback = StepsizeCallback(cfl = cfl) -glm_speed_callback = GlmSpeedCallback(glm_scale=0.5, cfl=cfl) +glm_speed_callback = GlmSpeedCallback(glm_scale = 0.5, cfl = cfl) callbacks = CallbackSet(summary_callback, analysis_callback, @@ -104,7 +102,7 @@ callbacks = CallbackSet(summary_callback, # run the simulation stage_callbacks = (SubcellLimiterIDPCorrection(), BoundsCheckCallback()) -sol = Trixi.solve(ode, Trixi.SimpleSSPRK33(stage_callbacks=stage_callbacks); - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = Trixi.solve(ode, Trixi.SimpleSSPRK33(stage_callbacks = stage_callbacks); + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/tree_2d_dgsem/elixir_mhdmulti_convergence.jl b/examples/tree_2d_dgsem/elixir_mhdmulti_convergence.jl index a7551f48937..4f1f8c5f2b7 100644 --- a/examples/tree_2d_dgsem/elixir_mhdmulti_convergence.jl +++ b/examples/tree_2d_dgsem/elixir_mhdmulti_convergence.jl @@ -5,25 +5,24 @@ using Trixi ############################################################################### # semidiscretization of the compressible ideal GLM-MHD equations -equations = IdealGlmMhdMulticomponentEquations2D(gammas = (5/3, 5/3, 5/3), - gas_constants = (2.08, 2.08, 2.08)) +equations = IdealGlmMhdMulticomponentEquations2D(gammas = (5 / 3, 5 / 3, 5 / 3), + gas_constants = (2.08, 2.08, 2.08)) initial_condition = initial_condition_convergence_test volume_flux = (flux_hindenlang_gassner, flux_nonconservative_powell) -solver = DGSEM(polydeg=3, surface_flux=(flux_lax_friedrichs, flux_nonconservative_powell), - volume_integral=VolumeIntegralFluxDifferencing(volume_flux)) +solver = DGSEM(polydeg = 3, + surface_flux = (flux_lax_friedrichs, flux_nonconservative_powell), + volume_integral = VolumeIntegralFluxDifferencing(volume_flux)) coordinates_min = (0.0, 0.0) coordinates_max = (sqrt(2), sqrt(2)) mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=2, - n_cells_max=10_000) - + initial_refinement_level = 2, + n_cells_max = 10_000) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver) - ############################################################################### # ODE solvers, callbacks etc. @@ -33,19 +32,20 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval, save_analysis=true) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval, + save_analysis = true) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=10, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 10, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) cfl = 1.0 -stepsize_callback = StepsizeCallback(cfl=cfl) +stepsize_callback = StepsizeCallback(cfl = cfl) -glm_speed_callback = GlmSpeedCallback(glm_scale=0.5, cfl=cfl) +glm_speed_callback = GlmSpeedCallback(glm_scale = 0.5, cfl = cfl) callbacks = CallbackSet(summary_callback, analysis_callback, @@ -54,11 +54,10 @@ callbacks = CallbackSet(summary_callback, stepsize_callback, glm_speed_callback) - ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/tree_2d_dgsem/elixir_mhdmulti_ec.jl b/examples/tree_2d_dgsem/elixir_mhdmulti_ec.jl index ec2f3c21cdd..a7db9eeee96 100644 --- a/examples/tree_2d_dgsem/elixir_mhdmulti_ec.jl +++ b/examples/tree_2d_dgsem/elixir_mhdmulti_ec.jl @@ -5,25 +5,24 @@ using Trixi ############################################################################### # semidiscretization of the compressible ideal GLM-MHD equations -equations = IdealGlmMhdMulticomponentEquations2D(gammas = (1.4, 1.4), - gas_constants = (1.0, 1.0)) +equations = IdealGlmMhdMulticomponentEquations2D(gammas = (1.4, 1.4), + gas_constants = (1.0, 1.0)) initial_condition = initial_condition_weak_blast_wave volume_flux = (flux_hindenlang_gassner, flux_nonconservative_powell) -solver = DGSEM(polydeg=3, surface_flux=(flux_hindenlang_gassner, flux_nonconservative_powell), - volume_integral=VolumeIntegralFluxDifferencing(volume_flux)) +solver = DGSEM(polydeg = 3, + surface_flux = (flux_hindenlang_gassner, flux_nonconservative_powell), + volume_integral = VolumeIntegralFluxDifferencing(volume_flux)) coordinates_min = (-2.0, -2.0) -coordinates_max = ( 2.0, 2.0) +coordinates_max = (2.0, 2.0) mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=4, - n_cells_max=10_000) - + initial_refinement_level = 4, + n_cells_max = 10_000) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver) - ############################################################################### # ODE solvers, callbacks etc. @@ -33,19 +32,19 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=10, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 10, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) cfl = 1.0 -stepsize_callback = StepsizeCallback(cfl=cfl) +stepsize_callback = StepsizeCallback(cfl = cfl) -glm_speed_callback = GlmSpeedCallback(glm_scale=0.5, cfl=cfl) +glm_speed_callback = GlmSpeedCallback(glm_scale = 0.5, cfl = cfl) callbacks = CallbackSet(summary_callback, analysis_callback, @@ -54,11 +53,10 @@ callbacks = CallbackSet(summary_callback, stepsize_callback, glm_speed_callback) - ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/tree_2d_dgsem/elixir_mhdmulti_es.jl b/examples/tree_2d_dgsem/elixir_mhdmulti_es.jl index 3cd9c621ae3..fcaabdc7a58 100644 --- a/examples/tree_2d_dgsem/elixir_mhdmulti_es.jl +++ b/examples/tree_2d_dgsem/elixir_mhdmulti_es.jl @@ -5,25 +5,24 @@ using Trixi ############################################################################### # semidiscretization of the compressible ideal GLM-MHD equations -equations = IdealGlmMhdMulticomponentEquations2D(gammas = (5/3, 5/3), - gas_constants = (0.2, 0.2)) +equations = IdealGlmMhdMulticomponentEquations2D(gammas = (5 / 3, 5 / 3), + gas_constants = (0.2, 0.2)) initial_condition = initial_condition_weak_blast_wave volume_flux = (flux_hindenlang_gassner, flux_nonconservative_powell) -solver = DGSEM(polydeg=3, surface_flux=(flux_lax_friedrichs, flux_nonconservative_powell), - volume_integral=VolumeIntegralFluxDifferencing(volume_flux)) +solver = DGSEM(polydeg = 3, + surface_flux = (flux_lax_friedrichs, flux_nonconservative_powell), + volume_integral = VolumeIntegralFluxDifferencing(volume_flux)) coordinates_min = (-2.0, -2.0) -coordinates_max = ( 2.0, 2.0) +coordinates_max = (2.0, 2.0) mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=4, - n_cells_max=10_000) - + initial_refinement_level = 4, + n_cells_max = 10_000) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver) - ############################################################################### # ODE solvers, callbacks etc. @@ -33,19 +32,19 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=10, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 10, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) cfl = 1.0 -stepsize_callback = StepsizeCallback(cfl=cfl) +stepsize_callback = StepsizeCallback(cfl = cfl) -glm_speed_callback = GlmSpeedCallback(glm_scale=0.5, cfl=cfl) +glm_speed_callback = GlmSpeedCallback(glm_scale = 0.5, cfl = cfl) callbacks = CallbackSet(summary_callback, analysis_callback, @@ -54,11 +53,10 @@ callbacks = CallbackSet(summary_callback, stepsize_callback, glm_speed_callback) - ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/tree_2d_dgsem/elixir_mhdmulti_rotor.jl b/examples/tree_2d_dgsem/elixir_mhdmulti_rotor.jl index 55a4004f794..5ca21cc5e9c 100644 --- a/examples/tree_2d_dgsem/elixir_mhdmulti_rotor.jl +++ b/examples/tree_2d_dgsem/elixir_mhdmulti_rotor.jl @@ -2,10 +2,9 @@ using OrdinaryDiffEq using Trixi - ############################################################################### # semidiscretization of the compressible ideal GLM-MHD equations -equations = IdealGlmMhdMulticomponentEquations2D(gammas = (1.4, 1.4), +equations = IdealGlmMhdMulticomponentEquations2D(gammas = (1.4, 1.4), gas_constants = (1.0, 1.0)) """ @@ -14,62 +13,60 @@ equations = IdealGlmMhdMulticomponentEquations2D(gammas = (1.4, 1.4), The classical MHD rotor test case adapted to two density components. """ function initial_condition_rotor(x, t, equations::IdealGlmMhdMulticomponentEquations2D) - # setup taken from Derigs et al. DMV article (2018) - # domain must be [0, 1] x [0, 1], γ = 1.4 - dx = x[1] - 0.5 - dy = x[2] - 0.5 - r = sqrt(dx^2 + dy^2) - f = (0.115 - r)/0.015 - if r <= 0.1 - rho1 = 10.0 - rho2 = 5.0 - v1 = -20.0*dy - v2 = 20.0*dx - elseif r >= 0.115 - rho1 = 1.0 - rho2 = 0.5 - v1 = 0.0 - v2 = 0.0 - else - rho1 = 1.0 + 9.0*f - rho2 = 0.5 + 4.5*f - v1 = -20.0*f*dy - v2 = 20.0*f*dx - end - v3 = 0.0 - p = 1.0 - B1 = 5.0/sqrt(4.0*pi) - B2 = 0.0 - B3 = 0.0 - psi = 0.0 - return prim2cons(SVector(v1, v2, v3, p, B1, B2, B3, psi, rho1, rho2), equations) + # setup taken from Derigs et al. DMV article (2018) + # domain must be [0, 1] x [0, 1], γ = 1.4 + dx = x[1] - 0.5 + dy = x[2] - 0.5 + r = sqrt(dx^2 + dy^2) + f = (0.115 - r) / 0.015 + if r <= 0.1 + rho1 = 10.0 + rho2 = 5.0 + v1 = -20.0 * dy + v2 = 20.0 * dx + elseif r >= 0.115 + rho1 = 1.0 + rho2 = 0.5 + v1 = 0.0 + v2 = 0.0 + else + rho1 = 1.0 + 9.0 * f + rho2 = 0.5 + 4.5 * f + v1 = -20.0 * f * dy + v2 = 20.0 * f * dx + end + v3 = 0.0 + p = 1.0 + B1 = 5.0 / sqrt(4.0 * pi) + B2 = 0.0 + B3 = 0.0 + psi = 0.0 + return prim2cons(SVector(v1, v2, v3, p, B1, B2, B3, psi, rho1, rho2), equations) end initial_condition = initial_condition_rotor surface_flux = (flux_lax_friedrichs, flux_nonconservative_powell) -volume_flux = (flux_hindenlang_gassner, flux_nonconservative_powell) +volume_flux = (flux_hindenlang_gassner, flux_nonconservative_powell) polydeg = 3 basis = LobattoLegendreBasis(polydeg) indicator_sc = IndicatorHennemannGassner(equations, basis, - alpha_max=0.8, - alpha_min=0.001, - alpha_smooth=true, - variable=density_pressure) + alpha_max = 0.8, + alpha_min = 0.001, + alpha_smooth = true, + variable = density_pressure) volume_integral = VolumeIntegralShockCapturingHG(indicator_sc; - volume_flux_dg=volume_flux, - volume_flux_fv=surface_flux) + volume_flux_dg = volume_flux, + volume_flux_fv = surface_flux) solver = DGSEM(basis, surface_flux, volume_integral) coordinates_min = (0.0, 0.0) coordinates_max = (1.0, 1.0) mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=4, - n_cells_max=10_000) - + initial_refinement_level = 4, + n_cells_max = 10_000) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver) - ############################################################################### # ODE solvers, callbacks etc. @@ -79,32 +76,32 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=100, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 100, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) amr_indicator = IndicatorHennemannGassner(semi, - alpha_max=0.5, - alpha_min=0.001, - alpha_smooth=false, - variable=density_pressure) + alpha_max = 0.5, + alpha_min = 0.001, + alpha_smooth = false, + variable = density_pressure) amr_controller = ControllerThreeLevel(semi, amr_indicator, - base_level=4, - max_level =6, max_threshold=0.01) + base_level = 4, + max_level = 6, max_threshold = 0.01) amr_callback = AMRCallback(semi, amr_controller, - interval=6, - adapt_initial_condition=true, - adapt_initial_condition_only_refine=true) + interval = 6, + adapt_initial_condition = true, + adapt_initial_condition_only_refine = true) cfl = 1.0 -stepsize_callback = StepsizeCallback(cfl=cfl) +stepsize_callback = StepsizeCallback(cfl = cfl) -glm_speed_callback = GlmSpeedCallback(glm_scale=0.5, cfl=cfl) +glm_speed_callback = GlmSpeedCallback(glm_scale = 0.5, cfl = cfl) callbacks = CallbackSet(summary_callback, analysis_callback, @@ -117,7 +114,7 @@ callbacks = CallbackSet(summary_callback, ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/tree_2d_dgsem/elixir_navierstokes_convergence.jl b/examples/tree_2d_dgsem/elixir_navierstokes_convergence.jl index b68e9e6c97e..57558224854 100644 --- a/examples/tree_2d_dgsem/elixir_navierstokes_convergence.jl +++ b/examples/tree_2d_dgsem/elixir_navierstokes_convergence.jl @@ -8,163 +8,170 @@ prandtl_number() = 0.72 mu() = 0.01 equations = CompressibleEulerEquations2D(1.4) -equations_parabolic = CompressibleNavierStokesDiffusion2D(equations, mu=mu(), Prandtl=prandtl_number(), - gradient_variables=GradientVariablesPrimitive()) +equations_parabolic = CompressibleNavierStokesDiffusion2D(equations, mu = mu(), + Prandtl = prandtl_number(), + gradient_variables = GradientVariablesPrimitive()) # Create DG solver with polynomial degree = 3 and (local) Lax-Friedrichs/Rusanov flux as surface flux -solver = DGSEM(polydeg=3, surface_flux=flux_lax_friedrichs, - volume_integral=VolumeIntegralWeakForm()) +solver = DGSEM(polydeg = 3, surface_flux = flux_lax_friedrichs, + volume_integral = VolumeIntegralWeakForm()) coordinates_min = (-1.0, -1.0) # minimum coordinates (min(x), min(y)) -coordinates_max = ( 1.0, 1.0) # maximum coordinates (max(x), max(y)) +coordinates_max = (1.0, 1.0) # maximum coordinates (max(x), max(y)) # Create a uniformly refined mesh with periodic boundaries mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=4, - periodicity=(true, false), - n_cells_max=30_000) # set maximum capacity of tree data structure + initial_refinement_level = 4, + periodicity = (true, false), + n_cells_max = 30_000) # set maximum capacity of tree data structure # Note: the initial condition cannot be specialized to `CompressibleNavierStokesDiffusion2D` # since it is called by both the parabolic solver (which passes in `CompressibleNavierStokesDiffusion2D`) # and by the initial condition (which passes in `CompressibleEulerEquations2D`). # This convergence test setup was originally derived by Andrew Winters (@andrewwinters5000) function initial_condition_navier_stokes_convergence_test(x, t, equations) - # Amplitude and shift - A = 0.5 - c = 2.0 + # Amplitude and shift + A = 0.5 + c = 2.0 - # convenience values for trig. functions - pi_x = pi * x[1] - pi_y = pi * x[2] - pi_t = pi * t + # convenience values for trig. functions + pi_x = pi * x[1] + pi_y = pi * x[2] + pi_t = pi * t - rho = c + A * sin(pi_x) * cos(pi_y) * cos(pi_t) - v1 = sin(pi_x) * log(x[2] + 2.0) * (1.0 - exp(-A * (x[2] - 1.0)) ) * cos(pi_t) - v2 = v1 - p = rho^2 + rho = c + A * sin(pi_x) * cos(pi_y) * cos(pi_t) + v1 = sin(pi_x) * log(x[2] + 2.0) * (1.0 - exp(-A * (x[2] - 1.0))) * cos(pi_t) + v2 = v1 + p = rho^2 - return prim2cons(SVector(rho, v1, v2, p), equations) + return prim2cons(SVector(rho, v1, v2, p), equations) end @inline function source_terms_navier_stokes_convergence_test(u, x, t, equations) - y = x[2] - - # TODO: parabolic - # we currently need to hardcode these parameters until we fix the "combined equation" issue - # see also https://github.com/trixi-framework/Trixi.jl/pull/1160 - inv_gamma_minus_one = inv(equations.gamma - 1) - Pr = prandtl_number() - mu_ = mu() - - # Same settings as in `initial_condition` - # Amplitude and shift - A = 0.5 - c = 2.0 - - # convenience values for trig. functions - pi_x = pi * x[1] - pi_y = pi * x[2] - pi_t = pi * t - - # compute the manufactured solution and all necessary derivatives - rho = c + A * sin(pi_x) * cos(pi_y) * cos(pi_t) - rho_t = -pi * A * sin(pi_x) * cos(pi_y) * sin(pi_t) - rho_x = pi * A * cos(pi_x) * cos(pi_y) * cos(pi_t) - rho_y = -pi * A * sin(pi_x) * sin(pi_y) * cos(pi_t) - rho_xx = -pi * pi * A * sin(pi_x) * cos(pi_y) * cos(pi_t) - rho_yy = -pi * pi * A * sin(pi_x) * cos(pi_y) * cos(pi_t) - - v1 = sin(pi_x) * log(y + 2.0) * (1.0 - exp(-A * (y - 1.0))) * cos(pi_t) - v1_t = -pi * sin(pi_x) * log(y + 2.0) * (1.0 - exp(-A * (y - 1.0))) * sin(pi_t) - v1_x = pi * cos(pi_x) * log(y + 2.0) * (1.0 - exp(-A * (y - 1.0))) * cos(pi_t) - v1_y = sin(pi_x) * (A * log(y + 2.0) * exp(-A * (y - 1.0)) + (1.0 - exp(-A * (y - 1.0))) / (y + 2.0)) * cos(pi_t) - v1_xx = -pi * pi * sin(pi_x) * log(y + 2.0) * (1.0 - exp(-A * (y - 1.0))) * cos(pi_t) - v1_xy = pi * cos(pi_x) * (A * log(y + 2.0) * exp(-A * (y - 1.0)) + (1.0 - exp(-A * (y - 1.0))) / (y + 2.0)) * cos(pi_t) - v1_yy = (sin(pi_x) * ( 2.0 * A * exp(-A * (y - 1.0)) / (y + 2.0) - - A * A * log(y + 2.0) * exp(-A * (y - 1.0)) - - (1.0 - exp(-A * (y - 1.0))) / ((y + 2.0) * (y + 2.0))) * cos(pi_t)) - v2 = v1 - v2_t = v1_t - v2_x = v1_x - v2_y = v1_y - v2_xx = v1_xx - v2_xy = v1_xy - v2_yy = v1_yy - - p = rho * rho - p_t = 2.0 * rho * rho_t - p_x = 2.0 * rho * rho_x - p_y = 2.0 * rho * rho_y - p_xx = 2.0 * rho * rho_xx + 2.0 * rho_x * rho_x - p_yy = 2.0 * rho * rho_yy + 2.0 * rho_y * rho_y - - # Note this simplifies slightly because the ansatz assumes that v1 = v2 - E = p * inv_gamma_minus_one + 0.5 * rho * (v1^2 + v2^2) - E_t = p_t * inv_gamma_minus_one + rho_t * v1^2 + 2.0 * rho * v1 * v1_t - E_x = p_x * inv_gamma_minus_one + rho_x * v1^2 + 2.0 * rho * v1 * v1_x - E_y = p_y * inv_gamma_minus_one + rho_y * v1^2 + 2.0 * rho * v1 * v1_y - - # Some convenience constants - T_const = equations.gamma * inv_gamma_minus_one / Pr - inv_rho_cubed = 1.0 / (rho^3) - - # compute the source terms - # density equation - du1 = rho_t + rho_x * v1 + rho * v1_x + rho_y * v2 + rho * v2_y - - # x-momentum equation - du2 = ( rho_t * v1 + rho * v1_t + p_x + rho_x * v1^2 - + 2.0 * rho * v1 * v1_x - + rho_y * v1 * v2 - + rho * v1_y * v2 - + rho * v1 * v2_y - # stress tensor from x-direction - - 4.0 / 3.0 * v1_xx * mu_ - + 2.0 / 3.0 * v2_xy * mu_ - - v1_yy * mu_ - - v2_xy * mu_ ) - # y-momentum equation - du3 = ( rho_t * v2 + rho * v2_t + p_y + rho_x * v1 * v2 - + rho * v1_x * v2 - + rho * v1 * v2_x - + rho_y * v2^2 - + 2.0 * rho * v2 * v2_y - # stress tensor from y-direction - - v1_xy * mu_ - - v2_xx * mu_ - - 4.0 / 3.0 * v2_yy * mu_ - + 2.0 / 3.0 * v1_xy * mu_ ) - # total energy equation - du4 = ( E_t + v1_x * (E + p) + v1 * (E_x + p_x) - + v2_y * (E + p) + v2 * (E_y + p_y) - # stress tensor and temperature gradient terms from x-direction - - 4.0 / 3.0 * v1_xx * v1 * mu_ - + 2.0 / 3.0 * v2_xy * v1 * mu_ - - 4.0 / 3.0 * v1_x * v1_x * mu_ - + 2.0 / 3.0 * v2_y * v1_x * mu_ - - v1_xy * v2 * mu_ - - v2_xx * v2 * mu_ - - v1_y * v2_x * mu_ - - v2_x * v2_x * mu_ - - T_const * inv_rho_cubed * ( p_xx * rho * rho - - 2.0 * p_x * rho * rho_x - + 2.0 * p * rho_x * rho_x - - p * rho * rho_xx ) * mu_ - # stress tensor and temperature gradient terms from y-direction - - v1_yy * v1 * mu_ - - v2_xy * v1 * mu_ - - v1_y * v1_y * mu_ - - v2_x * v1_y * mu_ - - 4.0 / 3.0 * v2_yy * v2 * mu_ - + 2.0 / 3.0 * v1_xy * v2 * mu_ - - 4.0 / 3.0 * v2_y * v2_y * mu_ - + 2.0 / 3.0 * v1_x * v2_y * mu_ - - T_const * inv_rho_cubed * ( p_yy * rho * rho - - 2.0 * p_y * rho * rho_y - + 2.0 * p * rho_y * rho_y - - p * rho * rho_yy ) * mu_ ) - - return SVector(du1, du2, du3, du4) + y = x[2] + + # TODO: parabolic + # we currently need to hardcode these parameters until we fix the "combined equation" issue + # see also https://github.com/trixi-framework/Trixi.jl/pull/1160 + inv_gamma_minus_one = inv(equations.gamma - 1) + Pr = prandtl_number() + mu_ = mu() + + # Same settings as in `initial_condition` + # Amplitude and shift + A = 0.5 + c = 2.0 + + # convenience values for trig. functions + pi_x = pi * x[1] + pi_y = pi * x[2] + pi_t = pi * t + + # compute the manufactured solution and all necessary derivatives + rho = c + A * sin(pi_x) * cos(pi_y) * cos(pi_t) + rho_t = -pi * A * sin(pi_x) * cos(pi_y) * sin(pi_t) + rho_x = pi * A * cos(pi_x) * cos(pi_y) * cos(pi_t) + rho_y = -pi * A * sin(pi_x) * sin(pi_y) * cos(pi_t) + rho_xx = -pi * pi * A * sin(pi_x) * cos(pi_y) * cos(pi_t) + rho_yy = -pi * pi * A * sin(pi_x) * cos(pi_y) * cos(pi_t) + + v1 = sin(pi_x) * log(y + 2.0) * (1.0 - exp(-A * (y - 1.0))) * cos(pi_t) + v1_t = -pi * sin(pi_x) * log(y + 2.0) * (1.0 - exp(-A * (y - 1.0))) * sin(pi_t) + v1_x = pi * cos(pi_x) * log(y + 2.0) * (1.0 - exp(-A * (y - 1.0))) * cos(pi_t) + v1_y = sin(pi_x) * + (A * log(y + 2.0) * exp(-A * (y - 1.0)) + + (1.0 - exp(-A * (y - 1.0))) / (y + 2.0)) * cos(pi_t) + v1_xx = -pi * pi * sin(pi_x) * log(y + 2.0) * (1.0 - exp(-A * (y - 1.0))) * cos(pi_t) + v1_xy = pi * cos(pi_x) * + (A * log(y + 2.0) * exp(-A * (y - 1.0)) + + (1.0 - exp(-A * (y - 1.0))) / (y + 2.0)) * cos(pi_t) + v1_yy = (sin(pi_x) * + (2.0 * A * exp(-A * (y - 1.0)) / (y + 2.0) - + A * A * log(y + 2.0) * exp(-A * (y - 1.0)) - + (1.0 - exp(-A * (y - 1.0))) / ((y + 2.0) * (y + 2.0))) * cos(pi_t)) + v2 = v1 + v2_t = v1_t + v2_x = v1_x + v2_y = v1_y + v2_xx = v1_xx + v2_xy = v1_xy + v2_yy = v1_yy + + p = rho * rho + p_t = 2.0 * rho * rho_t + p_x = 2.0 * rho * rho_x + p_y = 2.0 * rho * rho_y + p_xx = 2.0 * rho * rho_xx + 2.0 * rho_x * rho_x + p_yy = 2.0 * rho * rho_yy + 2.0 * rho_y * rho_y + + # Note this simplifies slightly because the ansatz assumes that v1 = v2 + E = p * inv_gamma_minus_one + 0.5 * rho * (v1^2 + v2^2) + E_t = p_t * inv_gamma_minus_one + rho_t * v1^2 + 2.0 * rho * v1 * v1_t + E_x = p_x * inv_gamma_minus_one + rho_x * v1^2 + 2.0 * rho * v1 * v1_x + E_y = p_y * inv_gamma_minus_one + rho_y * v1^2 + 2.0 * rho * v1 * v1_y + + # Some convenience constants + T_const = equations.gamma * inv_gamma_minus_one / Pr + inv_rho_cubed = 1.0 / (rho^3) + + # compute the source terms + # density equation + du1 = rho_t + rho_x * v1 + rho * v1_x + rho_y * v2 + rho * v2_y + + # x-momentum equation + du2 = (rho_t * v1 + rho * v1_t + p_x + rho_x * v1^2 + + 2.0 * rho * v1 * v1_x + + rho_y * v1 * v2 + + rho * v1_y * v2 + + rho * v1 * v2_y - + # stress tensor from x-direction + 4.0 / 3.0 * v1_xx * mu_ + + 2.0 / 3.0 * v2_xy * mu_ - + v1_yy * mu_ - + v2_xy * mu_) + # y-momentum equation + du3 = (rho_t * v2 + rho * v2_t + p_y + rho_x * v1 * v2 + + rho * v1_x * v2 + + rho * v1 * v2_x + + rho_y * v2^2 + + 2.0 * rho * v2 * v2_y - + # stress tensor from y-direction + v1_xy * mu_ - + v2_xx * mu_ - + 4.0 / 3.0 * v2_yy * mu_ + + 2.0 / 3.0 * v1_xy * mu_) + # total energy equation + du4 = (E_t + v1_x * (E + p) + v1 * (E_x + p_x) + + v2_y * (E + p) + v2 * (E_y + p_y) - + # stress tensor and temperature gradient terms from x-direction + 4.0 / 3.0 * v1_xx * v1 * mu_ + + 2.0 / 3.0 * v2_xy * v1 * mu_ - + 4.0 / 3.0 * v1_x * v1_x * mu_ + + 2.0 / 3.0 * v2_y * v1_x * mu_ - + v1_xy * v2 * mu_ - + v2_xx * v2 * mu_ - + v1_y * v2_x * mu_ - + v2_x * v2_x * mu_ - + T_const * inv_rho_cubed * + (p_xx * rho * rho - + 2.0 * p_x * rho * rho_x + + 2.0 * p * rho_x * rho_x - + p * rho * rho_xx) * mu_ - + # stress tensor and temperature gradient terms from y-direction + v1_yy * v1 * mu_ - + v2_xy * v1 * mu_ - + v2_x * v1_y * mu_ - + 4.0 / 3.0 * v2_yy * v2 * mu_ + + 2.0 / 3.0 * v1_xy - + 4.0 / 3.0 * v2_y * v2_y * mu_ + + 2.0 / 3.0 * v1_x * v2_y * mu_ + - + - + (p_yy * rho * rho - + 2.0 * p_y * rho * rho_y + - - + p * rho * rho_yy) * mu_) + + return SVector(du1, du2, du3, du4) end initial_condition = initial_condition_navier_stokes_convergence_test @@ -175,23 +182,26 @@ velocity_bc_top_bottom = NoSlip() do x, t, equations return SVector(u[2], u[3]) end heat_bc_top_bottom = Adiabatic((x, t, equations) -> 0.0) -boundary_condition_top_bottom = BoundaryConditionNavierStokesWall(velocity_bc_top_bottom, heat_bc_top_bottom) +boundary_condition_top_bottom = BoundaryConditionNavierStokesWall(velocity_bc_top_bottom, + heat_bc_top_bottom) # define inviscid boundary conditions boundary_conditions = (; x_neg = boundary_condition_periodic, - x_pos = boundary_condition_periodic, - y_neg = boundary_condition_slip_wall, - y_pos = boundary_condition_slip_wall) + x_pos = boundary_condition_periodic, + y_neg = boundary_condition_slip_wall, + y_pos = boundary_condition_slip_wall) # define viscous boundary conditions boundary_conditions_parabolic = (; x_neg = boundary_condition_periodic, - x_pos = boundary_condition_periodic, - y_neg = boundary_condition_top_bottom, - y_pos = boundary_condition_top_bottom) + x_pos = boundary_condition_periodic, + y_neg = boundary_condition_top_bottom, + y_pos = boundary_condition_top_bottom) -semi = SemidiscretizationHyperbolicParabolic(mesh, (equations, equations_parabolic), initial_condition, solver; - boundary_conditions=(boundary_conditions, boundary_conditions_parabolic), - source_terms=source_terms_navier_stokes_convergence_test) +semi = SemidiscretizationHyperbolicParabolic(mesh, (equations, equations_parabolic), + initial_condition, solver; + boundary_conditions = (boundary_conditions, + boundary_conditions_parabolic), + source_terms = source_terms_navier_stokes_convergence_test) ############################################################################### # ODE solvers, callbacks etc. @@ -201,16 +211,15 @@ tspan = (0.0, 0.5) ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() -alive_callback = AliveCallback(alive_interval=10) +alive_callback = AliveCallback(alive_interval = 10) analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) callbacks = CallbackSet(summary_callback, alive_callback, analysis_callback) ############################################################################### # run the simulation time_int_tol = 1e-8 -sol = solve(ode, RDPK3SpFSAL49(); abstol=time_int_tol, reltol=time_int_tol, dt = 1e-5, - ode_default_options()..., callback=callbacks) +sol = solve(ode, RDPK3SpFSAL49(); abstol = time_int_tol, reltol = time_int_tol, dt = 1e-5, + ode_default_options()..., callback = callbacks) summary_callback() # print the timer summary - diff --git a/examples/tree_2d_dgsem/elixir_navierstokes_lid_driven_cavity.jl b/examples/tree_2d_dgsem/elixir_navierstokes_lid_driven_cavity.jl index 3314343ccca..7bd1ec0c647 100644 --- a/examples/tree_2d_dgsem/elixir_navierstokes_lid_driven_cavity.jl +++ b/examples/tree_2d_dgsem/elixir_navierstokes_lid_driven_cavity.jl @@ -9,28 +9,27 @@ prandtl_number() = 0.72 mu() = 0.001 equations = CompressibleEulerEquations2D(1.4) -equations_parabolic = CompressibleNavierStokesDiffusion2D(equations, mu=mu(), - Prandtl=prandtl_number()) +equations_parabolic = CompressibleNavierStokesDiffusion2D(equations, mu = mu(), + Prandtl = prandtl_number()) # Create DG solver with polynomial degree = 3 and (local) Lax-Friedrichs/Rusanov flux as surface flux -solver = DGSEM(polydeg=3, surface_flux=flux_lax_friedrichs) +solver = DGSEM(polydeg = 3, surface_flux = flux_lax_friedrichs) coordinates_min = (-1.0, -1.0) # minimum coordinates (min(x), min(y)) -coordinates_max = ( 1.0, 1.0) # maximum coordinates (max(x), max(y)) +coordinates_max = (1.0, 1.0) # maximum coordinates (max(x), max(y)) # Create a uniformly refined mesh mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=4, - periodicity=false, - n_cells_max=30_000) # set maximum capacity of tree data structure - + initial_refinement_level = 4, + periodicity = false, + n_cells_max = 30_000) # set maximum capacity of tree data structure function initial_condition_cavity(x, t, equations::CompressibleEulerEquations2D) - Ma = 0.1 - rho = 1.0 - u, v = 0.0, 0.0 - p = 1.0 / (Ma^2 * equations.gamma) - return prim2cons(SVector(rho, u, v, p), equations) + Ma = 0.1 + rho = 1.0 + u, v = 0.0, 0.0 + p = 1.0 / (Ma^2 * equations.gamma) + return prim2cons(SVector(rho, u, v, p), equations) end initial_condition = initial_condition_cavity @@ -45,15 +44,15 @@ boundary_condition_cavity = BoundaryConditionNavierStokesWall(velocity_bc_cavity boundary_conditions = boundary_condition_slip_wall boundary_conditions_parabolic = (; x_neg = boundary_condition_cavity, - y_neg = boundary_condition_cavity, - y_pos = boundary_condition_lid, - x_pos = boundary_condition_cavity) + y_neg = boundary_condition_cavity, + y_pos = boundary_condition_lid, + x_pos = boundary_condition_cavity) # A semidiscretization collects data structures and functions for the spatial discretization semi = SemidiscretizationHyperbolicParabolic(mesh, (equations, equations_parabolic), initial_condition, solver; - boundary_conditions=(boundary_conditions, - boundary_conditions_parabolic)) + boundary_conditions = (boundary_conditions, + boundary_conditions_parabolic)) ############################################################################### # ODE solvers, callbacks etc. @@ -63,17 +62,15 @@ tspan = (0.0, 25.0) ode = semidiscretize(semi, tspan); summary_callback = SummaryCallback() -alive_callback = AliveCallback(alive_interval=100) +alive_callback = AliveCallback(alive_interval = 100) analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) callbacks = CallbackSet(summary_callback, alive_callback, analysis_callback) ############################################################################### # run the simulation time_int_tol = 1e-8 -sol = solve(ode, RDPK3SpFSAL49(); abstol=time_int_tol, reltol=time_int_tol, - ode_default_options()..., callback=callbacks) +sol = solve(ode, RDPK3SpFSAL49(); abstol = time_int_tol, reltol = time_int_tol, + ode_default_options()..., callback = callbacks) summary_callback() # print the timer summary - - diff --git a/examples/tree_2d_dgsem/elixir_navierstokes_shearlayer_amr.jl b/examples/tree_2d_dgsem/elixir_navierstokes_shearlayer_amr.jl index 06e8f06d3ca..4d92ea261e9 100644 --- a/examples/tree_2d_dgsem/elixir_navierstokes_shearlayer_amr.jl +++ b/examples/tree_2d_dgsem/elixir_navierstokes_shearlayer_amr.jl @@ -7,11 +7,11 @@ using Trixi # TODO: parabolic; unify names of these accessor functions prandtl_number() = 0.72 -mu() = 1.0/3.0 * 10^(-5) # equivalent to Re = 30,000 +mu() = 1.0 / 3.0 * 10^(-5) # equivalent to Re = 30,000 equations = CompressibleEulerEquations2D(1.4) -equations_parabolic = CompressibleNavierStokesDiffusion2D(equations, mu=mu(), - Prandtl=prandtl_number()) +equations_parabolic = CompressibleNavierStokesDiffusion2D(equations, mu = mu(), + Prandtl = prandtl_number()) """ A compressible version of the double shear layer initial condition. Adapted from @@ -22,32 +22,31 @@ Brown and Minion (1995). [DOI: 10.1006/jcph.1995.1205](https://doi.org/10.1006/jcph.1995.1205) """ function initial_condition_shear_layer(x, t, equations::CompressibleEulerEquations2D) - # Shear layer parameters - k = 80 - delta = 0.05 - u0 = 1.0 - - Ms = 0.1 # maximum Mach number - - rho = 1.0 - v1 = x[2] <= 0.5 ? u0 * tanh(k*(x[2] - 0.25)) : u0 * tanh(k*(0.75 -x[2])) - v2 = u0 * delta * sin(2*pi*(x[1]+ 0.25)) - p = (u0 / Ms)^2 * rho / equations.gamma # scaling to get Ms - - return prim2cons(SVector(rho, v1, v2, p), equations) + # Shear layer parameters + k = 80 + delta = 0.05 + u0 = 1.0 + + Ms = 0.1 # maximum Mach number + + rho = 1.0 + v1 = x[2] <= 0.5 ? u0 * tanh(k * (x[2] - 0.25)) : u0 * tanh(k * (0.75 - x[2])) + v2 = u0 * delta * sin(2 * pi * (x[1] + 0.25)) + p = (u0 / Ms)^2 * rho / equations.gamma # scaling to get Ms + + return prim2cons(SVector(rho, v1, v2, p), equations) end initial_condition = initial_condition_shear_layer volume_flux = flux_ranocha -solver = DGSEM(polydeg=3, surface_flux=flux_hllc, - volume_integral=VolumeIntegralFluxDifferencing(volume_flux)) +solver = DGSEM(polydeg = 3, surface_flux = flux_hllc, + volume_integral = VolumeIntegralFluxDifferencing(volume_flux)) coordinates_min = (0.0, 0.0) coordinates_max = (1.0, 1.0) mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=4, - n_cells_max=100_000) - + initial_refinement_level = 4, + n_cells_max = 100_000) semi = SemidiscretizationHyperbolicParabolic(mesh, (equations, equations_parabolic), initial_condition, solver) @@ -61,26 +60,26 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 2000 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) -alive_callback = AliveCallback(analysis_interval=analysis_interval,) +alive_callback = AliveCallback(analysis_interval = analysis_interval) # This uses velocity-based AMR @inline function v1(u, equations::CompressibleEulerEquations2D) - rho, rho_v1, _, _ = u - return rho_v1 / rho + rho, rho_v1, _, _ = u + return rho_v1 / rho end -amr_indicator = IndicatorLöhner(semi, variable=v1) +amr_indicator = IndicatorLöhner(semi, variable = v1) amr_controller = ControllerThreeLevel(semi, amr_indicator, base_level = 3, - med_level = 5, med_threshold=0.2, - max_level = 7, max_threshold=0.5) + med_level = 5, med_threshold = 0.2, + max_level = 7, max_threshold = 0.5) amr_callback = AMRCallback(semi, amr_controller, - interval=50, - adapt_initial_condition=true, - adapt_initial_condition_only_refine=true) + interval = 50, + adapt_initial_condition = true, + adapt_initial_condition_only_refine = true) -stepsize_callback = StepsizeCallback(cfl=1.3) +stepsize_callback = StepsizeCallback(cfl = 1.3) callbacks = CallbackSet(summary_callback, analysis_callback, @@ -91,7 +90,7 @@ callbacks = CallbackSet(summary_callback, ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); -summary_callback() # print the timer summary \ No newline at end of file +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); +summary_callback() # print the timer summary diff --git a/examples/tree_2d_dgsem/elixir_navierstokes_taylor_green_vortex.jl b/examples/tree_2d_dgsem/elixir_navierstokes_taylor_green_vortex.jl index c3cbc858f7b..a3e38bf6d92 100644 --- a/examples/tree_2d_dgsem/elixir_navierstokes_taylor_green_vortex.jl +++ b/examples/tree_2d_dgsem/elixir_navierstokes_taylor_green_vortex.jl @@ -10,8 +10,8 @@ prandtl_number() = 0.72 mu() = 6.25e-4 # equivalent to Re = 1600 equations = CompressibleEulerEquations2D(1.4) -equations_parabolic = CompressibleNavierStokesDiffusion2D(equations, mu=mu(), - Prandtl=prandtl_number()) +equations_parabolic = CompressibleNavierStokesDiffusion2D(equations, mu = mu(), + Prandtl = prandtl_number()) """ initial_condition_taylor_green_vortex(x, t, equations::CompressibleEulerEquations2D) @@ -22,30 +22,30 @@ This forms the basis behind the 3D case found for instance in Simulation of the Compressible Taylor Green Vortex using High-Order Flux Reconstruction Schemes [DOI: 10.2514/6.2014-3210](https://doi.org/10.2514/6.2014-3210) """ -function initial_condition_taylor_green_vortex(x, t, equations::CompressibleEulerEquations2D) - A = 1.0 # magnitude of speed - Ms = 0.1 # maximum Mach number - - rho = 1.0 - v1 = A * sin(x[1]) * cos(x[2]) - v2 = -A * cos(x[1]) * sin(x[2]) - p = (A / Ms)^2 * rho / equations.gamma # scaling to get Ms - p = p + 1.0/4.0 * A^2 * rho * (cos(2*x[1]) + cos(2*x[2])) - - return prim2cons(SVector(rho, v1, v2, p), equations) +function initial_condition_taylor_green_vortex(x, t, + equations::CompressibleEulerEquations2D) + A = 1.0 # magnitude of speed + Ms = 0.1 # maximum Mach number + + rho = 1.0 + v1 = A * sin(x[1]) * cos(x[2]) + v2 = -A * cos(x[1]) * sin(x[2]) + p = (A / Ms)^2 * rho / equations.gamma # scaling to get Ms + p = p + 1.0 / 4.0 * A^2 * rho * (cos(2 * x[1]) + cos(2 * x[2])) + + return prim2cons(SVector(rho, v1, v2, p), equations) end initial_condition = initial_condition_taylor_green_vortex volume_flux = flux_ranocha -solver = DGSEM(polydeg=3, surface_flux=flux_hllc, - volume_integral=VolumeIntegralFluxDifferencing(volume_flux)) +solver = DGSEM(polydeg = 3, surface_flux = flux_hllc, + volume_integral = VolumeIntegralFluxDifferencing(volume_flux)) coordinates_min = (-1.0, -1.0) .* pi -coordinates_max = ( 1.0, 1.0) .* pi +coordinates_max = (1.0, 1.0) .* pi mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=4, - n_cells_max=100_000) - + initial_refinement_level = 4, + n_cells_max = 100_000) semi = SemidiscretizationHyperbolicParabolic(mesh, (equations, equations_parabolic), initial_condition, solver) @@ -59,11 +59,12 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval, save_analysis=true, - extra_analysis_integrals=(energy_kinetic, - energy_internal)) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval, + save_analysis = true, + extra_analysis_integrals = (energy_kinetic, + energy_internal)) -alive_callback = AliveCallback(analysis_interval=analysis_interval,) +alive_callback = AliveCallback(analysis_interval = analysis_interval) callbacks = CallbackSet(summary_callback, analysis_callback, @@ -73,6 +74,6 @@ callbacks = CallbackSet(summary_callback, # run the simulation time_int_tol = 1e-9 -sol = solve(ode, RDPK3SpFSAL49(); abstol=time_int_tol, reltol=time_int_tol, - ode_default_options()..., callback=callbacks) -summary_callback() # print the timer summary \ No newline at end of file +sol = solve(ode, RDPK3SpFSAL49(); abstol = time_int_tol, reltol = time_int_tol, + ode_default_options()..., callback = callbacks) +summary_callback() # print the timer summary diff --git a/examples/tree_2d_dgsem/elixir_shallowwater_conical_island.jl b/examples/tree_2d_dgsem/elixir_shallowwater_conical_island.jl index 7c60e35b03e..349b3741869 100644 --- a/examples/tree_2d_dgsem/elixir_shallowwater_conical_island.jl +++ b/examples/tree_2d_dgsem/elixir_shallowwater_conical_island.jl @@ -7,7 +7,7 @@ using Trixi # # TODO: TrixiShallowWater: wet/dry example elixir -equations = ShallowWaterEquations2D(gravity_constant=9.81, H0=1.4) +equations = ShallowWaterEquations2D(gravity_constant = 9.81, H0 = 1.4) """ initial_condition_conical_island(x, t, equations::ShallowWaterEquations2D) @@ -21,29 +21,29 @@ boundary condition with the initial values. Due to the dry cells at the boundary effect of an outflow which can be seen in the simulation. """ function initial_condition_conical_island(x, t, equations::ShallowWaterEquations2D) - # Set the background values + # Set the background values - v1 = 0.0 - v2 = 0.0 + v1 = 0.0 + v2 = 0.0 - x1, x2 = x - b = max(0.1, 1.0 - 4.0 * sqrt(x1^2 + x2^2)) + x1, x2 = x + b = max(0.1, 1.0 - 4.0 * sqrt(x1^2 + x2^2)) - # use a logistic function to transfer water height value smoothly - L = equations.H0 # maximum of function - x0 = 0.3 # center point of function - k = -25.0 # sharpness of transfer + # use a logistic function to transfer water height value smoothly + L = equations.H0 # maximum of function + x0 = 0.3 # center point of function + k = -25.0 # sharpness of transfer - H = max(b, L/(1.0 + exp(-k*(sqrt(x1^2+x2^2) - x0)))) + H = max(b, L / (1.0 + exp(-k * (sqrt(x1^2 + x2^2) - x0)))) - # It is mandatory to shift the water level at dry areas to make sure the water height h - # stays positive. The system would not be stable for h set to a hard 0 due to division by h in - # the computation of velocity, e.g., (h v1) / h. Therefore, a small dry state threshold - # with a default value of 500*eps() ≈ 1e-13 in double precision, is set in the constructor above - # for the ShallowWaterEquations and added to the initial condition if h = 0. - # This default value can be changed within the constructor call depending on the simulation setup. - H = max(H, b + equations.threshold_limiter) - return prim2cons(SVector(H, v1, v2, b), equations) + # It is mandatory to shift the water level at dry areas to make sure the water height h + # stays positive. The system would not be stable for h set to a hard 0 due to division by h in + # the computation of velocity, e.g., (h v1) / h. Therefore, a small dry state threshold + # with a default value of 500*eps() ≈ 1e-13 in double precision, is set in the constructor above + # for the ShallowWaterEquations and added to the initial condition if h = 0. + # This default value can be changed within the constructor call depending on the simulation setup. + H = max(H, b + equations.threshold_limiter) + return prim2cons(SVector(H, v1, v2, b), equations) end initial_condition = initial_condition_conical_island @@ -53,19 +53,20 @@ boundary_conditions = BoundaryConditionDirichlet(initial_condition) # Get the DG approximation space volume_flux = (flux_wintermeyer_etal, flux_nonconservative_wintermeyer_etal) -surface_flux = (FluxHydrostaticReconstruction(flux_hll_chen_noelle, hydrostatic_reconstruction_chen_noelle), +surface_flux = (FluxHydrostaticReconstruction(flux_hll_chen_noelle, + hydrostatic_reconstruction_chen_noelle), flux_nonconservative_chen_noelle) basis = LobattoLegendreBasis(4) indicator_sc = IndicatorHennemannGassnerShallowWater(equations, basis, - alpha_max=0.5, - alpha_min=0.001, - alpha_smooth=true, - variable=waterheight_pressure) + alpha_max = 0.5, + alpha_min = 0.001, + alpha_smooth = true, + variable = waterheight_pressure) volume_integral = VolumeIntegralShockCapturingHG(indicator_sc; - volume_flux_dg=volume_flux, - volume_flux_fv=surface_flux) + volume_flux_dg = volume_flux, + volume_flux_fv = surface_flux) solver = DGSEM(basis, surface_flux, volume_integral) @@ -75,13 +76,13 @@ solver = DGSEM(basis, surface_flux, volume_integral) coordinates_min = (-1.0, -1.0) coordinates_max = (1.0, 1.0) mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=4, - n_cells_max=10_000, - periodicity=false) + initial_refinement_level = 4, + n_cells_max = 10_000, + periodicity = false) # Create the semi discretization object semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver, - boundary_conditions=boundary_conditions) + boundary_conditions = boundary_conditions) ############################################################################### # ODE solver @@ -95,22 +96,22 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 1000 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=100, - save_initial_solution=true, - save_final_solution=true) +save_solution = SaveSolutionCallback(interval = 100, + save_initial_solution = true, + save_final_solution = true) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, save_solution) ############################################################################### # run the simulation -stage_limiter! = PositivityPreservingLimiterShallowWater(variables=(Trixi.waterheight,)) +stage_limiter! = PositivityPreservingLimiterShallowWater(variables = (Trixi.waterheight,)) sol = solve(ode, SSPRK43(stage_limiter!); - ode_default_options()..., callback=callbacks); + ode_default_options()..., callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/tree_2d_dgsem/elixir_shallowwater_ec.jl b/examples/tree_2d_dgsem/elixir_shallowwater_ec.jl index eed0a350e7e..bc528ae7756 100644 --- a/examples/tree_2d_dgsem/elixir_shallowwater_ec.jl +++ b/examples/tree_2d_dgsem/elixir_shallowwater_ec.jl @@ -6,7 +6,7 @@ using Trixi # semidiscretization of the shallow water equations with a discontinuous # bottom topography function -equations = ShallowWaterEquations2D(gravity_constant=9.81) +equations = ShallowWaterEquations2D(gravity_constant = 9.81) # Note, this initial condition is used to compute errors in the analysis callback but the initialization is # overwritten by `initial_condition_ec_discontinuous_bottom` below. @@ -16,17 +16,18 @@ initial_condition = initial_condition_weak_blast_wave # Get the DG approximation space volume_flux = (flux_wintermeyer_etal, flux_nonconservative_wintermeyer_etal) -solver = DGSEM(polydeg=4, surface_flux=(flux_fjordholm_etal, flux_nonconservative_fjordholm_etal), - volume_integral=VolumeIntegralFluxDifferencing(volume_flux)) +solver = DGSEM(polydeg = 4, + surface_flux = (flux_fjordholm_etal, flux_nonconservative_fjordholm_etal), + volume_integral = VolumeIntegralFluxDifferencing(volume_flux)) ############################################################################### # Get the TreeMesh and setup a periodic mesh coordinates_min = (-1.0, -1.0) -coordinates_max = ( 1.0, 1.0) +coordinates_max = (1.0, 1.0) mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=2, - n_cells_max=10_000) + initial_refinement_level = 2, + n_cells_max = 10_000) # Create the semi discretization object semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver) @@ -46,45 +47,48 @@ ode = semidiscretize(semi, tspan) # In contrast to the usual signature of initial conditions, this one get passed the # `element_id` explicitly. In particular, this initial conditions works as intended # only for the TreeMesh2D with initial_refinement_level=2. -function initial_condition_ec_discontinuous_bottom(x, t, element_id, equations::ShallowWaterEquations2D) - # Set up polar coordinates - inicenter = SVector(0.7, 0.7) - x_norm = x[1] - inicenter[1] - y_norm = x[2] - inicenter[2] - r = sqrt(x_norm^2 + y_norm^2) - phi = atan(y_norm, x_norm) - sin_phi, cos_phi = sincos(phi) - - # Set the background values - H = 4.25 - v1 = 0.0 - v2 = 0.0 - b = 0.0 - - # setup the discontinuous water height and velocities - if element_id == 10 - H = 5.0 - v1 = 0.1882 * cos_phi - v2 = 0.1882 * sin_phi - end - - # Setup a discontinuous bottom topography using the element id number - if element_id == 7 - b = 2.0 + 0.5 * sin(2.0 * pi * x[1]) + 0.5 * cos(2.0 * pi * x[2]) - end - - return prim2cons(SVector(H, v1, v2, b), equations) +function initial_condition_ec_discontinuous_bottom(x, t, element_id, + equations::ShallowWaterEquations2D) + # Set up polar coordinates + inicenter = SVector(0.7, 0.7) + x_norm = x[1] - inicenter[1] + y_norm = x[2] - inicenter[2] + r = sqrt(x_norm^2 + y_norm^2) + phi = atan(y_norm, x_norm) + sin_phi, cos_phi = sincos(phi) + + # Set the background values + H = 4.25 + v1 = 0.0 + v2 = 0.0 + b = 0.0 + + # setup the discontinuous water height and velocities + if element_id == 10 + H = 5.0 + v1 = 0.1882 * cos_phi + v2 = 0.1882 * sin_phi + end + + # Setup a discontinuous bottom topography using the element id number + if element_id == 7 + b = 2.0 + 0.5 * sin(2.0 * pi * x[1]) + 0.5 * cos(2.0 * pi * x[2]) + end + + return prim2cons(SVector(H, v1, v2, b), equations) end # point to the data we want to augment u = Trixi.wrap_array(ode.u0, semi) # reset the initial condition for element in eachelement(semi.solver, semi.cache) - for j in eachnode(semi.solver), i in eachnode(semi.solver) - x_node = Trixi.get_node_coords(semi.cache.elements.node_coordinates, equations, semi.solver, i, j, element) - u_node = initial_condition_ec_discontinuous_bottom(x_node, first(tspan), element, equations) - Trixi.set_node_vars!(u, u_node, equations, semi.solver, i, j, element) - end + for j in eachnode(semi.solver), i in eachnode(semi.solver) + x_node = Trixi.get_node_coords(semi.cache.elements.node_coordinates, equations, + semi.solver, i, j, element) + u_node = initial_condition_ec_discontinuous_bottom(x_node, first(tspan), element, + equations) + Trixi.set_node_vars!(u, u_node, equations, semi.solver, i, j, element) + end end ############################################################################### @@ -93,15 +97,15 @@ end summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(dt=0.2, - save_initial_solution=true, - save_final_solution=true) +save_solution = SaveSolutionCallback(dt = 0.2, + save_initial_solution = true, + save_final_solution = true) -stepsize_callback = StepsizeCallback(cfl=3.0) +stepsize_callback = StepsizeCallback(cfl = 3.0) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, save_solution, stepsize_callback) @@ -109,7 +113,7 @@ callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, sav ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/tree_2d_dgsem/elixir_shallowwater_parabolic_bowl.jl b/examples/tree_2d_dgsem/elixir_shallowwater_parabolic_bowl.jl index 03dcf017266..2008019cc31 100644 --- a/examples/tree_2d_dgsem/elixir_shallowwater_parabolic_bowl.jl +++ b/examples/tree_2d_dgsem/elixir_shallowwater_parabolic_bowl.jl @@ -7,7 +7,7 @@ using Trixi # # TODO: TrixiShallowWater: wet/dry example elixir -equations = ShallowWaterEquations2D(gravity_constant=9.81) +equations = ShallowWaterEquations2D(gravity_constant = 9.81) """ initial_condition_parabolic_bowl(x, t, equations:: ShallowWaterEquations2D) @@ -28,27 +28,27 @@ The particular setup below is taken from Section 6.2 of curvilinear meshes with wet/dry fronts accelerated by GPUs [DOI: 10.1016/j.jcp.2018.08.038](https://doi.org/10.1016/j.jcp.2018.08.038). """ -function initial_condition_parabolic_bowl(x, t, equations:: ShallowWaterEquations2D) - a = 1.0 - h_0 = 0.1 - sigma = 0.5 - ω = sqrt(2 * equations.gravity * h_0) / a - - v1 = -sigma * ω * sin(ω * t) - v2 = sigma * ω * cos(ω * t) - - b = h_0 * ((x[1])^2 + (x[2])^2) / a^2 - - H = sigma * h_0 / a^2 * (2 * x[1] * cos(ω * t) + 2 * x[2] * sin(ω * t) - sigma) + h_0 - - # It is mandatory to shift the water level at dry areas to make sure the water height h - # stays positive. The system would not be stable for h set to a hard 0 due to division by h in - # the computation of velocity, e.g., (h v1) / h. Therefore, a small dry state threshold - # with a default value of 500*eps() ≈ 1e-13 in double precision, is set in the constructor above - # for the ShallowWaterEquations and added to the initial condition if h = 0. - # This default value can be changed within the constructor call depending on the simulation setup. - H = max(H, b + equations.threshold_limiter) - return prim2cons(SVector(H, v1, v2, b), equations) +function initial_condition_parabolic_bowl(x, t, equations::ShallowWaterEquations2D) + a = 1.0 + h_0 = 0.1 + sigma = 0.5 + ω = sqrt(2 * equations.gravity * h_0) / a + + v1 = -sigma * ω * sin(ω * t) + v2 = sigma * ω * cos(ω * t) + + b = h_0 * ((x[1])^2 + (x[2])^2) / a^2 + + H = sigma * h_0 / a^2 * (2 * x[1] * cos(ω * t) + 2 * x[2] * sin(ω * t) - sigma) + h_0 + + # It is mandatory to shift the water level at dry areas to make sure the water height h + # stays positive. The system would not be stable for h set to a hard 0 due to division by h in + # the computation of velocity, e.g., (h v1) / h. Therefore, a small dry state threshold + # with a default value of 500*eps() ≈ 1e-13 in double precision, is set in the constructor above + # for the ShallowWaterEquations and added to the initial condition if h = 0. + # This default value can be changed within the constructor call depending on the simulation setup. + H = max(H, b + equations.threshold_limiter) + return prim2cons(SVector(H, v1, v2, b), equations) end initial_condition = initial_condition_parabolic_bowl @@ -56,23 +56,23 @@ initial_condition = initial_condition_parabolic_bowl # Get the DG approximation space volume_flux = (flux_wintermeyer_etal, flux_nonconservative_wintermeyer_etal) -surface_flux = (FluxHydrostaticReconstruction(flux_hll_chen_noelle, hydrostatic_reconstruction_chen_noelle), +surface_flux = (FluxHydrostaticReconstruction(flux_hll_chen_noelle, + hydrostatic_reconstruction_chen_noelle), flux_nonconservative_chen_noelle) basis = LobattoLegendreBasis(7) indicator_sc = IndicatorHennemannGassnerShallowWater(equations, basis, - alpha_max=0.6, - alpha_min=0.001, - alpha_smooth=true, - variable=waterheight_pressure) + alpha_max = 0.6, + alpha_min = 0.001, + alpha_smooth = true, + variable = waterheight_pressure) volume_integral = VolumeIntegralShockCapturingHG(indicator_sc; - volume_flux_dg=volume_flux, - volume_flux_fv=surface_flux) + volume_flux_dg = volume_flux, + volume_flux_fv = surface_flux) solver = DGSEM(basis, surface_flux, volume_integral) - ############################################################################### # Create the TreeMesh for the domain [-2, 2]^2 @@ -80,8 +80,8 @@ coordinates_min = (-2.0, -2.0) coordinates_max = (2.0, 2.0) mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=5, - n_cells_max=10_000) + initial_refinement_level = 5, + n_cells_max = 10_000) # create the semi discretization object semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver) @@ -95,19 +95,20 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 1000 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval, save_analysis=false, - extra_analysis_integrals=(energy_kinetic, - energy_internal)) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval, + save_analysis = false, + extra_analysis_integrals = (energy_kinetic, + energy_internal)) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=100, - save_initial_solution=true, - save_final_solution=true) +save_solution = SaveSolutionCallback(interval = 100, + save_initial_solution = true, + save_final_solution = true) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, save_solution) -stage_limiter! = PositivityPreservingLimiterShallowWater(variables=(Trixi.waterheight,)) +stage_limiter! = PositivityPreservingLimiterShallowWater(variables = (Trixi.waterheight,)) ############################################################################### # run the simulation @@ -115,6 +116,6 @@ stage_limiter! = PositivityPreservingLimiterShallowWater(variables=(Trixi.waterh callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, save_solution) sol = solve(ode, SSPRK43(stage_limiter!); - ode_default_options()..., callback=callbacks); + ode_default_options()..., callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/tree_2d_dgsem/elixir_shallowwater_source_terms.jl b/examples/tree_2d_dgsem/elixir_shallowwater_source_terms.jl index 6d4f6fe518c..c92e885c161 100644 --- a/examples/tree_2d_dgsem/elixir_shallowwater_source_terms.jl +++ b/examples/tree_2d_dgsem/elixir_shallowwater_source_terms.jl @@ -5,17 +5,17 @@ using Trixi ############################################################################### # semidiscretization of the shallow water equations -equations = ShallowWaterEquations2D(gravity_constant=9.81) +equations = ShallowWaterEquations2D(gravity_constant = 9.81) initial_condition = initial_condition_convergence_test # MMS EOC test - ############################################################################### # Get the DG approximation space volume_flux = (flux_wintermeyer_etal, flux_nonconservative_wintermeyer_etal) -solver = DGSEM(polydeg=3, surface_flux=(flux_lax_friedrichs, flux_nonconservative_fjordholm_etal), - volume_integral=VolumeIntegralFluxDifferencing(volume_flux)) +solver = DGSEM(polydeg = 3, + surface_flux = (flux_lax_friedrichs, flux_nonconservative_fjordholm_etal), + volume_integral = VolumeIntegralFluxDifferencing(volume_flux)) ############################################################################### # Get the TreeMesh and setup a periodic mesh @@ -23,13 +23,13 @@ solver = DGSEM(polydeg=3, surface_flux=(flux_lax_friedrichs, flux_nonconservativ coordinates_min = (0.0, 0.0) coordinates_max = (sqrt(2.0), sqrt(2.0)) mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=3, - n_cells_max=10_000, - periodicity=true) + initial_refinement_level = 3, + n_cells_max = 10_000, + periodicity = true) # create the semi discretization object semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver, - source_terms=source_terms_convergence_test) + source_terms = source_terms_convergence_test) ############################################################################### # ODE solvers, callbacks etc. @@ -40,13 +40,13 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 500 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=200, - save_initial_solution=true, - save_final_solution=true) +save_solution = SaveSolutionCallback(interval = 200, + save_initial_solution = true, + save_final_solution = true) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, save_solution) @@ -54,6 +54,6 @@ callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, sav # run the simulation # use a Runge-Kutta method with automatic (error based) time step size control -sol = solve(ode, RDPK3SpFSAL49(); abstol=1.0e-8, reltol=1.0e-8, - ode_default_options()..., callback=callbacks); +sol = solve(ode, RDPK3SpFSAL49(); abstol = 1.0e-8, reltol = 1.0e-8, + ode_default_options()..., callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/tree_2d_dgsem/elixir_shallowwater_source_terms_dirichlet.jl b/examples/tree_2d_dgsem/elixir_shallowwater_source_terms_dirichlet.jl index c3da957b764..f7544b1e32e 100644 --- a/examples/tree_2d_dgsem/elixir_shallowwater_source_terms_dirichlet.jl +++ b/examples/tree_2d_dgsem/elixir_shallowwater_source_terms_dirichlet.jl @@ -5,7 +5,7 @@ using Trixi ############################################################################### # Semidiscretization of the shallow water equations -equations = ShallowWaterEquations2D(gravity_constant=9.81) +equations = ShallowWaterEquations2D(gravity_constant = 9.81) initial_condition = initial_condition_convergence_test @@ -15,8 +15,9 @@ boundary_condition = BoundaryConditionDirichlet(initial_condition) # Get the DG approximation space volume_flux = (flux_wintermeyer_etal, flux_nonconservative_wintermeyer_etal) -solver = DGSEM(polydeg=3, surface_flux=(flux_lax_friedrichs, flux_nonconservative_fjordholm_etal), - volume_integral=VolumeIntegralFluxDifferencing(volume_flux)) +solver = DGSEM(polydeg = 3, + surface_flux = (flux_lax_friedrichs, flux_nonconservative_fjordholm_etal), + volume_integral = VolumeIntegralFluxDifferencing(volume_flux)) ############################################################################### # Get the TreeMesh and setup a periodic mesh @@ -24,14 +25,14 @@ solver = DGSEM(polydeg=3, surface_flux=(flux_lax_friedrichs, flux_nonconservativ coordinates_min = (0.0, 0.0) coordinates_max = (sqrt(2.0), sqrt(2.0)) mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=3, - n_cells_max=10_000, - periodicity=false) + initial_refinement_level = 3, + n_cells_max = 10_000, + periodicity = false) # create the semi discretization object semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver, boundary_conditions = boundary_condition, - source_terms=source_terms_convergence_test) + source_terms = source_terms_convergence_test) ############################################################################### # ODE solvers, callbacks etc. @@ -42,13 +43,13 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 500 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=200, - save_initial_solution=true, - save_final_solution=true) +save_solution = SaveSolutionCallback(interval = 200, + save_initial_solution = true, + save_final_solution = true) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, save_solution) @@ -56,6 +57,6 @@ callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, sav # run the simulation # use a Runge-Kutta method with automatic (error based) time step size control -sol = solve(ode, RDPK3SpFSAL49(); abstol=1.0e-8, reltol=1.0e-8, - ode_default_options()..., callback=callbacks); +sol = solve(ode, RDPK3SpFSAL49(); abstol = 1.0e-8, reltol = 1.0e-8, + ode_default_options()..., callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/tree_2d_dgsem/elixir_shallowwater_twolayer_convergence.jl b/examples/tree_2d_dgsem/elixir_shallowwater_twolayer_convergence.jl index 402361c8823..f7c8ab3a249 100644 --- a/examples/tree_2d_dgsem/elixir_shallowwater_twolayer_convergence.jl +++ b/examples/tree_2d_dgsem/elixir_shallowwater_twolayer_convergence.jl @@ -5,7 +5,8 @@ using Trixi ############################################################################### # Semidiscretization of the two-layer shallow water equations -equations = ShallowWaterTwoLayerEquations2D(gravity_constant=10.0, rho_upper=0.9, rho_lower=1.0) +equations = ShallowWaterTwoLayerEquations2D(gravity_constant = 10.0, rho_upper = 0.9, + rho_lower = 1.0) initial_condition = initial_condition_convergence_test @@ -13,9 +14,9 @@ initial_condition = initial_condition_convergence_test # Get the DG approximation space volume_flux = (flux_wintermeyer_etal, flux_nonconservative_wintermeyer_etal) -solver = DGSEM(polydeg=3, surface_flux=(flux_fjordholm_etal, flux_nonconservative_fjordholm_etal), - volume_integral=VolumeIntegralFluxDifferencing(volume_flux)) - +solver = DGSEM(polydeg = 3, + surface_flux = (flux_fjordholm_etal, flux_nonconservative_fjordholm_etal), + volume_integral = VolumeIntegralFluxDifferencing(volume_flux)) ############################################################################### # Get the TreeMesh and setup a periodic mesh @@ -23,13 +24,13 @@ solver = DGSEM(polydeg=3, surface_flux=(flux_fjordholm_etal, flux_nonconservativ coordinates_min = (0.0, 0.0) coordinates_max = (sqrt(2.0), sqrt(2.0)) mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=3, - n_cells_max=20_000, - periodicity=true) + initial_refinement_level = 3, + n_cells_max = 20_000, + periodicity = true) # Create the semi discretization object semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver, - source_terms=source_terms_convergence_test) + source_terms = source_terms_convergence_test) ############################################################################### # ODE solvers, callbacks etc. @@ -40,13 +41,13 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 500 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=500, - save_initial_solution=true, - save_final_solution=true) +save_solution = SaveSolutionCallback(interval = 500, + save_initial_solution = true, + save_final_solution = true) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, save_solution) @@ -54,6 +55,6 @@ callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, sav # run the simulation # use a Runge-Kutta method with automatic (error based) time step size control -sol = solve(ode, RDPK3SpFSAL49(), abstol=1.0e-8, reltol=1.0e-8, -save_everystep=false, callback=callbacks); +sol = solve(ode, RDPK3SpFSAL49(), abstol = 1.0e-8, reltol = 1.0e-8, + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/tree_2d_dgsem/elixir_shallowwater_twolayer_well_balanced.jl b/examples/tree_2d_dgsem/elixir_shallowwater_twolayer_well_balanced.jl index ba4bcd25774..1495e6d8568 100644 --- a/examples/tree_2d_dgsem/elixir_shallowwater_twolayer_well_balanced.jl +++ b/examples/tree_2d_dgsem/elixir_shallowwater_twolayer_well_balanced.jl @@ -6,21 +6,24 @@ using Trixi # Semidiscretization of the two-layer shallow water equations with a bottom topography function # to test well-balancedness -equations = ShallowWaterTwoLayerEquations2D(gravity_constant=9.81, H0=0.6, rho_upper=0.9, rho_lower=1.0) +equations = ShallowWaterTwoLayerEquations2D(gravity_constant = 9.81, H0 = 0.6, + rho_upper = 0.9, rho_lower = 1.0) # An initial condition with constant total water height, zero velocities and a bottom topography to # test well-balancedness function initial_condition_well_balanced(x, t, equations::ShallowWaterTwoLayerEquations2D) - H_lower = 0.5 - H_upper = 0.6 - v1_upper = 0.0 - v2_upper = 0.0 - v1_lower = 0.0 - v2_lower = 0.0 - b = (((x[1] - 0.5)^2 + (x[2] - 0.5)^2) < 0.04 ? 0.2 * (cos(4 * pi * sqrt((x[1] - 0.5)^2 + (x[2] + - -0.5)^2)) + 1) : 0.0) - - return prim2cons(SVector(H_upper, v1_upper, v2_upper, H_lower, v1_lower, v2_lower, b), equations) + H_lower = 0.5 + H_upper = 0.6 + v1_upper = 0.0 + v2_upper = 0.0 + v1_lower = 0.0 + v2_lower = 0.0 + b = (((x[1] - 0.5)^2 + (x[2] - 0.5)^2) < 0.04 ? + 0.2 * (cos(4 * pi * sqrt((x[1] - 0.5)^2 + (x[2] + + -0.5)^2)) + 1) : 0.0) + + return prim2cons(SVector(H_upper, v1_upper, v2_upper, H_lower, v1_lower, v2_lower, b), + equations) end initial_condition = initial_condition_well_balanced @@ -30,8 +33,8 @@ initial_condition = initial_condition_well_balanced volume_flux = (flux_wintermeyer_etal, flux_nonconservative_wintermeyer_etal) surface_flux = (flux_es_fjordholm_etal, flux_nonconservative_fjordholm_etal) -solver = DGSEM(polydeg=3, surface_flux=surface_flux, - volume_integral=VolumeIntegralFluxDifferencing(volume_flux)) +solver = DGSEM(polydeg = 3, surface_flux = surface_flux, + volume_integral = VolumeIntegralFluxDifferencing(volume_flux)) ############################################################################### # Get the TreeMesh and setup a periodic mesh @@ -39,9 +42,9 @@ solver = DGSEM(polydeg=3, surface_flux=surface_flux, coordinates_min = (0.0, 0.0) coordinates_max = (1.0, 1.0) mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=3, - n_cells_max=10_000, - periodicity=true) + initial_refinement_level = 3, + n_cells_max = 10_000, + periodicity = true) # Create the semi discretization object semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver) @@ -55,16 +58,16 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 1000 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval, - extra_analysis_integrals=(lake_at_rest_error,)) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval, + extra_analysis_integrals = (lake_at_rest_error,)) -stepsize_callback = StepsizeCallback(cfl=1.0) +stepsize_callback = StepsizeCallback(cfl = 1.0) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=1000, - save_initial_solution=true, - save_final_solution=true) +save_solution = SaveSolutionCallback(interval = 1000, + save_initial_solution = true, + save_final_solution = true) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, save_solution, stepsize_callback) @@ -72,7 +75,7 @@ callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, sav ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/tree_2d_dgsem/elixir_shallowwater_well_balanced.jl b/examples/tree_2d_dgsem/elixir_shallowwater_well_balanced.jl index 23efdcb7366..13023dfaba2 100644 --- a/examples/tree_2d_dgsem/elixir_shallowwater_well_balanced.jl +++ b/examples/tree_2d_dgsem/elixir_shallowwater_well_balanced.jl @@ -6,21 +6,21 @@ using Trixi # semidiscretization of the shallow water equations with a discontinuous # bottom topography function -equations = ShallowWaterEquations2D(gravity_constant=9.81, H0=3.25) +equations = ShallowWaterEquations2D(gravity_constant = 9.81, H0 = 3.25) # An initial condition with constant total water height and zero velocities to test well-balancedness. # Note, this routine is used to compute errors in the analysis callback but the initialization is # overwritten by `initial_condition_discontinuous_well_balancedness` below. function initial_condition_well_balancedness(x, t, equations::ShallowWaterEquations2D) - # Set the background values - H = equations.H0 - v1 = 0.0 - v2 = 0.0 - # bottom topography taken from Pond.control in [HOHQMesh](https://github.com/trixi-framework/HOHQMesh) - x1, x2 = x - b = ( 1.5 / exp( 0.5 * ((x1 - 1.0)^2 + (x2 - 1.0)^2) ) - + 0.75 / exp( 0.5 * ((x1 + 1.0)^2 + (x2 + 1.0)^2) ) ) - return prim2cons(SVector(H, v1, v2, b), equations) + # Set the background values + H = equations.H0 + v1 = 0.0 + v2 = 0.0 + # bottom topography taken from Pond.control in [HOHQMesh](https://github.com/trixi-framework/HOHQMesh) + x1, x2 = x + b = (1.5 / exp(0.5 * ((x1 - 1.0)^2 + (x2 - 1.0)^2)) + + 0.75 / exp(0.5 * ((x1 + 1.0)^2 + (x2 + 1.0)^2))) + return prim2cons(SVector(H, v1, v2, b), equations) end initial_condition = initial_condition_well_balancedness @@ -30,17 +30,17 @@ initial_condition = initial_condition_well_balancedness volume_flux = (flux_wintermeyer_etal, flux_nonconservative_wintermeyer_etal) surface_flux = (flux_fjordholm_etal, flux_nonconservative_fjordholm_etal) -solver = DGSEM(polydeg=4, surface_flux=surface_flux, - volume_integral=VolumeIntegralFluxDifferencing(volume_flux)) +solver = DGSEM(polydeg = 4, surface_flux = surface_flux, + volume_integral = VolumeIntegralFluxDifferencing(volume_flux)) ############################################################################### # Get the TreeMesh and setup a periodic mesh coordinates_min = (-1.0, -1.0) -coordinates_max = ( 1.0, 1.0) +coordinates_max = (1.0, 1.0) mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=2, - n_cells_max=10_000) + initial_refinement_level = 2, + n_cells_max = 10_000) # Create the semi discretization object semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver) @@ -61,30 +61,33 @@ ode = semidiscretize(semi, tspan) # In contrast to the usual signature of initial conditions, this one get passed the # `element_id` explicitly. In particular, this initial conditions works as intended # only for the TreeMesh2D with initial_refinement_level=2. -function initial_condition_discontinuous_well_balancedness(x, t, element_id, equations::ShallowWaterEquations2D) - # Set the background values - H = equations.H0 - v1 = 0.0 - v2 = 0.0 - b = 0.0 - - # Setup a discontinuous bottom topography using the element id number - if element_id == 7 - b = 2.0 + 0.5 * sin(2.0 * pi * x[1]) + 0.5 * cos(2.0 * pi * x[2]) - end - - return prim2cons(SVector(H, v1, v2, b), equations) +function initial_condition_discontinuous_well_balancedness(x, t, element_id, + equations::ShallowWaterEquations2D) + # Set the background values + H = equations.H0 + v1 = 0.0 + v2 = 0.0 + b = 0.0 + + # Setup a discontinuous bottom topography using the element id number + if element_id == 7 + b = 2.0 + 0.5 * sin(2.0 * pi * x[1]) + 0.5 * cos(2.0 * pi * x[2]) + end + + return prim2cons(SVector(H, v1, v2, b), equations) end # point to the data we want to augment u = Trixi.wrap_array(ode.u0, semi) # reset the initial condition for element in eachelement(semi.solver, semi.cache) - for j in eachnode(semi.solver), i in eachnode(semi.solver) - x_node = Trixi.get_node_coords(semi.cache.elements.node_coordinates, equations, semi.solver, i, j, element) - u_node = initial_condition_discontinuous_well_balancedness(x_node, first(tspan), element, equations) - Trixi.set_node_vars!(u, u_node, equations, semi.solver, i, j, element) - end + for j in eachnode(semi.solver), i in eachnode(semi.solver) + x_node = Trixi.get_node_coords(semi.cache.elements.node_coordinates, equations, + semi.solver, i, j, element) + u_node = initial_condition_discontinuous_well_balancedness(x_node, first(tspan), + element, equations) + Trixi.set_node_vars!(u, u_node, equations, semi.solver, i, j, element) + end end ############################################################################### @@ -93,16 +96,16 @@ end summary_callback = SummaryCallback() analysis_interval = 1000 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval, - extra_analysis_integrals=(lake_at_rest_error,)) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval, + extra_analysis_integrals = (lake_at_rest_error,)) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=1000, - save_initial_solution=true, - save_final_solution=true) +save_solution = SaveSolutionCallback(interval = 1000, + save_initial_solution = true, + save_final_solution = true) -stepsize_callback = StepsizeCallback(cfl=3.0) +stepsize_callback = StepsizeCallback(cfl = 3.0) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, save_solution, stepsize_callback) @@ -110,7 +113,7 @@ callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, sav ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/tree_2d_dgsem/elixir_shallowwater_well_balanced_wall.jl b/examples/tree_2d_dgsem/elixir_shallowwater_well_balanced_wall.jl index 66cd27f6864..f50bd4e4f65 100644 --- a/examples/tree_2d_dgsem/elixir_shallowwater_well_balanced_wall.jl +++ b/examples/tree_2d_dgsem/elixir_shallowwater_well_balanced_wall.jl @@ -5,21 +5,21 @@ using Trixi # semidiscretization of the shallow water equations with a discontinuous # bottom topography function -equations = ShallowWaterEquations2D(gravity_constant=9.81, H0=3.25) +equations = ShallowWaterEquations2D(gravity_constant = 9.81, H0 = 3.25) # An initial condition with constant total water height and zero velocities to test well-balancedness. # Note, this routine is used to compute errors in the analysis callback but the initialization is # overwritten by `initial_condition_discontinuous_well_balancedness` below. function initial_condition_well_balancedness(x, t, equations::ShallowWaterEquations2D) - # Set the background values - H = equations.H0 - v1 = 0.0 - v2 = 0.0 - # bottom topography taken from Pond.control in [HOHQMesh](https://github.com/trixi-framework/HOHQMesh) - x1, x2 = x - b = ( 1.5 / exp( 0.5 * ((x1 - 1.0)^2 + (x2 - 1.0)^2) ) - + 0.75 / exp( 0.5 * ((x1 + 1.0)^2 + (x2 + 1.0)^2) ) ) - return prim2cons(SVector(H, v1, v2, b), equations) + # Set the background values + H = equations.H0 + v1 = 0.0 + v2 = 0.0 + # bottom topography taken from Pond.control in [HOHQMesh](https://github.com/trixi-framework/HOHQMesh) + x1, x2 = x + b = (1.5 / exp(0.5 * ((x1 - 1.0)^2 + (x2 - 1.0)^2)) + + 0.75 / exp(0.5 * ((x1 + 1.0)^2 + (x2 + 1.0)^2))) + return prim2cons(SVector(H, v1, v2, b), equations) end initial_condition = initial_condition_well_balancedness @@ -31,8 +31,8 @@ boundary_condition = boundary_condition_slip_wall volume_flux = (flux_wintermeyer_etal, flux_nonconservative_wintermeyer_etal) surface_flux = (flux_fjordholm_etal, flux_nonconservative_fjordholm_etal) -solver = DGSEM(polydeg=4, surface_flux=surface_flux, - volume_integral=VolumeIntegralFluxDifferencing(volume_flux)) +solver = DGSEM(polydeg = 4, surface_flux = surface_flux, + volume_integral = VolumeIntegralFluxDifferencing(volume_flux)) ############################################################################### # Get the TreeMesh and setup a periodic mesh @@ -40,8 +40,8 @@ solver = DGSEM(polydeg=4, surface_flux=surface_flux, coordinates_min = (-1.0, -1.0) coordinates_max = (1.0, 1.0) mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=2, - n_cells_max=10_000, + initial_refinement_level = 2, + n_cells_max = 10_000, periodicity = false) # create the semi discretization object @@ -64,30 +64,33 @@ ode = semidiscretize(semi, tspan) # In contrast to the usual signature of initial conditions, this one get passed the # `element_id` explicitly. In particular, this initial conditions works as intended # only for the TreeMesh2D with initial_refinement_level=2. -function initial_condition_discontinuous_well_balancedness(x, t, element_id, equations::ShallowWaterEquations2D) - # Set the background values - H = equations.H0 - v1 = 0.0 - v2 = 0.0 - b = 0.0 - - # Setup a discontinuous bottom topography using the element id number - if element_id == 7 - b = 2.0 + 0.5 * sin(2.0 * pi * x[1]) + 0.5 * cos(2.0 * pi * x[2]) - end - - return prim2cons(SVector(H, v1, v2, b), equations) +function initial_condition_discontinuous_well_balancedness(x, t, element_id, + equations::ShallowWaterEquations2D) + # Set the background values + H = equations.H0 + v1 = 0.0 + v2 = 0.0 + b = 0.0 + + # Setup a discontinuous bottom topography using the element id number + if element_id == 7 + b = 2.0 + 0.5 * sin(2.0 * pi * x[1]) + 0.5 * cos(2.0 * pi * x[2]) + end + + return prim2cons(SVector(H, v1, v2, b), equations) end # point to the data we want to augment u = Trixi.wrap_array(ode.u0, semi) # reset the initial condition for element in eachelement(semi.solver, semi.cache) - for j in eachnode(semi.solver), i in eachnode(semi.solver) - x_node = Trixi.get_node_coords(semi.cache.elements.node_coordinates, equations, semi.solver, i, j, element) - u_node = initial_condition_discontinuous_well_balancedness(x_node, first(tspan), element, equations) - Trixi.set_node_vars!(u, u_node, equations, semi.solver, i, j, element) - end + for j in eachnode(semi.solver), i in eachnode(semi.solver) + x_node = Trixi.get_node_coords(semi.cache.elements.node_coordinates, equations, + semi.solver, i, j, element) + u_node = initial_condition_discontinuous_well_balancedness(x_node, first(tspan), + element, equations) + Trixi.set_node_vars!(u, u_node, equations, semi.solver, i, j, element) + end end ############################################################################### @@ -96,16 +99,16 @@ end summary_callback = SummaryCallback() analysis_interval = 1000 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval, - extra_analysis_integrals=(lake_at_rest_error,)) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval, + extra_analysis_integrals = (lake_at_rest_error,)) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=1000, - save_initial_solution=true, - save_final_solution=true) +save_solution = SaveSolutionCallback(interval = 1000, + save_initial_solution = true, + save_final_solution = true) -stepsize_callback = StepsizeCallback(cfl=3.0) +stepsize_callback = StepsizeCallback(cfl = 3.0) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, save_solution, stepsize_callback) @@ -113,7 +116,7 @@ callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, sav ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); -summary_callback() # print the timer summary \ No newline at end of file +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); +summary_callback() # print the timer summary diff --git a/examples/tree_2d_dgsem/elixir_shallowwater_well_balanced_wet_dry.jl b/examples/tree_2d_dgsem/elixir_shallowwater_well_balanced_wet_dry.jl index 6fede2fa4ea..034411c2b54 100644 --- a/examples/tree_2d_dgsem/elixir_shallowwater_well_balanced_wet_dry.jl +++ b/examples/tree_2d_dgsem/elixir_shallowwater_well_balanced_wet_dry.jl @@ -8,7 +8,7 @@ using Printf: @printf, @sprintf # # TODO: TrixiShallowWater: wet/dry example elixir -equations = ShallowWaterEquations2D(gravity_constant=9.812) +equations = ShallowWaterEquations2D(gravity_constant = 9.812) """ initial_condition_well_balanced_chen_noelle(x, t, equations:: ShallowWaterEquations2D) @@ -23,28 +23,29 @@ The initial condition is taken from Section 5.2 of the paper: A new hydrostatic reconstruction scheme based on subcell reconstructions [DOI:10.1137/15M1053074](https://dx.doi.org/10.1137/15M1053074) """ -function initial_condition_complex_bottom_well_balanced(x, t, equations::ShallowWaterEquations2D) - v1 = 0 - v2 = 0 - b = sin(4 * pi * x[1]) + 3 - - if x[1] >= 0.5 - b = sin(4 * pi * x[1]) + 1 - end - - H = max(b, 2.5) - if x[1] >= 0.5 - H = max(b, 1.5) - end - - # It is mandatory to shift the water level at dry areas to make sure the water height h - # stays positive. The system would not be stable for h set to a hard 0 due to division by h in - # the computation of velocity, e.g., (h v1) / h. Therefore, a small dry state threshold - # with a default value of 500*eps() ≈ 1e-13 in double precision, is set in the constructor above - # for the ShallowWaterEquations and added to the initial condition if h = 0. - # This default value can be changed within the constructor call depending on the simulation setup. - H = max(H, b + equations.threshold_limiter) - return prim2cons(SVector(H, v1, v2, b), equations) +function initial_condition_complex_bottom_well_balanced(x, t, + equations::ShallowWaterEquations2D) + v1 = 0 + v2 = 0 + b = sin(4 * pi * x[1]) + 3 + + if x[1] >= 0.5 + b = sin(4 * pi * x[1]) + 1 + end + + H = max(b, 2.5) + if x[1] >= 0.5 + H = max(b, 1.5) + end + + # It is mandatory to shift the water level at dry areas to make sure the water height h + # stays positive. The system would not be stable for h set to a hard 0 due to division by h in + # the computation of velocity, e.g., (h v1) / h. Therefore, a small dry state threshold + # with a default value of 500*eps() ≈ 1e-13 in double precision, is set in the constructor above + # for the ShallowWaterEquations and added to the initial condition if h = 0. + # This default value can be changed within the constructor call depending on the simulation setup. + H = max(H, b + equations.threshold_limiter) + return prim2cons(SVector(H, v1, v2, b), equations) end initial_condition = initial_condition_complex_bottom_well_balanced @@ -53,19 +54,20 @@ initial_condition = initial_condition_complex_bottom_well_balanced # Get the DG approximation space volume_flux = (flux_wintermeyer_etal, flux_nonconservative_wintermeyer_etal) -surface_flux = (FluxHydrostaticReconstruction(flux_hll_chen_noelle, hydrostatic_reconstruction_chen_noelle), +surface_flux = (FluxHydrostaticReconstruction(flux_hll_chen_noelle, + hydrostatic_reconstruction_chen_noelle), flux_nonconservative_chen_noelle) basis = LobattoLegendreBasis(3) indicator_sc = IndicatorHennemannGassnerShallowWater(equations, basis, - alpha_max=0.5, - alpha_min=0.001, - alpha_smooth=true, - variable=waterheight_pressure) + alpha_max = 0.5, + alpha_min = 0.001, + alpha_smooth = true, + variable = waterheight_pressure) volume_integral = VolumeIntegralShockCapturingHG(indicator_sc; - volume_flux_dg=volume_flux, - volume_flux_fv=surface_flux) + volume_flux_dg = volume_flux, + volume_flux_fv = surface_flux) solver = DGSEM(basis, surface_flux, volume_integral) @@ -76,8 +78,8 @@ coordinates_min = (0.0, 0.0) coordinates_max = (1.0, 1.0) mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=3, - n_cells_max=10_000) + initial_refinement_level = 3, + n_cells_max = 10_000) # create the semi discretization object semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver) @@ -102,18 +104,20 @@ ode = semidiscretize(semi, tspan) u = Trixi.wrap_array(ode.u0, semi) # reset the initial condition for element in eachelement(semi.solver, semi.cache) - for j in eachnode(semi.solver), i in eachnode(semi.solver) - x_node = Trixi.get_node_coords(semi.cache.elements.node_coordinates, equations, semi.solver, i, j, element) - # We know that the discontinuity is a vertical line. Slightly augment the x value by a factor - # of unit roundoff to avoid the repeted value from the LGL nodes at at interface. - if i == 1 - x_node = SVector(nextfloat(x_node[1]) , x_node[2]) - elseif i == nnodes(semi.solver) - x_node = SVector(prevfloat(x_node[1]) , x_node[2]) + for j in eachnode(semi.solver), i in eachnode(semi.solver) + x_node = Trixi.get_node_coords(semi.cache.elements.node_coordinates, equations, + semi.solver, i, j, element) + # We know that the discontinuity is a vertical line. Slightly augment the x value by a factor + # of unit roundoff to avoid the repeted value from the LGL nodes at at interface. + if i == 1 + x_node = SVector(nextfloat(x_node[1]), x_node[2]) + elseif i == nnodes(semi.solver) + x_node = SVector(prevfloat(x_node[1]), x_node[2]) + end + u_node = initial_condition_complex_bottom_well_balanced(x_node, first(tspan), + equations) + Trixi.set_node_vars!(u, u_node, equations, semi.solver, i, j, element) end - u_node = initial_condition_complex_bottom_well_balanced(x_node, first(tspan), equations) - Trixi.set_node_vars!(u, u_node, equations, semi.solver, i, j, element) - end end ############################################################################### @@ -122,27 +126,27 @@ end summary_callback = SummaryCallback() analysis_interval = 1000 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval, save_analysis=false) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval, + save_analysis = false) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=1000, - save_initial_solution=true, - save_final_solution=true) - -stepsize_callback = StepsizeCallback(cfl=2.0) +save_solution = SaveSolutionCallback(interval = 1000, + save_initial_solution = true, + save_final_solution = true) +stepsize_callback = StepsizeCallback(cfl = 2.0) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, save_solution, stepsize_callback) -stage_limiter! = PositivityPreservingLimiterShallowWater(variables=(Trixi.waterheight,)) +stage_limiter! = PositivityPreservingLimiterShallowWater(variables = (Trixi.waterheight,)) ############################################################################### # run the simulation -sol = solve(ode, SSPRK43(stage_limiter!); dt=1.0, - ode_default_options()..., callback=callbacks, adaptive=false); +sol = solve(ode, SSPRK43(stage_limiter!); dt = 1.0, + ode_default_options()..., callback = callbacks, adaptive = false); summary_callback() # print the timer summary @@ -157,34 +161,38 @@ summary_callback() # print the timer summary function lake_at_rest_error_two_level(u, x, equations::ShallowWaterEquations2D) h, _, _, b = u - # For well-balancedness testing with possible wet/dry regions the reference - # water height `H0` accounts for the possibility that the bottom topography - # can emerge out of the water as well as for the threshold offset to avoid - # division by a "hard" zero water heights as well. + # For well-balancedness testing with possible wet/dry regions the reference + # water height `H0` accounts for the possibility that the bottom topography + # can emerge out of the water as well as for the threshold offset to avoid + # division by a "hard" zero water heights as well. - if x[1] < 0.5 - H0_wet_dry = max( 2.5 , b + equations.threshold_limiter ) - else - H0_wet_dry = max( 1.5 , b + equations.threshold_limiter ) - end + if x[1] < 0.5 + H0_wet_dry = max(2.5, b + equations.threshold_limiter) + else + H0_wet_dry = max(1.5, b + equations.threshold_limiter) + end - return abs(H0_wet_dry - (h + b)) + return abs(H0_wet_dry - (h + b)) end # point to the data we want to analyze u = Trixi.wrap_array(sol[end], semi) # Perform the actual integration of the well-balancedness error over the domain -l1_well_balance_error = Trixi.integrate_via_indices(u, mesh, equations, semi.solver, semi.cache; normalize=true) do u, i, j, element, equations, solver - x_node = Trixi.get_node_coords(semi.cache.elements.node_coordinates, equations, solver, i, j, element) - # We know that the discontinuity is a vertical line. Slightly augment the x value by a factor - # of unit roundoff to avoid the repeted value from the LGL nodes at at interface. - if i == 1 - x_node = SVector(nextfloat(x_node[1]) , x_node[2]) - elseif i == nnodes(semi.solver) - x_node = SVector(prevfloat(x_node[1]) , x_node[2]) - end - u_local = Trixi.get_node_vars(u, equations, solver, i, j, element) - return lake_at_rest_error_two_level(u_local, x_node, equations) +l1_well_balance_error = Trixi.integrate_via_indices(u, mesh, equations, semi.solver, + semi.cache; + normalize = true) do u, i, j, element, + equations, solver + x_node = Trixi.get_node_coords(semi.cache.elements.node_coordinates, equations, solver, + i, j, element) + # We know that the discontinuity is a vertical line. Slightly augment the x value by a factor + # of unit roundoff to avoid the repeted value from the LGL nodes at at interface. + if i == 1 + x_node = SVector(nextfloat(x_node[1]), x_node[2]) + elseif i == nnodes(semi.solver) + x_node = SVector(prevfloat(x_node[1]), x_node[2]) + end + u_local = Trixi.get_node_vars(u, equations, solver, i, j, element) + return lake_at_rest_error_two_level(u_local, x_node, equations) end # report the well-balancedness lake-at-rest error to the screen diff --git a/examples/tree_2d_fdsbp/elixir_advection_extended.jl b/examples/tree_2d_fdsbp/elixir_advection_extended.jl index 6e599d9f42d..8716a9a6b78 100644 --- a/examples/tree_2d_fdsbp/elixir_advection_extended.jl +++ b/examples/tree_2d_fdsbp/elixir_advection_extended.jl @@ -13,22 +13,21 @@ equations = LinearScalarAdvectionEquation2D(advection_velocity) initial_condition = initial_condition_convergence_test D_SBP = derivative_operator(SummationByPartsOperators.MattssonNordström2004(), - derivative_order=1, accuracy_order=4, - xmin=0.0, xmax=1.0, N=100) + derivative_order = 1, accuracy_order = 4, + xmin = 0.0, xmax = 1.0, N = 100) solver = FDSBP(D_SBP, - surface_integral=SurfaceIntegralStrongForm(flux_lax_friedrichs), - volume_integral=VolumeIntegralStrongForm()) + surface_integral = SurfaceIntegralStrongForm(flux_lax_friedrichs), + volume_integral = VolumeIntegralStrongForm()) coordinates_min = (-1.0, -1.0) -coordinates_max = ( 1.0, 1.0) +coordinates_max = (1.0, 1.0) mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=1, - n_cells_max=30_000, - periodicity=true) + initial_refinement_level = 1, + n_cells_max = 30_000, + periodicity = true) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver) - ############################################################################### # ODE solvers, callbacks etc. @@ -38,19 +37,18 @@ ode = semidiscretize(semi, tspan); summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval, - extra_analysis_integrals=(energy_total,)) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval, + extra_analysis_integrals = (energy_total,)) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback) - ############################################################################### # run the simulation -sol = solve(ode, RDPK3SpFSAL49(); abstol=1.0e-9, reltol=1.0e-9, - ode_default_options()..., callback=callbacks) +sol = solve(ode, RDPK3SpFSAL49(); abstol = 1.0e-9, reltol = 1.0e-9, + ode_default_options()..., callback = callbacks) summary_callback() diff --git a/examples/tree_2d_fdsbp/elixir_euler_convergence.jl b/examples/tree_2d_fdsbp/elixir_euler_convergence.jl index 2a6c291f0bf..123be02bd17 100644 --- a/examples/tree_2d_fdsbp/elixir_euler_convergence.jl +++ b/examples/tree_2d_fdsbp/elixir_euler_convergence.jl @@ -13,23 +13,24 @@ initial_condition = initial_condition_convergence_test source_terms = source_terms_convergence_test D_upw = upwind_operators(SummationByPartsOperators.Mattsson2017, - derivative_order=1, - accuracy_order=4, - xmin=-1.0, xmax=1.0, - N=16) + derivative_order = 1, + accuracy_order = 4, + xmin = -1.0, xmax = 1.0, + N = 16) flux_splitting = splitting_steger_warming solver = FDSBP(D_upw, - surface_integral=SurfaceIntegralUpwind(flux_splitting), - volume_integral=VolumeIntegralUpwind(flux_splitting)) + surface_integral = SurfaceIntegralUpwind(flux_splitting), + volume_integral = VolumeIntegralUpwind(flux_splitting)) coordinates_min = (-1.0, -1.0) -coordinates_max = ( 1.0, 1.0) +coordinates_max = (1.0, 1.0) mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=3, - n_cells_max=30_000, - periodicity=true) + initial_refinement_level = 3, + n_cells_max = 30_000, + periodicity = true) -semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver, source_terms = source_terms_convergence_test) +semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver, + source_terms = source_terms_convergence_test) ############################################################################### # ODE solvers, callbacks etc. @@ -40,15 +41,15 @@ ode = semidiscretize(semi, tspan); summary_callback = SummaryCallback() analysis_interval = 1000 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval, - extra_analysis_integrals=(energy_total,)) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval, + extra_analysis_integrals = (energy_total,)) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=1000, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 1000, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) callbacks = CallbackSet(summary_callback, analysis_callback, @@ -58,6 +59,6 @@ callbacks = CallbackSet(summary_callback, ############################################################################### # run the simulation -sol = solve(ode, SSPRK43(); abstol=1.0e-9, reltol=1.0e-9, - ode_default_options()..., callback=callbacks) +sol = solve(ode, SSPRK43(); abstol = 1.0e-9, reltol = 1.0e-9, + ode_default_options()..., callback = callbacks) summary_callback() diff --git a/examples/tree_2d_fdsbp/elixir_euler_kelvin_helmholtz_instability.jl b/examples/tree_2d_fdsbp/elixir_euler_kelvin_helmholtz_instability.jl index e63343852ab..4c41b84af33 100644 --- a/examples/tree_2d_fdsbp/elixir_euler_kelvin_helmholtz_instability.jl +++ b/examples/tree_2d_fdsbp/elixir_euler_kelvin_helmholtz_instability.jl @@ -9,42 +9,42 @@ using Trixi equations = CompressibleEulerEquations2D(1.4) -function initial_condition_kelvin_helmholtz_instability(x, t, equations::CompressibleEulerEquations2D) - # change discontinuity to tanh - # typical resolution 128^2, 256^2 - # domain size is [-1,+1]^2 - slope = 15 - amplitude = 0.02 - B = tanh(slope * x[2] + 7.5) - tanh(slope * x[2] - 7.5) - rho = 0.5 + 0.75 * B - v1 = 0.5 * (B - 1) - v2 = 0.1 * sin(2 * pi * x[1]) - p = 1.0 - return prim2cons(SVector(rho, v1, v2, p), equations) +function initial_condition_kelvin_helmholtz_instability(x, t, + equations::CompressibleEulerEquations2D) + # change discontinuity to tanh + # typical resolution 128^2, 256^2 + # domain size is [-1,+1]^2 + slope = 15 + amplitude = 0.02 + B = tanh(slope * x[2] + 7.5) - tanh(slope * x[2] - 7.5) + rho = 0.5 + 0.75 * B + v1 = 0.5 * (B - 1) + v2 = 0.1 * sin(2 * pi * x[1]) + p = 1.0 + return prim2cons(SVector(rho, v1, v2, p), equations) end initial_condition = initial_condition_kelvin_helmholtz_instability D_upw = upwind_operators(SummationByPartsOperators.Mattsson2017, - derivative_order=1, - accuracy_order=4, - xmin=-1.0, xmax=1.0, - N=16) + derivative_order = 1, + accuracy_order = 4, + xmin = -1.0, xmax = 1.0, + N = 16) flux_splitting = splitting_vanleer_haenel solver = FDSBP(D_upw, - surface_integral=SurfaceIntegralUpwind(flux_splitting), - volume_integral=VolumeIntegralUpwind(flux_splitting)) + surface_integral = SurfaceIntegralUpwind(flux_splitting), + volume_integral = VolumeIntegralUpwind(flux_splitting)) coordinates_min = (-1.0, -1.0) -coordinates_max = ( 1.0, 1.0) +coordinates_max = (1.0, 1.0) mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=4, - n_cells_max=30_000, - periodicity=true) + initial_refinement_level = 4, + n_cells_max = 30_000, + periodicity = true) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver) - ############################################################################### # ODE solvers, callbacks etc. @@ -54,27 +54,26 @@ ode = semidiscretize(semi, tspan); summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval, - save_analysis=true, - extra_analysis_integrals=(entropy, - energy_total,)) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval, + save_analysis = true, + extra_analysis_integrals = (entropy, + energy_total)) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=1000, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 1000, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) callbacks = CallbackSet(summary_callback, analysis_callback, save_solution, alive_callback) - ############################################################################### # run the simulation -sol = solve(ode, SSPRK43(); abstol=1.0e-6, reltol=1.0e-6, dt=1e-3, - ode_default_options()..., callback=callbacks) +sol = solve(ode, SSPRK43(); abstol = 1.0e-6, reltol = 1.0e-6, dt = 1e-3, + ode_default_options()..., callback = callbacks) summary_callback() diff --git a/examples/tree_2d_fdsbp/elixir_euler_vortex.jl b/examples/tree_2d_fdsbp/elixir_euler_vortex.jl index c1bee8f9c4d..d0847cc8016 100644 --- a/examples/tree_2d_fdsbp/elixir_euler_vortex.jl +++ b/examples/tree_2d_fdsbp/elixir_euler_vortex.jl @@ -19,62 +19,61 @@ The classical isentropic vortex test case of [NASA/CR-97-206253](https://ntrs.nasa.gov/citations/19980007543) """ function initial_condition_isentropic_vortex(x, t, equations::CompressibleEulerEquations2D) - # needs appropriate mesh size, e.g. [-10,-10]x[10,10] - # for error convergence: make sure that the end time is such that the is back at the initial state!! - # for the current velocity and domain size: t_end should be a multiple of 20s - # initial center of the vortex - inicenter = SVector(0.0, 0.0) - # size and strength of the vortex - iniamplitude = 5.0 - # base flow - rho = 1.0 - v1 = 1.0 - v2 = 1.0 - vel = SVector(v1, v2) - p = 25.0 - rt = p / rho # ideal gas equation - t_loc = 0.0 - cent = inicenter + vel*t_loc # advection of center - # ATTENTION: handle periodic BC, but only for v1 = v2 = 1.0 (!!!!) - - cent = x - cent # distance to center point - - #cent=cross(iniaxis,cent) # distance to axis, tangent vector, length r - # cross product with iniaxis = [0, 0, 1] - cent = SVector(-cent[2], cent[1]) - r2 = cent[1]^2 + cent[2]^2 - du = iniamplitude/(2*π)*exp(0.5*(1-r2)) # vel. perturbation - dtemp = -(equations.gamma-1)/(2*equations.gamma*rt)*du^2 # isentropic - rho = rho * (1+dtemp)^(1/(equations.gamma-1)) - vel = vel + du*cent - v1, v2 = vel - p = p * (1+dtemp)^(equations.gamma/(equations.gamma-1)) - prim = SVector(rho, v1, v2, p) - return prim2cons(prim, equations) + # needs appropriate mesh size, e.g. [-10,-10]x[10,10] + # for error convergence: make sure that the end time is such that the is back at the initial state!! + # for the current velocity and domain size: t_end should be a multiple of 20s + # initial center of the vortex + inicenter = SVector(0.0, 0.0) + # size and strength of the vortex + iniamplitude = 5.0 + # base flow + rho = 1.0 + v1 = 1.0 + v2 = 1.0 + vel = SVector(v1, v2) + p = 25.0 + rt = p / rho # ideal gas equation + t_loc = 0.0 + cent = inicenter + vel * t_loc # advection of center + # ATTENTION: handle periodic BC, but only for v1 = v2 = 1.0 (!!!!) + + cent = x - cent # distance to center point + + #cent=cross(iniaxis,cent) # distance to axis, tangent vector, length r + # cross product with iniaxis = [0, 0, 1] + cent = SVector(-cent[2], cent[1]) + r2 = cent[1]^2 + cent[2]^2 + du = iniamplitude / (2 * π) * exp(0.5 * (1 - r2)) # vel. perturbation + dtemp = -(equations.gamma - 1) / (2 * equations.gamma * rt) * du^2 # isentropic + rho = rho * (1 + dtemp)^(1 / (equations.gamma - 1)) + vel = vel + du * cent + v1, v2 = vel + p = p * (1 + dtemp)^(equations.gamma / (equations.gamma - 1)) + prim = SVector(rho, v1, v2, p) + return prim2cons(prim, equations) end initial_condition = initial_condition_isentropic_vortex D_upw = upwind_operators(SummationByPartsOperators.Mattsson2017, - derivative_order=1, - accuracy_order=4, - xmin=-1.0, xmax=1.0, - N=16) + derivative_order = 1, + accuracy_order = 4, + xmin = -1.0, xmax = 1.0, + N = 16) flux_splitting = splitting_steger_warming solver = FDSBP(D_upw, - surface_integral=SurfaceIntegralUpwind(flux_splitting), - volume_integral=VolumeIntegralUpwind(flux_splitting)) + surface_integral = SurfaceIntegralUpwind(flux_splitting), + volume_integral = VolumeIntegralUpwind(flux_splitting)) coordinates_min = (-10.0, -10.0) -coordinates_max = ( 10.0, 10.0) +coordinates_max = (10.0, 10.0) mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=3, - n_cells_max=30_000, - periodicity=true) + initial_refinement_level = 3, + n_cells_max = 30_000, + periodicity = true) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver) - ############################################################################### # ODE solvers, callbacks etc. @@ -84,24 +83,23 @@ ode = semidiscretize(semi, tspan); summary_callback = SummaryCallback() analysis_interval = 1000 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=1000, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 1000, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) callbacks = CallbackSet(summary_callback, analysis_callback, save_solution, alive_callback) - ############################################################################### # run the simulation -sol = solve(ode, SSPRK43(); abstol=1.0e-6, reltol=1.0e-6, dt=1e-3, - ode_default_options()..., callback=callbacks) +sol = solve(ode, SSPRK43(); abstol = 1.0e-6, reltol = 1.0e-6, dt = 1e-3, + ode_default_options()..., callback = callbacks) summary_callback() diff --git a/examples/tree_3d_dgsem/elixir_advection_amr.jl b/examples/tree_3d_dgsem/elixir_advection_amr.jl index 67664eed563..19a9bd18a8a 100644 --- a/examples/tree_3d_dgsem/elixir_advection_amr.jl +++ b/examples/tree_3d_dgsem/elixir_advection_amr.jl @@ -9,18 +9,16 @@ advection_velocity = (0.2, -0.7, 0.5) equations = LinearScalarAdvectionEquation3D(advection_velocity) initial_condition = initial_condition_gauss -solver = DGSEM(polydeg=3, surface_flux=flux_lax_friedrichs) +solver = DGSEM(polydeg = 3, surface_flux = flux_lax_friedrichs) coordinates_min = (-5.0, -5.0, -5.0) -coordinates_max = ( 5.0, 5.0, 5.0) +coordinates_max = (5.0, 5.0, 5.0) mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=4, - n_cells_max=30_000) - + initial_refinement_level = 4, + n_cells_max = 30_000) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver) - ############################################################################### # ODE solvers, callbacks etc. @@ -30,26 +28,26 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval, - extra_analysis_integrals=(entropy,)) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval, + extra_analysis_integrals = (entropy,)) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=100, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 100, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) -amr_controller = ControllerThreeLevel(semi, IndicatorMax(semi, variable=first), - base_level=4, - med_level=5, med_threshold=0.1, - max_level=6, max_threshold=0.6) +amr_controller = ControllerThreeLevel(semi, IndicatorMax(semi, variable = first), + base_level = 4, + med_level = 5, med_threshold = 0.1, + max_level = 6, max_threshold = 0.6) amr_callback = AMRCallback(semi, amr_controller, - interval=5, - adapt_initial_condition=true, - adapt_initial_condition_only_refine=true) + interval = 5, + adapt_initial_condition = true, + adapt_initial_condition_only_refine = true) -stepsize_callback = StepsizeCallback(cfl=1.2) +stepsize_callback = StepsizeCallback(cfl = 1.2) callbacks = CallbackSet(summary_callback, analysis_callback, @@ -61,7 +59,7 @@ callbacks = CallbackSet(summary_callback, ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/tree_3d_dgsem/elixir_advection_basic.jl b/examples/tree_3d_dgsem/elixir_advection_basic.jl index da91a70fe6d..3ea50423be7 100644 --- a/examples/tree_3d_dgsem/elixir_advection_basic.jl +++ b/examples/tree_3d_dgsem/elixir_advection_basic.jl @@ -9,19 +9,19 @@ advection_velocity = (0.2, -0.7, 0.5) equations = LinearScalarAdvectionEquation3D(advection_velocity) # Create DG solver with polynomial degree = 3 and (local) Lax-Friedrichs/Rusanov flux as surface flux -solver = DGSEM(polydeg=3, surface_flux=flux_lax_friedrichs) +solver = DGSEM(polydeg = 3, surface_flux = flux_lax_friedrichs) coordinates_min = (-1.0, -1.0, -1.0) # minimum coordinates (min(x), min(y), min(z)) -coordinates_max = ( 1.0, 1.0, 1.0) # maximum coordinates (max(x), max(y), max(z)) +coordinates_max = (1.0, 1.0, 1.0) # maximum coordinates (max(x), max(y), max(z)) # Create a uniformly refined mesh with periodic boundaries mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=3, - n_cells_max=30_000) # set maximum capacity of tree data structure + initial_refinement_level = 3, + n_cells_max = 30_000) # set maximum capacity of tree data structure # A semidiscretization collects data structures and functions for the spatial discretization -semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition_convergence_test, solver) - +semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition_convergence_test, + solver) ############################################################################### # ODE solvers, callbacks etc. @@ -34,26 +34,26 @@ ode = semidiscretize(semi, (0.0, 1.0)); summary_callback = SummaryCallback() # The AnalysisCallback allows to analyse the solution in regular intervals and prints the results -analysis_callback = AnalysisCallback(semi, interval=100) +analysis_callback = AnalysisCallback(semi, interval = 100) # The SaveSolutionCallback allows to save the solution to a file in regular intervals -save_solution = SaveSolutionCallback(interval=100, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 100, + solution_variables = cons2prim) # # The StepsizeCallback handles the re-calculation of the maximum Δt after each time step -stepsize_callback = StepsizeCallback(cfl=1.2) +stepsize_callback = StepsizeCallback(cfl = 1.2) # Create a CallbackSet to collect all callbacks such that they can be passed to the ODE solver -callbacks = CallbackSet(summary_callback, analysis_callback, save_solution, stepsize_callback) - +callbacks = CallbackSet(summary_callback, analysis_callback, save_solution, + stepsize_callback) ############################################################################### # run the simulation # OrdinaryDiffEq's `solve` method evolves the solution in time and executes the passed callbacks -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); # Print the timer summary summary_callback() diff --git a/examples/tree_3d_dgsem/elixir_advection_diffusion_amr.jl b/examples/tree_3d_dgsem/elixir_advection_diffusion_amr.jl index 0fab685b642..6a8f8d02590 100644 --- a/examples/tree_3d_dgsem/elixir_advection_diffusion_amr.jl +++ b/examples/tree_3d_dgsem/elixir_advection_diffusion_amr.jl @@ -11,27 +11,28 @@ equations = LinearScalarAdvectionEquation3D(advection_velocity) diffusivity() = 5.0e-4 equations_parabolic = LaplaceDiffusion3D(diffusivity(), equations) -solver = DGSEM(polydeg=3, surface_flux=flux_lax_friedrichs) +solver = DGSEM(polydeg = 3, surface_flux = flux_lax_friedrichs) coordinates_min = (-1.0, -1.0, -1.0) -coordinates_max = ( 1.0, 1.0, 1.0) +coordinates_max = (1.0, 1.0, 1.0) mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=4, - n_cells_max=80_000) + initial_refinement_level = 4, + n_cells_max = 80_000) # Define initial condition -function initial_condition_diffusive_convergence_test(x, t, equation::LinearScalarAdvectionEquation3D) - # Store translated coordinate for easy use of exact solution - x_trans = x - equation.advection_velocity * t - - nu = diffusivity() - c = 1.0 - A = 0.5 - L = 2 - f = 1/L - omega = 2 * pi * f - scalar = c + A * sin(omega * sum(x_trans)) * exp(-2 * nu * omega^2 * t) - return SVector(scalar) +function initial_condition_diffusive_convergence_test(x, t, + equation::LinearScalarAdvectionEquation3D) + # Store translated coordinate for easy use of exact solution + x_trans = x - equation.advection_velocity * t + + nu = diffusivity() + c = 1.0 + A = 0.5 + L = 2 + f = 1 / L + omega = 2 * pi * f + scalar = c + A * sin(omega * sum(x_trans)) * exp(-2 * nu * omega^2 * t) + return SVector(scalar) end initial_condition = initial_condition_diffusive_convergence_test @@ -43,9 +44,8 @@ boundary_conditions_parabolic = boundary_condition_periodic semi = SemidiscretizationHyperbolicParabolic(mesh, (equations, equations_parabolic), initial_condition, solver; - boundary_conditions=(boundary_conditions, - boundary_conditions_parabolic)) - + boundary_conditions = (boundary_conditions, + boundary_conditions_parabolic)) ############################################################################### # ODE solvers, callbacks etc. @@ -56,26 +56,26 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval, - extra_analysis_integrals=(entropy,)) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval, + extra_analysis_integrals = (entropy,)) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=100, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 100, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) -amr_controller = ControllerThreeLevel(semi, IndicatorMax(semi, variable=first), - base_level=3, - med_level=4, med_threshold=1.2, - max_level=5, max_threshold=1.45) +amr_controller = ControllerThreeLevel(semi, IndicatorMax(semi, variable = first), + base_level = 3, + med_level = 4, med_threshold = 1.2, + max_level = 5, max_threshold = 1.45) amr_callback = AMRCallback(semi, amr_controller, - interval=5, - adapt_initial_condition=true, - adapt_initial_condition_only_refine=true) + interval = 5, + adapt_initial_condition = true, + adapt_initial_condition_only_refine = true) -stepsize_callback = StepsizeCallback(cfl=1.0) +stepsize_callback = StepsizeCallback(cfl = 1.0) callbacks = CallbackSet(summary_callback, analysis_callback, @@ -87,7 +87,7 @@ callbacks = CallbackSet(summary_callback, ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); -summary_callback() # print the timer summary \ No newline at end of file +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); +summary_callback() # print the timer summary diff --git a/examples/tree_3d_dgsem/elixir_advection_diffusion_nonperiodic.jl b/examples/tree_3d_dgsem/elixir_advection_diffusion_nonperiodic.jl index 5dc6e6338a7..4c30406680a 100644 --- a/examples/tree_3d_dgsem/elixir_advection_diffusion_nonperiodic.jl +++ b/examples/tree_3d_dgsem/elixir_advection_diffusion_nonperiodic.jl @@ -10,16 +10,16 @@ equations = LinearScalarAdvectionEquation3D(advection_velocity) equations_parabolic = LaplaceDiffusion3D(diffusivity(), equations) # Create DG solver with polynomial degree = 3 and (local) Lax-Friedrichs/Rusanov flux as surface flux -solver = DGSEM(polydeg=3, surface_flux=flux_lax_friedrichs) +solver = DGSEM(polydeg = 3, surface_flux = flux_lax_friedrichs) coordinates_min = (-1.0, -0.5, -0.25) # minimum coordinates (min(x), min(y), min(z)) -coordinates_max = ( 0.0, 0.5, 0.25) # maximum coordinates (max(x), max(y), max(z)) +coordinates_max = (0.0, 0.5, 0.25) # maximum coordinates (max(x), max(y), max(z)) # Create a uniformly refined mesh with periodic boundaries mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=3, - periodicity=false, - n_cells_max=30_000) # set maximum capacity of tree data structure + initial_refinement_level = 3, + periodicity = false, + n_cells_max = 30_000) # set maximum capacity of tree data structure # Example setup taken from # - Truman Ellis, Jesse Chan, and Leszek Demkowicz (2016). @@ -28,24 +28,24 @@ mesh = TreeMesh(coordinates_min, coordinates_max, # to numerical partial differential equations. # [DOI](https://doi.org/10.1007/978-3-319-41640-3_6). function initial_condition_eriksson_johnson(x, t, equations) - l = 4 - epsilon = diffusivity() # TODO: this requires epsilon < .6 due to sqrt - lambda_1 = (-1 + sqrt(1 - 4 * epsilon * l)) / (-2 * epsilon) - lambda_2 = (-1 - sqrt(1 - 4 * epsilon * l)) / (-2 * epsilon) - r1 = (1 + sqrt(1 + 4 * pi^2 * epsilon^2)) / (2 * epsilon) - s1 = (1 - sqrt(1 + 4 * pi^2 * epsilon^2)) / (2 * epsilon) - u = exp(-l * t) * (exp(lambda_1 * x[1]) - exp(lambda_2 * x[1])) + - cos(pi * x[2]) * (exp(s1 * x[1]) - exp(r1 * x[1])) / (exp(-s1) - exp(-r1)) - return SVector{1}(u) + l = 4 + epsilon = diffusivity() # TODO: this requires epsilon < .6 due to sqrt + lambda_1 = (-1 + sqrt(1 - 4 * epsilon * l)) / (-2 * epsilon) + lambda_2 = (-1 - sqrt(1 - 4 * epsilon * l)) / (-2 * epsilon) + r1 = (1 + sqrt(1 + 4 * pi^2 * epsilon^2)) / (2 * epsilon) + s1 = (1 - sqrt(1 + 4 * pi^2 * epsilon^2)) / (2 * epsilon) + u = exp(-l * t) * (exp(lambda_1 * x[1]) - exp(lambda_2 * x[1])) + + cos(pi * x[2]) * (exp(s1 * x[1]) - exp(r1 * x[1])) / (exp(-s1) - exp(-r1)) + return SVector{1}(u) end initial_condition = initial_condition_eriksson_johnson boundary_conditions = (; x_neg = BoundaryConditionDirichlet(initial_condition), - y_neg = BoundaryConditionDirichlet(initial_condition), - z_neg = boundary_condition_do_nothing, - y_pos = BoundaryConditionDirichlet(initial_condition), - x_pos = boundary_condition_do_nothing, - z_pos = boundary_condition_do_nothing) + y_neg = BoundaryConditionDirichlet(initial_condition), + z_neg = boundary_condition_do_nothing, + y_pos = BoundaryConditionDirichlet(initial_condition), + x_pos = boundary_condition_do_nothing, + z_pos = boundary_condition_do_nothing) boundary_conditions_parabolic = BoundaryConditionDirichlet(initial_condition) @@ -53,9 +53,8 @@ boundary_conditions_parabolic = BoundaryConditionDirichlet(initial_condition) semi = SemidiscretizationHyperbolicParabolic(mesh, (equations, equations_parabolic), initial_condition, solver; - boundary_conditions=(boundary_conditions, - boundary_conditions_parabolic)) - + boundary_conditions = (boundary_conditions, + boundary_conditions_parabolic)) ############################################################################### # ODE solvers, callbacks etc. @@ -70,22 +69,21 @@ summary_callback = SummaryCallback() # The AnalysisCallback allows to analyse the solution in regular intervals and prints the results analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) # The AliveCallback prints short status information in regular intervals -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) # Create a CallbackSet to collect all callbacks such that they can be passed to the ODE solver callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback) - ############################################################################### # run the simulation # OrdinaryDiffEq's `solve` method evolves the solution in time and executes the passed callbacks time_int_tol = 1.0e-11 -sol = solve(ode, RDPK3SpFSAL49(); abstol=time_int_tol, reltol=time_int_tol, - ode_default_options()..., callback=callbacks) +sol = solve(ode, RDPK3SpFSAL49(); abstol = time_int_tol, reltol = time_int_tol, + ode_default_options()..., callback = callbacks) # Print the timer summary summary_callback() diff --git a/examples/tree_3d_dgsem/elixir_advection_extended.jl b/examples/tree_3d_dgsem/elixir_advection_extended.jl index d820f47f25c..efc20c64f6d 100644 --- a/examples/tree_3d_dgsem/elixir_advection_extended.jl +++ b/examples/tree_3d_dgsem/elixir_advection_extended.jl @@ -18,21 +18,20 @@ initial_condition = initial_condition_convergence_test boundary_conditions = boundary_condition_periodic # Create DG solver with polynomial degree = 3 and (local) Lax-Friedrichs/Rusanov flux as surface flux -solver = DGSEM(polydeg=3, surface_flux=flux_lax_friedrichs) +solver = DGSEM(polydeg = 3, surface_flux = flux_lax_friedrichs) coordinates_min = (-1.0, -1.0, -1.0) # minimum coordinates (min(x), min(y), min(z)) -coordinates_max = ( 1.0, 1.0, 1.0) # maximum coordinates (max(x), max(y), max(z)) +coordinates_max = (1.0, 1.0, 1.0) # maximum coordinates (max(x), max(y), max(z)) # Create a uniformly refined mesh with periodic boundaries mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=3, - n_cells_max=30_000, # set maximum capacity of tree data structure - periodicity=true) + initial_refinement_level = 3, + n_cells_max = 30_000, # set maximum capacity of tree data structure + periodicity = true) # A semidiscretization collects data structures and functions for the spatial discretization semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver, - boundary_conditions=boundary_conditions) - + boundary_conditions = boundary_conditions) ############################################################################### # ODE solvers, callbacks etc. @@ -47,24 +46,24 @@ summary_callback = SummaryCallback() # The AnalysisCallback allows to analyse the solution in regular intervals and prints the results analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval, - extra_analysis_integrals=(entropy, energy_total)) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval, + extra_analysis_integrals = (entropy, energy_total)) # The AliveCallback prints short status information in regular intervals -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) # The SaveRestartCallback allows to save a file from which a Trixi simulation can be restarted -save_restart = SaveRestartCallback(interval=100, - save_final_restart=true) +save_restart = SaveRestartCallback(interval = 100, + save_final_restart = true) # The SaveSolutionCallback allows to save the solution to a file in regular intervals -save_solution = SaveSolutionCallback(interval=100, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 100, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) # The StepsizeCallback handles the re-calculation of the maximum Δt after each time step -stepsize_callback = StepsizeCallback(cfl=1.2) +stepsize_callback = StepsizeCallback(cfl = 1.2) # Create a CallbackSet to collect all callbacks such that they can be passed to the ODE solver callbacks = CallbackSet(summary_callback, @@ -72,14 +71,13 @@ callbacks = CallbackSet(summary_callback, save_restart, save_solution, stepsize_callback) - ############################################################################### # run the simulation # OrdinaryDiffEq's `solve` method evolves the solution in time and executes the passed callbacks -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); # Print the timer summary summary_callback() diff --git a/examples/tree_3d_dgsem/elixir_advection_mortar.jl b/examples/tree_3d_dgsem/elixir_advection_mortar.jl index 7b24f152b6a..d27a19c7dcf 100644 --- a/examples/tree_3d_dgsem/elixir_advection_mortar.jl +++ b/examples/tree_3d_dgsem/elixir_advection_mortar.jl @@ -9,23 +9,21 @@ advection_velocity = (0.2, -0.7, 0.5) equations = LinearScalarAdvectionEquation3D(advection_velocity) initial_condition = initial_condition_convergence_test -solver = DGSEM(polydeg=3, surface_flux=flux_lax_friedrichs) +solver = DGSEM(polydeg = 3, surface_flux = flux_lax_friedrichs) coordinates_min = (-1.0, -1.0, -1.0) -coordinates_max = ( 1.0, 1.0, 1.0) -refinement_patches = ( - (type="box", coordinates_min=(0.0, -1.0, -1.0), coordinates_max=(1.0, 1.0, 1.0)), - (type="box", coordinates_min=(0.0, -0.5, -0.5), coordinates_max=(0.5, 0.5, 0.5)), -) +coordinates_max = (1.0, 1.0, 1.0) +refinement_patches = ((type = "box", coordinates_min = (0.0, -1.0, -1.0), + coordinates_max = (1.0, 1.0, 1.0)), + (type = "box", coordinates_min = (0.0, -0.5, -0.5), + coordinates_max = (0.5, 0.5, 0.5))) mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=2, - refinement_patches=refinement_patches, - n_cells_max=10_000,) - + initial_refinement_level = 2, + refinement_patches = refinement_patches, + n_cells_max = 10_000) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver) - ############################################################################### # ODE solvers, callbacks etc. @@ -35,17 +33,17 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval, - extra_analysis_integrals=(entropy,)) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval, + extra_analysis_integrals = (entropy,)) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=100, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 100, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) -stepsize_callback = StepsizeCallback(cfl=1.2) +stepsize_callback = StepsizeCallback(cfl = 1.2) callbacks = CallbackSet(summary_callback, analysis_callback, @@ -53,11 +51,10 @@ callbacks = CallbackSet(summary_callback, save_solution, stepsize_callback) - ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/tree_3d_dgsem/elixir_advection_restart.jl b/examples/tree_3d_dgsem/elixir_advection_restart.jl index b7835ed061f..f81e013fc0a 100644 --- a/examples/tree_3d_dgsem/elixir_advection_restart.jl +++ b/examples/tree_3d_dgsem/elixir_advection_restart.jl @@ -7,7 +7,6 @@ using Trixi trixi_include(@__MODULE__, joinpath(@__DIR__, "elixir_advection_extended.jl")) - ############################################################################### # adapt the parameters that have changed compared to "elixir_advection_extended.jl" @@ -26,14 +25,13 @@ ode = semidiscretize(semi, tspan, restart_filename); # Do not overwrite the initial snapshot written by elixir_advection_extended.jl. save_solution.condition.save_initial_solution = false -integrator = init(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=dt, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +integrator = init(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = dt, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); # Get the last time index and work with that. load_timestep!(integrator, restart_filename) - ############################################################################### # run the simulation diff --git a/examples/tree_3d_dgsem/elixir_euler_amr.jl b/examples/tree_3d_dgsem/elixir_euler_amr.jl index f226a6b446d..9bd7f74c688 100644 --- a/examples/tree_3d_dgsem/elixir_euler_amr.jl +++ b/examples/tree_3d_dgsem/elixir_euler_amr.jl @@ -14,30 +14,28 @@ A Gaussian pulse in the density with constant velocity and pressure; reduces the compressible Euler equations to the linear advection equations. """ function initial_condition_density_pulse(x, t, equations::CompressibleEulerEquations3D) - rho = 1 + exp(-(x[1]^2 + x[2]^2 + x[3]^2))/2 - v1 = 1 - v2 = 1 - v3 = 1 - rho_v1 = rho * v1 - rho_v2 = rho * v2 - rho_v3 = rho * v3 - p = 1 - rho_e = p/(equations.gamma - 1) + 1/2 * rho * (v1^2 + v2^2 + v3^2) - return SVector(rho, rho_v1, rho_v2, rho_v3, rho_e) + rho = 1 + exp(-(x[1]^2 + x[2]^2 + x[3]^2)) / 2 + v1 = 1 + v2 = 1 + v3 = 1 + rho_v1 = rho * v1 + rho_v2 = rho * v2 + rho_v3 = rho * v3 + p = 1 + rho_e = p / (equations.gamma - 1) + 1 / 2 * rho * (v1^2 + v2^2 + v3^2) + return SVector(rho, rho_v1, rho_v2, rho_v3, rho_e) end initial_condition = initial_condition_density_pulse -solver = DGSEM(polydeg=3, surface_flux=flux_lax_friedrichs) +solver = DGSEM(polydeg = 3, surface_flux = flux_lax_friedrichs) coordinates_min = (-5.0, -5.0, -5.0) -coordinates_max = ( 5.0, 5.0, 5.0) +coordinates_max = (5.0, 5.0, 5.0) mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=4, - n_cells_max=10_000) - + initial_refinement_level = 4, + n_cells_max = 10_000) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver) - ############################################################################### # ODE solvers, callbacks etc. @@ -47,40 +45,39 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval, - extra_analysis_integrals=(entropy,)) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval, + extra_analysis_integrals = (entropy,)) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_restart = SaveRestartCallback(interval=100, - save_final_restart=true) +save_restart = SaveRestartCallback(interval = 100, + save_final_restart = true) -save_solution = SaveSolutionCallback(interval=100, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 100, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) -amr_controller = ControllerThreeLevel(semi, IndicatorMax(semi, variable=first), - base_level=4, - med_level=5, med_threshold=1.05, - max_level=6, max_threshold=1.3) +amr_controller = ControllerThreeLevel(semi, IndicatorMax(semi, variable = first), + base_level = 4, + med_level = 5, med_threshold = 1.05, + max_level = 6, max_threshold = 1.3) amr_callback = AMRCallback(semi, amr_controller, - interval=5, - adapt_initial_condition=true, - adapt_initial_condition_only_refine=true) + interval = 5, + adapt_initial_condition = true, + adapt_initial_condition_only_refine = true) -stepsize_callback = StepsizeCallback(cfl=0.9) +stepsize_callback = StepsizeCallback(cfl = 0.9) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, save_restart, save_solution, amr_callback, stepsize_callback); - ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/tree_3d_dgsem/elixir_euler_blob_amr.jl b/examples/tree_3d_dgsem/elixir_euler_blob_amr.jl index a8d112f5b05..0ce886620cc 100644 --- a/examples/tree_3d_dgsem/elixir_euler_blob_amr.jl +++ b/examples/tree_3d_dgsem/elixir_euler_blob_amr.jl @@ -4,7 +4,7 @@ using Trixi ############################################################################### # semidiscretization of the compressible Euler equations -gamma = 5/3 +gamma = 5 / 3 equations = CompressibleEulerEquations3D(gamma) """ @@ -16,63 +16,65 @@ The blob test case taken from [arXiv: astro-ph/0610051](https://arxiv.org/abs/astro-ph/0610051) """ function initial_condition_blob(x, t, equations::CompressibleEulerEquations3D) - # blob test case, see Agertz et al. https://arxiv.org/pdf/astro-ph/0610051.pdf - # other reference: https://arxiv.org/pdf/astro-ph/0610051.pdf - # change discontinuity to tanh - # typical domain is rectangular, we change it to a square - # resolution 128^3, 256^3 - # domain size is [-20.0,20.0]^3 - # gamma = 5/3 for this test case - R = 1.0 # radius of the blob - # background density - rho = 1.0 - Chi = 10.0 # density contrast - # reference time of characteristic growth of KH instability equal to 1.0 - tau_kh = 1.0 - tau_cr = tau_kh / 1.6 # crushing time - # determine background velocity - v1 = 2 * R * sqrt(Chi) / tau_cr - v2 = 0.0 - v3 = 0.0 - Ma0 = 2.7 # background flow Mach number Ma=v/c - c = v1 / Ma0 # sound speed - # use perfect gas assumption to compute background pressure via the sound speed c^2 = gamma * pressure/density - p = c * c * rho / equations.gamma - # initial center of the blob - inicenter = [-15, 0, 0] - x_rel = x - inicenter - r = sqrt(x_rel[1]^2 + x_rel[2]^2 + x_rel[3]^2) - # steepness of the tanh transition zone - slope = 2 - # density blob - rho = rho + (Chi - 1) * 0.5 * (1 + (tanh(slope * (r + R)) - (tanh(slope *(r - R)) + 1))) - # velocity blob is zero - v1 = v1 - v1 * 0.5 * (1 + (tanh(slope *(r + R)) - (tanh(slope *(r - R)) + 1))) - return prim2cons(SVector(rho, v1, v2, v3, p), equations) + # blob test case, see Agertz et al. https://arxiv.org/pdf/astro-ph/0610051.pdf + # other reference: https://arxiv.org/pdf/astro-ph/0610051.pdf + # change discontinuity to tanh + # typical domain is rectangular, we change it to a square + # resolution 128^3, 256^3 + # domain size is [-20.0,20.0]^3 + # gamma = 5/3 for this test case + R = 1.0 # radius of the blob + # background density + rho = 1.0 + Chi = 10.0 # density contrast + # reference time of characteristic growth of KH instability equal to 1.0 + tau_kh = 1.0 + tau_cr = tau_kh / 1.6 # crushing time + # determine background velocity + v1 = 2 * R * sqrt(Chi) / tau_cr + v2 = 0.0 + v3 = 0.0 + Ma0 = 2.7 # background flow Mach number Ma=v/c + c = v1 / Ma0 # sound speed + # use perfect gas assumption to compute background pressure via the sound speed c^2 = gamma * pressure/density + p = c * c * rho / equations.gamma + # initial center of the blob + inicenter = [-15, 0, 0] + x_rel = x - inicenter + r = sqrt(x_rel[1]^2 + x_rel[2]^2 + x_rel[3]^2) + # steepness of the tanh transition zone + slope = 2 + # density blob + rho = rho + + (Chi - 1) * 0.5 * (1 + (tanh(slope * (r + R)) - (tanh(slope * (r - R)) + 1))) + # velocity blob is zero + v1 = v1 - v1 * 0.5 * (1 + (tanh(slope * (r + R)) - (tanh(slope * (r - R)) + 1))) + return prim2cons(SVector(rho, v1, v2, v3, p), equations) end initial_condition = initial_condition_blob volume_flux = flux_ranocha -solver = DGSEM(polydeg=3, surface_flux=flux_hllc, - volume_integral=VolumeIntegralFluxDifferencing(volume_flux)) +solver = DGSEM(polydeg = 3, surface_flux = flux_hllc, + volume_integral = VolumeIntegralFluxDifferencing(volume_flux)) coordinates_min = (-20.0, -20.0, -20.0) -coordinates_max = ( 20.0, 20.0, 20.0) - -refinement_patches = ( - (type="box", coordinates_min=(-20.0, -10.0, -10.0), coordinates_max=(-10.0, 10.0, 10.0)), - (type="box", coordinates_min=(-20.0, -5.0, -5.0), coordinates_max=(-10.0, 5.0, 5.0)), - (type="box", coordinates_min=(-17.0, -2.0, -2.0), coordinates_max=(-13.0, 2.0, 2.0)), - (type="box", coordinates_min=(-17.0, -2.0, -2.0), coordinates_max=(-13.0, 2.0, 2.0)), -) +coordinates_max = (20.0, 20.0, 20.0) + +refinement_patches = ((type = "box", coordinates_min = (-20.0, -10.0, -10.0), + coordinates_max = (-10.0, 10.0, 10.0)), + (type = "box", coordinates_min = (-20.0, -5.0, -5.0), + coordinates_max = (-10.0, 5.0, 5.0)), + (type = "box", coordinates_min = (-17.0, -2.0, -2.0), + coordinates_max = (-13.0, 2.0, 2.0)), + (type = "box", coordinates_min = (-17.0, -2.0, -2.0), + coordinates_max = (-13.0, 2.0, 2.0))) mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=2, - refinement_patches=refinement_patches, - n_cells_max=100_000,) + initial_refinement_level = 2, + refinement_patches = refinement_patches, + n_cells_max = 100_000) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver) - ############################################################################### # ODE solvers, callbacks etc. @@ -82,41 +84,40 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 200 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=200, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 200, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) amr_indicator = IndicatorLöhner(semi, - variable=Trixi.density) + variable = Trixi.density) amr_controller = ControllerThreeLevel(semi, amr_indicator, - base_level=1, - med_level =0, med_threshold=0.1, # med_level = current level - max_level =6, max_threshold=0.3) + base_level = 1, + med_level = 0, med_threshold = 0.1, # med_level = current level + max_level = 6, max_threshold = 0.3) amr_callback = AMRCallback(semi, amr_controller, - interval=3, - adapt_initial_condition=false, - adapt_initial_condition_only_refine=true) + interval = 3, + adapt_initial_condition = false, + adapt_initial_condition_only_refine = true) -stepsize_callback = StepsizeCallback(cfl=1.7) +stepsize_callback = StepsizeCallback(cfl = 1.7) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, save_solution, amr_callback, stepsize_callback) - -stage_limiter! = PositivityPreservingLimiterZhangShu(thresholds=(1.0e-4, 1.0e-4), - variables=(Trixi.density, pressure)) +stage_limiter! = PositivityPreservingLimiterZhangShu(thresholds = (1.0e-4, 1.0e-4), + variables = (Trixi.density, pressure)) ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(stage_limiter!, williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(stage_limiter!, williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/tree_3d_dgsem/elixir_euler_convergence.jl b/examples/tree_3d_dgsem/elixir_euler_convergence.jl index 2eeb280ae1f..170b292a42f 100644 --- a/examples/tree_3d_dgsem/elixir_euler_convergence.jl +++ b/examples/tree_3d_dgsem/elixir_euler_convergence.jl @@ -9,19 +9,17 @@ equations = CompressibleEulerEquations3D(2.0) initial_condition = initial_condition_eoc_test_coupled_euler_gravity -solver = DGSEM(polydeg=3, surface_flux=flux_hll, - volume_integral=VolumeIntegralWeakForm()) +solver = DGSEM(polydeg = 3, surface_flux = flux_hll, + volume_integral = VolumeIntegralWeakForm()) coordinates_min = (0.0, 0.0, 0.0) coordinates_max = (2.0, 2.0, 2.0) mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=2, - n_cells_max=10_000) - + initial_refinement_level = 2, + n_cells_max = 10_000) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver, - source_terms=source_terms_eoc_test_euler) - + source_terms = source_terms_eoc_test_euler) ############################################################################### # ODE solvers, callbacks etc. @@ -32,27 +30,26 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=100, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 100, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) -stepsize_callback = StepsizeCallback(cfl=1.1) +stepsize_callback = StepsizeCallback(cfl = 1.1) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, save_solution, stepsize_callback) - ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/tree_3d_dgsem/elixir_euler_convergence_pure_fv.jl b/examples/tree_3d_dgsem/elixir_euler_convergence_pure_fv.jl index dbf5747784c..4789b46dacc 100644 --- a/examples/tree_3d_dgsem/elixir_euler_convergence_pure_fv.jl +++ b/examples/tree_3d_dgsem/elixir_euler_convergence_pure_fv.jl @@ -9,19 +9,17 @@ equations = CompressibleEulerEquations3D(1.4) initial_condition = initial_condition_convergence_test -solver = DGSEM(polydeg=3, surface_flux=flux_hllc, - volume_integral=VolumeIntegralPureLGLFiniteVolume(flux_hllc)) +solver = DGSEM(polydeg = 3, surface_flux = flux_hllc, + volume_integral = VolumeIntegralPureLGLFiniteVolume(flux_hllc)) coordinates_min = (0.0, 0.0, 0.0) coordinates_max = (2.0, 2.0, 2.0) mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=2, - n_cells_max=10_000) - + initial_refinement_level = 2, + n_cells_max = 10_000) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver, - source_terms=source_terms_convergence_test) - + source_terms = source_terms_convergence_test) ############################################################################### # ODE solvers, callbacks etc. @@ -32,27 +30,26 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=100, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 100, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) -stepsize_callback = StepsizeCallback(cfl=0.6) +stepsize_callback = StepsizeCallback(cfl = 0.6) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, save_solution, stepsize_callback) - ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/tree_3d_dgsem/elixir_euler_density_pulse.jl b/examples/tree_3d_dgsem/elixir_euler_density_pulse.jl index ee788321c66..cad8fc578c8 100644 --- a/examples/tree_3d_dgsem/elixir_euler_density_pulse.jl +++ b/examples/tree_3d_dgsem/elixir_euler_density_pulse.jl @@ -14,33 +14,31 @@ A Gaussian pulse in the density with constant velocity and pressure; reduces the compressible Euler equations to the linear advection equations. """ function initial_condition_density_pulse(x, t, equations::CompressibleEulerEquations3D) - rho = 1 + exp(-(x[1]^2 + x[2]^2 + x[3]^2))/2 - v1 = 1 - v2 = 1 - v3 = 1 - rho_v1 = rho * v1 - rho_v2 = rho * v2 - rho_v3 = rho * v3 - p = 1 - rho_e = p/(equations.gamma - 1) + 1/2 * rho * (v1^2 + v2^2 + v3^2) - return SVector(rho, rho_v1, rho_v2, rho_v3, rho_e) + rho = 1 + exp(-(x[1]^2 + x[2]^2 + x[3]^2)) / 2 + v1 = 1 + v2 = 1 + v3 = 1 + rho_v1 = rho * v1 + rho_v2 = rho * v2 + rho_v3 = rho * v3 + p = 1 + rho_e = p / (equations.gamma - 1) + 1 / 2 * rho * (v1^2 + v2^2 + v3^2) + return SVector(rho, rho_v1, rho_v2, rho_v3, rho_e) end initial_condition = initial_condition_density_pulse volume_flux = flux_ranocha -solver = DGSEM(polydeg=3, surface_flux=flux_ranocha, - volume_integral=VolumeIntegralFluxDifferencing(volume_flux)) +solver = DGSEM(polydeg = 3, surface_flux = flux_ranocha, + volume_integral = VolumeIntegralFluxDifferencing(volume_flux)) coordinates_min = (-2.0, -2.0, -2.0) -coordinates_max = ( 2.0, 2.0, 2.0) +coordinates_max = (2.0, 2.0, 2.0) mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=3, - n_cells_max=100_000) - + initial_refinement_level = 3, + n_cells_max = 100_000) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver) - ############################################################################### # ODE solvers, callbacks etc. @@ -50,30 +48,29 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_restart = SaveRestartCallback(interval=100, - save_final_restart=true) +save_restart = SaveRestartCallback(interval = 100, + save_final_restart = true) -save_solution = SaveSolutionCallback(interval=100, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 100, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) -stepsize_callback = StepsizeCallback(cfl=1.1) +stepsize_callback = StepsizeCallback(cfl = 1.1) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, save_restart, save_solution, stepsize_callback) - ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/tree_3d_dgsem/elixir_euler_ec.jl b/examples/tree_3d_dgsem/elixir_euler_ec.jl index 08fd1b998d5..88d7cbc7ba5 100644 --- a/examples/tree_3d_dgsem/elixir_euler_ec.jl +++ b/examples/tree_3d_dgsem/elixir_euler_ec.jl @@ -10,19 +10,17 @@ equations = CompressibleEulerEquations3D(1.4) initial_condition = initial_condition_weak_blast_wave volume_flux = flux_ranocha -solver = DGSEM(polydeg=3, surface_flux=flux_ranocha, - volume_integral=VolumeIntegralFluxDifferencing(volume_flux)) +solver = DGSEM(polydeg = 3, surface_flux = flux_ranocha, + volume_integral = VolumeIntegralFluxDifferencing(volume_flux)) coordinates_min = (-2.0, -2.0, -2.0) -coordinates_max = ( 2.0, 2.0, 2.0) +coordinates_max = (2.0, 2.0, 2.0) mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=3, - n_cells_max=100_000) - + initial_refinement_level = 3, + n_cells_max = 100_000) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver) - ############################################################################### # ODE solvers, callbacks etc. @@ -32,27 +30,26 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=100, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 100, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) -stepsize_callback = StepsizeCallback(cfl=1.3) +stepsize_callback = StepsizeCallback(cfl = 1.3) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, save_solution, stepsize_callback) - ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/tree_3d_dgsem/elixir_euler_mortar.jl b/examples/tree_3d_dgsem/elixir_euler_mortar.jl index c9fc2dfed50..cf103dc26cf 100644 --- a/examples/tree_3d_dgsem/elixir_euler_mortar.jl +++ b/examples/tree_3d_dgsem/elixir_euler_mortar.jl @@ -8,22 +8,19 @@ using Trixi equations = CompressibleEulerEquations3D(1.4) initial_condition = initial_condition_convergence_test -solver = DGSEM(polydeg=3, surface_flux=flux_lax_friedrichs) +solver = DGSEM(polydeg = 3, surface_flux = flux_lax_friedrichs) coordinates_min = (0.0, 0.0, 0.0) coordinates_max = (2.0, 2.0, 2.0) -refinement_patches = ( - (type="box", coordinates_min=(0.5, 0.5, 0.5), coordinates_max=(1.5, 1.5, 1.5)), -) +refinement_patches = ((type = "box", coordinates_min = (0.5, 0.5, 0.5), + coordinates_max = (1.5, 1.5, 1.5)),) mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=2, - refinement_patches=refinement_patches, - n_cells_max=10_000) - + initial_refinement_level = 2, + refinement_patches = refinement_patches, + n_cells_max = 10_000) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver, - source_terms=source_terms_convergence_test) - + source_terms = source_terms_convergence_test) ############################################################################### # ODE solvers, callbacks etc. @@ -34,16 +31,16 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=100, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 100, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) -stepsize_callback = StepsizeCallback(cfl=0.6) +stepsize_callback = StepsizeCallback(cfl = 0.6) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, @@ -53,7 +50,7 @@ callbacks = CallbackSet(summary_callback, ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/tree_3d_dgsem/elixir_euler_sedov_blast_wave.jl b/examples/tree_3d_dgsem/elixir_euler_sedov_blast_wave.jl index 3641878149a..87774ada266 100644 --- a/examples/tree_3d_dgsem/elixir_euler_sedov_blast_wave.jl +++ b/examples/tree_3d_dgsem/elixir_euler_sedov_blast_wave.jl @@ -19,34 +19,34 @@ based on Should be used together with [`boundary_condition_sedov_self_gravity`](@ref). """ function initial_condition_sedov_self_gravity(x, t, equations::CompressibleEulerEquations3D) - # Calculate radius as distance from origin - r = sqrt(x[1]^2 + x[2]^2 + x[3]^2) - - # Setup based on https://flash.rochester.edu/site/flashcode/user_support/flash_ug_devel/node187.html#SECTION010114000000000000000 - r0 = 0.25 # = 4.0 * smallest dx (for domain length=8 and max-ref=7) - E = 1.0 - p_inner = (equations.gamma - 1) * E / (4/3 * pi * r0^3) - p_ambient = 1e-5 # = true Sedov setup - - # Calculate primitive variables - # use a logistic function to transfer density value smoothly - L = 1.0 # maximum of function - x0 = 1.0 # center point of function - k = -50.0 # sharpness of transfer - logistic_function_rho = L/(1.0 + exp(-k*(r - x0))) - rho_ambient = 1e-5 - rho = max(logistic_function_rho, rho_ambient) # clip background density to not be so tiny - - # velocities are zero - v1 = 0.0 - v2 = 0.0 - v3 = 0.0 - - # use a logistic function to transfer pressure value smoothly - logistic_function_p = p_inner/(1.0 + exp(-k*(r - r0))) - p = max(logistic_function_p, p_ambient) - - return prim2cons(SVector(rho, v1, v2, v3, p), equations) + # Calculate radius as distance from origin + r = sqrt(x[1]^2 + x[2]^2 + x[3]^2) + + # Setup based on https://flash.rochester.edu/site/flashcode/user_support/flash_ug_devel/node187.html#SECTION010114000000000000000 + r0 = 0.25 # = 4.0 * smallest dx (for domain length=8 and max-ref=7) + E = 1.0 + p_inner = (equations.gamma - 1) * E / (4 / 3 * pi * r0^3) + p_ambient = 1e-5 # = true Sedov setup + + # Calculate primitive variables + # use a logistic function to transfer density value smoothly + L = 1.0 # maximum of function + x0 = 1.0 # center point of function + k = -50.0 # sharpness of transfer + logistic_function_rho = L / (1.0 + exp(-k * (r - x0))) + rho_ambient = 1e-5 + rho = max(logistic_function_rho, rho_ambient) # clip background density to not be so tiny + + # velocities are zero + v1 = 0.0 + v2 = 0.0 + v3 = 0.0 + + # use a logistic function to transfer pressure value smoothly + logistic_function_p = p_inner / (1.0 + exp(-k * (r - r0))) + p = max(logistic_function_p, p_ambient) + + return prim2cons(SVector(rho, v1, v2, v3, p), equations) end initial_condition = initial_condition_sedov_self_gravity @@ -64,26 +64,26 @@ based on Should be used together with [`initial_condition_sedov_self_gravity`](@ref). """ function boundary_condition_sedov_self_gravity(u_inner, orientation, direction, x, t, - surface_flux_function, - equations::CompressibleEulerEquations3D) - # velocities are zero, density/pressure are ambient values according to - # initial_condition_sedov_self_gravity - rho = 1e-5 - v1 = 0.0 - v2 = 0.0 - v3 = 0.0 - p = 1e-5 - - u_boundary = prim2cons(SVector(rho, v1, v2, v3, p), equations) - - # Calculate boundary flux - if iseven(direction) # u_inner is "left" of boundary, u_boundary is "right" of boundary - flux = surface_flux_function(u_inner, u_boundary, orientation, equations) - else # u_boundary is "left" of boundary, u_inner is "right" of boundary - flux = surface_flux_function(u_boundary, u_inner, orientation, equations) - end - - return flux + surface_flux_function, + equations::CompressibleEulerEquations3D) + # velocities are zero, density/pressure are ambient values according to + # initial_condition_sedov_self_gravity + rho = 1e-5 + v1 = 0.0 + v2 = 0.0 + v3 = 0.0 + p = 1e-5 + + u_boundary = prim2cons(SVector(rho, v1, v2, v3, p), equations) + + # Calculate boundary flux + if iseven(direction) # u_inner is "left" of boundary, u_boundary is "right" of boundary + flux = surface_flux_function(u_inner, u_boundary, orientation, equations) + else # u_boundary is "left" of boundary, u_inner is "right" of boundary + flux = surface_flux_function(u_boundary, u_inner, orientation, equations) + end + + return flux end boundary_conditions = boundary_condition_sedov_self_gravity @@ -92,26 +92,24 @@ volume_flux = flux_ranocha polydeg = 3 basis = LobattoLegendreBasis(polydeg) indicator_sc = IndicatorHennemannGassner(equations, basis, - alpha_max=0.7, - alpha_min=0.001, - alpha_smooth=true, - variable=density_pressure) + alpha_max = 0.7, + alpha_min = 0.001, + alpha_smooth = true, + variable = density_pressure) volume_integral = VolumeIntegralShockCapturingHG(indicator_sc; - volume_flux_dg=volume_flux, - volume_flux_fv=surface_flux) + volume_flux_dg = volume_flux, + volume_flux_fv = surface_flux) solver = DGSEM(basis, surface_flux, volume_integral) coordinates_min = (-4.0, -4.0, -4.0) -coordinates_max = ( 4.0, 4.0, 4.0) +coordinates_max = (4.0, 4.0, 4.0) mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=2, - n_cells_max=1_000_000, - periodicity=false) - + initial_refinement_level = 2, + n_cells_max = 1_000_000, + periodicity = false) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver, - boundary_conditions=boundary_conditions) - + boundary_conditions = boundary_conditions) ############################################################################### # ODE solvers, callbacks etc. @@ -122,42 +120,41 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=100, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 100, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) amr_indicator = IndicatorHennemannGassner(semi, - alpha_max=1.0, - alpha_min=0.0, - alpha_smooth=false, - variable=density_pressure) + alpha_max = 1.0, + alpha_min = 0.0, + alpha_smooth = false, + variable = density_pressure) amr_controller = ControllerThreeLevel(semi, amr_indicator, - base_level=2, - max_level =7, max_threshold=0.0003) + base_level = 2, + max_level = 7, max_threshold = 0.0003) amr_callback = AMRCallback(semi, amr_controller, - interval=1, - adapt_initial_condition=true, - adapt_initial_condition_only_refine=true) + interval = 1, + adapt_initial_condition = true, + adapt_initial_condition_only_refine = true) -stepsize_callback = StepsizeCallback(cfl=0.35) +stepsize_callback = StepsizeCallback(cfl = 0.35) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, save_solution, amr_callback, stepsize_callback) - ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/tree_3d_dgsem/elixir_euler_shockcapturing.jl b/examples/tree_3d_dgsem/elixir_euler_shockcapturing.jl index 3015f6c50a4..0a90615016c 100644 --- a/examples/tree_3d_dgsem/elixir_euler_shockcapturing.jl +++ b/examples/tree_3d_dgsem/elixir_euler_shockcapturing.jl @@ -10,30 +10,28 @@ equations = CompressibleEulerEquations3D(1.4) initial_condition = initial_condition_weak_blast_wave surface_flux = flux_ranocha # OBS! Using a non-dissipative flux is only sensible to test EC, - # but not for real shock simulations +# but not for real shock simulations volume_flux = flux_ranocha polydeg = 3 basis = LobattoLegendreBasis(polydeg) indicator_sc = IndicatorHennemannGassner(equations, basis, - alpha_max=0.5, - alpha_min=0.001, - alpha_smooth=true, - variable=density_pressure) + alpha_max = 0.5, + alpha_min = 0.001, + alpha_smooth = true, + variable = density_pressure) volume_integral = VolumeIntegralShockCapturingHG(indicator_sc; - volume_flux_dg=volume_flux, - volume_flux_fv=surface_flux) + volume_flux_dg = volume_flux, + volume_flux_fv = surface_flux) solver = DGSEM(basis, surface_flux, volume_integral) coordinates_min = (-2.0, -2.0, -2.0) -coordinates_max = ( 2.0, 2.0, 2.0) +coordinates_max = (2.0, 2.0, 2.0) mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=3, - n_cells_max=100_000) - + initial_refinement_level = 3, + n_cells_max = 100_000) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver) - ############################################################################### # ODE solvers, callbacks etc. @@ -43,27 +41,26 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=100, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 100, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) -stepsize_callback = StepsizeCallback(cfl=1.4) +stepsize_callback = StepsizeCallback(cfl = 1.4) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, save_solution, stepsize_callback) - ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/tree_3d_dgsem/elixir_euler_shockcapturing_amr.jl b/examples/tree_3d_dgsem/elixir_euler_shockcapturing_amr.jl index 3d338cd7f01..be31fbbc42c 100644 --- a/examples/tree_3d_dgsem/elixir_euler_shockcapturing_amr.jl +++ b/examples/tree_3d_dgsem/elixir_euler_shockcapturing_amr.jl @@ -10,30 +10,28 @@ equations = CompressibleEulerEquations3D(1.4) initial_condition = initial_condition_weak_blast_wave surface_flux = flux_ranocha # OBS! Using a non-dissipative flux is only sensible to test EC, - # but not for real shock simulations +# but not for real shock simulations volume_flux = flux_ranocha polydeg = 3 basis = LobattoLegendreBasis(polydeg) indicator_sc = IndicatorHennemannGassner(equations, basis, - alpha_max=0.5, - alpha_min=0.001, - alpha_smooth=true, - variable=density_pressure) + alpha_max = 0.5, + alpha_min = 0.001, + alpha_smooth = true, + variable = density_pressure) volume_integral = VolumeIntegralShockCapturingHG(indicator_sc; - volume_flux_dg=volume_flux, - volume_flux_fv=surface_flux) + volume_flux_dg = volume_flux, + volume_flux_fv = surface_flux) solver = DGSEM(basis, surface_flux, volume_integral) coordinates_min = (-2.0, -2.0, -2.0) -coordinates_max = ( 2.0, 2.0, 2.0) +coordinates_max = (2.0, 2.0, 2.0) mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=3, - n_cells_max=100_000) - + initial_refinement_level = 3, + n_cells_max = 100_000) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver) - ############################################################################### # ODE solvers, callbacks etc. @@ -43,41 +41,39 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=100, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 100, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) amr_indicator = IndicatorHennemannGassner(semi, - alpha_smooth=false, - variable=density_pressure) + alpha_smooth = false, + variable = density_pressure) amr_controller = ControllerThreeLevel(semi, amr_indicator, - base_level=2, - max_level =4, max_threshold=0.0003) + base_level = 2, + max_level = 4, max_threshold = 0.0003) amr_callback = AMRCallback(semi, amr_controller, - interval=1, - adapt_initial_condition=true, - adapt_initial_condition_only_refine=true) + interval = 1, + adapt_initial_condition = true, + adapt_initial_condition_only_refine = true) -stepsize_callback = StepsizeCallback(cfl=1.3) +stepsize_callback = StepsizeCallback(cfl = 1.3) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, save_solution, amr_callback, stepsize_callback) - ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary - diff --git a/examples/tree_3d_dgsem/elixir_euler_source_terms.jl b/examples/tree_3d_dgsem/elixir_euler_source_terms.jl index 3445e9fc433..f0246c30490 100644 --- a/examples/tree_3d_dgsem/elixir_euler_source_terms.jl +++ b/examples/tree_3d_dgsem/elixir_euler_source_terms.jl @@ -9,19 +9,17 @@ equations = CompressibleEulerEquations3D(1.4) initial_condition = initial_condition_convergence_test -solver = DGSEM(polydeg=3, surface_flux=flux_lax_friedrichs, - volume_integral=VolumeIntegralWeakForm()) +solver = DGSEM(polydeg = 3, surface_flux = flux_lax_friedrichs, + volume_integral = VolumeIntegralWeakForm()) coordinates_min = (0.0, 0.0, 0.0) coordinates_max = (2.0, 2.0, 2.0) mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=2, - n_cells_max=10_000) - + initial_refinement_level = 2, + n_cells_max = 10_000) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver, - source_terms=source_terms_convergence_test) - + source_terms = source_terms_convergence_test) ############################################################################### # ODE solvers, callbacks etc. @@ -32,27 +30,26 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=100, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 100, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) -stepsize_callback = StepsizeCallback(cfl=0.6) +stepsize_callback = StepsizeCallback(cfl = 0.6) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, save_solution, stepsize_callback) - ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/tree_3d_dgsem/elixir_euler_taylor_green_vortex.jl b/examples/tree_3d_dgsem/elixir_euler_taylor_green_vortex.jl index 693f9ce9049..135ee673e44 100644 --- a/examples/tree_3d_dgsem/elixir_euler_taylor_green_vortex.jl +++ b/examples/tree_3d_dgsem/elixir_euler_taylor_green_vortex.jl @@ -12,35 +12,37 @@ equations = CompressibleEulerEquations3D(1.4) The classical inviscid Taylor-Green vortex. """ -function initial_condition_taylor_green_vortex(x, t, equations::CompressibleEulerEquations3D) - A = 1.0 # magnitude of speed - Ms = 0.1 # maximum Mach number - - rho = 1.0 - v1 = A * sin(x[1]) * cos(x[2]) * cos(x[3]) - v2 = -A * cos(x[1]) * sin(x[2]) * cos(x[3]) - v3 = 0.0 - p = (A / Ms)^2 * rho / equations.gamma # scaling to get Ms - p = p + 1.0/16.0 * A^2 * rho * (cos(2*x[1])*cos(2*x[3]) + 2*cos(2*x[2]) + 2*cos(2*x[1]) + cos(2*x[2])*cos(2*x[3])) - - return prim2cons(SVector(rho, v1, v2, v3, p), equations) +function initial_condition_taylor_green_vortex(x, t, + equations::CompressibleEulerEquations3D) + A = 1.0 # magnitude of speed + Ms = 0.1 # maximum Mach number + + rho = 1.0 + v1 = A * sin(x[1]) * cos(x[2]) * cos(x[3]) + v2 = -A * cos(x[1]) * sin(x[2]) * cos(x[3]) + v3 = 0.0 + p = (A / Ms)^2 * rho / equations.gamma # scaling to get Ms + p = p + + 1.0 / 16.0 * A^2 * rho * + (cos(2 * x[1]) * cos(2 * x[3]) + 2 * cos(2 * x[2]) + 2 * cos(2 * x[1]) + + cos(2 * x[2]) * cos(2 * x[3])) + + return prim2cons(SVector(rho, v1, v2, v3, p), equations) end initial_condition = initial_condition_taylor_green_vortex volume_flux = flux_ranocha -solver = DGSEM(polydeg=3, surface_flux=flux_lax_friedrichs, - volume_integral=VolumeIntegralFluxDifferencing(volume_flux)) +solver = DGSEM(polydeg = 3, surface_flux = flux_lax_friedrichs, + volume_integral = VolumeIntegralFluxDifferencing(volume_flux)) coordinates_min = (-1.0, -1.0, -1.0) .* pi -coordinates_max = ( 1.0, 1.0, 1.0) .* pi +coordinates_max = (1.0, 1.0, 1.0) .* pi mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=3, - n_cells_max=100_000) - + initial_refinement_level = 3, + n_cells_max = 100_000) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver) - ############################################################################### # ODE solvers, callbacks etc. @@ -50,27 +52,26 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=100, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 100, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) -stepsize_callback = StepsizeCallback(cfl=1.4) +stepsize_callback = StepsizeCallback(cfl = 1.4) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, save_solution, stepsize_callback) - ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/tree_3d_dgsem/elixir_eulergravity_convergence.jl b/examples/tree_3d_dgsem/elixir_eulergravity_convergence.jl index 6699ec9a4da..21ef661d0b6 100644 --- a/examples/tree_3d_dgsem/elixir_eulergravity_convergence.jl +++ b/examples/tree_3d_dgsem/elixir_eulergravity_convergence.jl @@ -15,12 +15,12 @@ solver_euler = DGSEM(polydeg, flux_hll) coordinates_min = (0.0, 0.0, 0.0) coordinates_max = (2.0, 2.0, 2.0) mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=2, - n_cells_max=10_000) - -semi_euler = SemidiscretizationHyperbolic(mesh, equations_euler, initial_condition, solver_euler, - source_terms=source_terms_eoc_test_coupled_euler_gravity) + initial_refinement_level = 2, + n_cells_max = 10_000) +semi_euler = SemidiscretizationHyperbolic(mesh, equations_euler, initial_condition, + solver_euler, + source_terms = source_terms_eoc_test_coupled_euler_gravity) ############################################################################### # semidiscretization of the hyperbolic diffusion equations @@ -28,22 +28,21 @@ equations_gravity = HyperbolicDiffusionEquations3D() solver_gravity = DGSEM(polydeg, flux_lax_friedrichs) -semi_gravity = SemidiscretizationHyperbolic(mesh, equations_gravity, initial_condition, solver_gravity, - source_terms=source_terms_harmonic) - +semi_gravity = SemidiscretizationHyperbolic(mesh, equations_gravity, initial_condition, + solver_gravity, + source_terms = source_terms_harmonic) ############################################################################### # combining both semidiscretizations for Euler + self-gravity -parameters = ParametersEulerGravity(background_density=2.0, # aka rho0 - gravitational_constant=1.0, # aka G - cfl=1.5, - resid_tol=1.0e-10, - n_iterations_max=1000, - timestep_gravity=timestep_gravity_erk52_3Sstar!) +parameters = ParametersEulerGravity(background_density = 2.0, # aka rho0 + gravitational_constant = 1.0, # aka G + cfl = 1.5, + resid_tol = 1.0e-10, + n_iterations_max = 1000, + timestep_gravity = timestep_gravity_erk52_3Sstar!) semi = SemidiscretizationEulerGravity(semi_euler, semi_gravity, parameters) - ############################################################################### # ODE solvers, callbacks etc. tspan = (0.0, 0.5) @@ -52,20 +51,20 @@ ode = semidiscretize(semi, tspan); summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi_euler, interval=analysis_interval, - save_analysis=true) +analysis_callback = AnalysisCallback(semi_euler, interval = analysis_interval, + save_analysis = true) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_restart = SaveRestartCallback(interval=100, - save_final_restart=true) +save_restart = SaveRestartCallback(interval = 100, + save_final_restart = true) -save_solution = SaveSolutionCallback(interval=10, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 10, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) -stepsize_callback = StepsizeCallback(cfl=1.1) +stepsize_callback = StepsizeCallback(cfl = 1.1) callbacks = CallbackSet(summary_callback, analysis_callback, @@ -74,11 +73,10 @@ callbacks = CallbackSet(summary_callback, save_solution, stepsize_callback) - ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary println("Number of gravity subcycles: ", semi.gravity_counter.ncalls_since_readout) diff --git a/examples/tree_3d_dgsem/elixir_hypdiff_lax_friedrichs.jl b/examples/tree_3d_dgsem/elixir_hypdiff_lax_friedrichs.jl index c7744ce23bd..7bba154a925 100644 --- a/examples/tree_3d_dgsem/elixir_hypdiff_lax_friedrichs.jl +++ b/examples/tree_3d_dgsem/elixir_hypdiff_lax_friedrichs.jl @@ -8,53 +8,52 @@ using Trixi equations = HyperbolicDiffusionEquations3D() function initial_condition_poisson_periodic(x, t, equations::HyperbolicDiffusionEquations3D) - # elliptic equation: -νΔϕ = f - # depending on initial constant state, c, for phi this converges to the solution ϕ + c - if iszero(t) - phi = 0.0 - q1 = 0.0 - q2 = 0.0 - q3 = 0.0 - else - phi = sin(2 * pi * x[1]) * sin(2 * pi * x[2]) * sin(2 * pi * x[3]) - q1 = 2 * pi * cos(2 * pi * x[1]) * sin(2 * pi * x[2]) * sin(2 * pi * x[3]) - q2 = 2 * pi * sin(2 * pi * x[1]) * cos(2 * pi * x[2]) * sin(2 * pi * x[3]) - q3 = 2 * pi * sin(2 * pi * x[1]) * sin(2 * pi * x[2]) * cos(2 * pi * x[3]) - end - return SVector(phi, q1, q2, q3) + # elliptic equation: -νΔϕ = f + # depending on initial constant state, c, for phi this converges to the solution ϕ + c + if iszero(t) + phi = 0.0 + q1 = 0.0 + q2 = 0.0 + q3 = 0.0 + else + phi = sin(2 * pi * x[1]) * sin(2 * pi * x[2]) * sin(2 * pi * x[3]) + q1 = 2 * pi * cos(2 * pi * x[1]) * sin(2 * pi * x[2]) * sin(2 * pi * x[3]) + q2 = 2 * pi * sin(2 * pi * x[1]) * cos(2 * pi * x[2]) * sin(2 * pi * x[3]) + q3 = 2 * pi * sin(2 * pi * x[1]) * sin(2 * pi * x[2]) * cos(2 * pi * x[3]) + end + return SVector(phi, q1, q2, q3) end initial_condition = initial_condition_poisson_periodic -@inline function source_terms_poisson_periodic(u, x, t, equations::HyperbolicDiffusionEquations3D) - # elliptic equation: -νΔϕ = f - # analytical solution: phi = sin(2πx)*sin(2πy) and f = -8νπ^2 sin(2πx)*sin(2πy) - @unpack inv_Tr = equations - C = -12 * equations.nu * pi^2 - - x1, x2, x3 = x - tmp1 = sinpi(2 * x1) - tmp2 = sinpi(2 * x2) - tmp3 = sinpi(2 * x3) - du1 = -C*tmp1*tmp2*tmp3 - du2 = -inv_Tr * u[2] - du3 = -inv_Tr * u[3] - du4 = -inv_Tr * u[4] - - return SVector(du1, du2, du3, du4) +@inline function source_terms_poisson_periodic(u, x, t, + equations::HyperbolicDiffusionEquations3D) + # elliptic equation: -νΔϕ = f + # analytical solution: phi = sin(2πx)*sin(2πy) and f = -8νπ^2 sin(2πx)*sin(2πy) + @unpack inv_Tr = equations + C = -12 * equations.nu * pi^2 + + x1, x2, x3 = x + tmp1 = sinpi(2 * x1) + tmp2 = sinpi(2 * x2) + tmp3 = sinpi(2 * x3) + du1 = -C * tmp1 * tmp2 * tmp3 + du2 = -inv_Tr * u[2] + du3 = -inv_Tr * u[3] + du4 = -inv_Tr * u[4] + + return SVector(du1, du2, du3, du4) end -solver = DGSEM(polydeg=3, surface_flux=flux_lax_friedrichs) +solver = DGSEM(polydeg = 3, surface_flux = flux_lax_friedrichs) coordinates_min = (0.0, 0.0, 0.0) coordinates_max = (1.0, 1.0, 1.0) mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=3, - n_cells_max=30_000) - + initial_refinement_level = 3, + n_cells_max = 30_000) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver, - source_terms=source_terms_poisson_periodic) - + source_terms = source_terms_poisson_periodic) ############################################################################### # ODE solvers, callbacks etc. @@ -65,20 +64,20 @@ ode = semidiscretize(semi, tspan); summary_callback = SummaryCallback() resid_tol = 5.0e-12 -steady_state_callback = SteadyStateCallback(abstol=resid_tol, reltol=0.0) +steady_state_callback = SteadyStateCallback(abstol = resid_tol, reltol = 0.0) analysis_interval = 200 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval, - extra_analysis_integrals=(entropy, energy_total)) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval, + extra_analysis_integrals = (entropy, energy_total)) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=100, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 100, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) -stepsize_callback = StepsizeCallback(cfl=2.4) +stepsize_callback = StepsizeCallback(cfl = 2.4) callbacks = CallbackSet(summary_callback, steady_state_callback, analysis_callback, alive_callback, @@ -89,6 +88,6 @@ callbacks = CallbackSet(summary_callback, steady_state_callback, # run the simulation sol = Trixi.solve(ode, Trixi.HypDiffN3Erk3Sstar52(), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/tree_3d_dgsem/elixir_hypdiff_nonperiodic.jl b/examples/tree_3d_dgsem/elixir_hypdiff_nonperiodic.jl index beefb22ea1e..831e01519b6 100644 --- a/examples/tree_3d_dgsem/elixir_hypdiff_nonperiodic.jl +++ b/examples/tree_3d_dgsem/elixir_hypdiff_nonperiodic.jl @@ -8,27 +8,25 @@ using Trixi equations = HyperbolicDiffusionEquations3D() initial_condition = initial_condition_poisson_nonperiodic -boundary_conditions = (x_neg=boundary_condition_poisson_nonperiodic, - x_pos=boundary_condition_poisson_nonperiodic, - y_neg=boundary_condition_periodic, - y_pos=boundary_condition_periodic, - z_neg=boundary_condition_periodic, - z_pos=boundary_condition_periodic) +boundary_conditions = (x_neg = boundary_condition_poisson_nonperiodic, + x_pos = boundary_condition_poisson_nonperiodic, + y_neg = boundary_condition_periodic, + y_pos = boundary_condition_periodic, + z_neg = boundary_condition_periodic, + z_pos = boundary_condition_periodic) -solver = DGSEM(polydeg=4, surface_flux=flux_lax_friedrichs) +solver = DGSEM(polydeg = 4, surface_flux = flux_lax_friedrichs) coordinates_min = (0.0, 0.0, 0.0) coordinates_max = (1.0, 1.0, 1.0) mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=2, - n_cells_max=30_000, - periodicity=(false, true, true)) - + initial_refinement_level = 2, + n_cells_max = 30_000, + periodicity = (false, true, true)) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver, - source_terms=source_terms_poisson_nonperiodic, - boundary_conditions=boundary_conditions) - + source_terms = source_terms_poisson_nonperiodic, + boundary_conditions = boundary_conditions) ############################################################################### # ODE solvers, callbacks etc. @@ -39,31 +37,30 @@ ode = semidiscretize(semi, tspan); summary_callback = SummaryCallback() resid_tol = 1.0e-5 -steady_state_callback = SteadyStateCallback(abstol=resid_tol, reltol=0.0) +steady_state_callback = SteadyStateCallback(abstol = resid_tol, reltol = 0.0) analysis_interval = 200 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval, - extra_analysis_integrals=(entropy, energy_total)) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval, + extra_analysis_integrals = (entropy, energy_total)) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=100, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 100, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) -stepsize_callback = StepsizeCallback(cfl=1.8) +stepsize_callback = StepsizeCallback(cfl = 1.8) callbacks = CallbackSet(summary_callback, steady_state_callback, analysis_callback, alive_callback, save_solution, stepsize_callback) - ############################################################################### # run the simulation sol = Trixi.solve(ode, Trixi.HypDiffN3Erk3Sstar52(), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/tree_3d_dgsem/elixir_lbm_constant.jl b/examples/tree_3d_dgsem/elixir_lbm_constant.jl index 269a0da2d50..ee38f62887d 100644 --- a/examples/tree_3d_dgsem/elixir_lbm_constant.jl +++ b/examples/tree_3d_dgsem/elixir_lbm_constant.jl @@ -5,22 +5,20 @@ using Trixi ############################################################################### # semidiscretization of the Lattice-Boltzmann equations for the D3Q27 scheme -equations = LatticeBoltzmannEquations3D(Ma=0.1, Re=Inf) +equations = LatticeBoltzmannEquations3D(Ma = 0.1, Re = Inf) initial_condition = initial_condition_constant -solver = DGSEM(polydeg=3, surface_flux=flux_godunov) +solver = DGSEM(polydeg = 3, surface_flux = flux_godunov) coordinates_min = (-1.0, -1.0, -1.0) -coordinates_max = ( 1.0, 1.0, 1.0) +coordinates_max = (1.0, 1.0, 1.0) mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=3, - n_cells_max=10_000,) - + initial_refinement_level = 3, + n_cells_max = 10_000) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver) - ############################################################################### # ODE solvers, callbacks etc. @@ -30,19 +28,19 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_restart = SaveRestartCallback(interval=100, - save_final_restart=true) +save_restart = SaveRestartCallback(interval = 100, + save_final_restart = true) -save_solution = SaveSolutionCallback(interval=100, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2macroscopic) +save_solution = SaveSolutionCallback(interval = 100, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2macroscopic) -stepsize_callback = StepsizeCallback(cfl=1.0) +stepsize_callback = StepsizeCallback(cfl = 1.0) collision_callback = LBMCollisionCallback() @@ -52,11 +50,10 @@ callbacks = CallbackSet(summary_callback, stepsize_callback, collision_callback) - ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/tree_3d_dgsem/elixir_lbm_taylor_green_vortex.jl b/examples/tree_3d_dgsem/elixir_lbm_taylor_green_vortex.jl index b3835eb1287..0980ee56be3 100644 --- a/examples/tree_3d_dgsem/elixir_lbm_taylor_green_vortex.jl +++ b/examples/tree_3d_dgsem/elixir_lbm_taylor_green_vortex.jl @@ -6,7 +6,7 @@ using Trixi # semidiscretization of the Lattice-Boltzmann equations for the D3Q27 scheme L = 1.0 # reference length -equations = LatticeBoltzmannEquations3D(Ma=0.1, Re=1600.0; L=L) +equations = LatticeBoltzmannEquations3D(Ma = 0.1, Re = 1600.0; L = L) """ initial_condition_taylor_green_vortex(x, t, equations::LatticeBoltzmannEquations3D) @@ -14,52 +14,51 @@ equations = LatticeBoltzmannEquations3D(Ma=0.1, Re=1600.0; L=L) Initialize the flow field to the Taylor-Green vortex setup """ function initial_condition_taylor_green_vortex(x, t, equations::LatticeBoltzmannEquations3D) - @unpack u0, rho0, L = equations + @unpack u0, rho0, L = equations - v1 = u0 * sin(x[1] / L) * cos(x[2] / L) * cos(x[3] / L) - v2 = -u0 * cos(x[1] / L) * sin(x[2] / L) * cos(x[3] / L) - v3 = 0 - p0 = (pressure(rho0, equations) + - rho0 * u0^2 / 16 * (cos(2 * x[1] / L) + cos(2 * x[2] / L)) * (cos(2 * x[3] / L) + 2)) - rho = density(p0, equations) + v1 = u0 * sin(x[1] / L) * cos(x[2] / L) * cos(x[3] / L) + v2 = -u0 * cos(x[1] / L) * sin(x[2] / L) * cos(x[3] / L) + v3 = 0 + p0 = (pressure(rho0, equations) + + rho0 * u0^2 / 16 * (cos(2 * x[1] / L) + cos(2 * x[2] / L)) * + (cos(2 * x[3] / L) + 2)) + rho = density(p0, equations) - return equilibrium_distribution(rho, v1, v2, v3, equations) + return equilibrium_distribution(rho, v1, v2, v3, equations) end initial_condition = initial_condition_taylor_green_vortex -solver = DGSEM(polydeg=3, surface_flux=flux_godunov) +solver = DGSEM(polydeg = 3, surface_flux = flux_godunov) -coordinates_min = (-pi*L, -pi*L, -pi*L) -coordinates_max = ( pi*L, pi*L, pi*L) +coordinates_min = (-pi * L, -pi * L, -pi * L) +coordinates_max = (pi * L, pi * L, pi * L) mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=5, - n_cells_max=300_000,) - + initial_refinement_level = 5, + n_cells_max = 300_000) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver) - ############################################################################### # ODE solvers, callbacks etc. -tspan = (0.0, 20*equations.L/equations.u0) # Final time is `20` in non-dimensional time +tspan = (0.0, 20 * equations.L / equations.u0) # Final time is `20` in non-dimensional time ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 20 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval, - save_analysis=true, - extra_analysis_integrals=(Trixi.energy_kinetic_nondimensional,)) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval, + save_analysis = true, + extra_analysis_integrals = (Trixi.energy_kinetic_nondimensional,)) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=100, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2macroscopic) +save_solution = SaveSolutionCallback(interval = 100, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2macroscopic) -stepsize_callback = StepsizeCallback(cfl=0.3) +stepsize_callback = StepsizeCallback(cfl = 0.3) collision_callback = LBMCollisionCallback() @@ -69,12 +68,11 @@ callbacks = CallbackSet(summary_callback, stepsize_callback, collision_callback) - ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks, - save_start=false, alias_u0=true); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks, + save_start = false, alias_u0 = true); summary_callback() # print the timer summary diff --git a/examples/tree_3d_dgsem/elixir_mhd_alfven_wave.jl b/examples/tree_3d_dgsem/elixir_mhd_alfven_wave.jl index 191982bf2d6..9aab5e58788 100644 --- a/examples/tree_3d_dgsem/elixir_mhd_alfven_wave.jl +++ b/examples/tree_3d_dgsem/elixir_mhd_alfven_wave.jl @@ -5,24 +5,23 @@ using Trixi ############################################################################### # semidiscretization of the compressible ideal GLM-MHD equations -equations = IdealGlmMhdEquations3D(5/3) +equations = IdealGlmMhdEquations3D(5 / 3) initial_condition = initial_condition_convergence_test volume_flux = (flux_hindenlang_gassner, flux_nonconservative_powell) -solver = DGSEM(polydeg=3, surface_flux=(flux_lax_friedrichs, flux_nonconservative_powell), - volume_integral=VolumeIntegralFluxDifferencing(volume_flux)) +solver = DGSEM(polydeg = 3, + surface_flux = (flux_lax_friedrichs, flux_nonconservative_powell), + volume_integral = VolumeIntegralFluxDifferencing(volume_flux)) coordinates_min = (-1.0, -1.0, -1.0) -coordinates_max = ( 1.0, 1.0, 1.0) +coordinates_max = (1.0, 1.0, 1.0) mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=2, - n_cells_max=10_000) - + initial_refinement_level = 2, + n_cells_max = 10_000) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver) - ############################################################################### # ODE solvers, callbacks etc. @@ -32,18 +31,18 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=10, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 10, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) cfl = 1.5 -stepsize_callback = StepsizeCallback(cfl=cfl) +stepsize_callback = StepsizeCallback(cfl = cfl) -glm_speed_callback = GlmSpeedCallback(glm_scale=0.5, cfl=cfl) +glm_speed_callback = GlmSpeedCallback(glm_scale = 0.5, cfl = cfl) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, @@ -51,11 +50,10 @@ callbacks = CallbackSet(summary_callback, stepsize_callback, glm_speed_callback) - ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/tree_3d_dgsem/elixir_mhd_alfven_wave_mortar.jl b/examples/tree_3d_dgsem/elixir_mhd_alfven_wave_mortar.jl index e23f7ce5460..3ce166a7fa7 100644 --- a/examples/tree_3d_dgsem/elixir_mhd_alfven_wave_mortar.jl +++ b/examples/tree_3d_dgsem/elixir_mhd_alfven_wave_mortar.jl @@ -5,24 +5,22 @@ using Trixi ############################################################################### # semidiscretization of the compressible ideal GLM-MHD equations -equations = IdealGlmMhdEquations3D(5/3) +equations = IdealGlmMhdEquations3D(5 / 3) initial_condition = initial_condition_convergence_test volume_flux = (flux_hindenlang_gassner, flux_nonconservative_powell) -solver = DGSEM(polydeg=3, surface_flux=(flux_hll, flux_nonconservative_powell), - volume_integral=VolumeIntegralFluxDifferencing(volume_flux)) +solver = DGSEM(polydeg = 3, surface_flux = (flux_hll, flux_nonconservative_powell), + volume_integral = VolumeIntegralFluxDifferencing(volume_flux)) coordinates_min = (-1.0, -1.0, -1.0) -coordinates_max = ( 1.0, 1.0, 1.0) -refinement_patches = ( - (type="box", coordinates_min=(-0.5, -0.5, -0.5), - coordinates_max=( 0.5, 0.5, 0.5)), -) +coordinates_max = (1.0, 1.0, 1.0) +refinement_patches = ((type = "box", coordinates_min = (-0.5, -0.5, -0.5), + coordinates_max = (0.5, 0.5, 0.5)),) mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=2, - refinement_patches=refinement_patches, - n_cells_max=10_000) + initial_refinement_level = 2, + refinement_patches = refinement_patches, + n_cells_max = 10_000) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver) @@ -35,18 +33,18 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=100, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 100, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) cfl = 1.0 -stepsize_callback = StepsizeCallback(cfl=cfl) +stepsize_callback = StepsizeCallback(cfl = cfl) -glm_speed_callback = GlmSpeedCallback(glm_scale=0.5, cfl=cfl) +glm_speed_callback = GlmSpeedCallback(glm_scale = 0.5, cfl = cfl) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, @@ -54,11 +52,10 @@ callbacks = CallbackSet(summary_callback, stepsize_callback, glm_speed_callback) - ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/tree_3d_dgsem/elixir_mhd_ec.jl b/examples/tree_3d_dgsem/elixir_mhd_ec.jl index 057ffcb031f..1f0088e82c9 100644 --- a/examples/tree_3d_dgsem/elixir_mhd_ec.jl +++ b/examples/tree_3d_dgsem/elixir_mhd_ec.jl @@ -10,19 +10,18 @@ equations = IdealGlmMhdEquations3D(1.4) initial_condition = initial_condition_weak_blast_wave volume_flux = (flux_hindenlang_gassner, flux_nonconservative_powell) -solver = DGSEM(polydeg=3, surface_flux=(flux_hindenlang_gassner, flux_nonconservative_powell), - volume_integral=VolumeIntegralFluxDifferencing(volume_flux)) +solver = DGSEM(polydeg = 3, + surface_flux = (flux_hindenlang_gassner, flux_nonconservative_powell), + volume_integral = VolumeIntegralFluxDifferencing(volume_flux)) coordinates_min = (-2.0, -2.0, -2.0) -coordinates_max = ( 2.0, 2.0, 2.0) +coordinates_max = (2.0, 2.0, 2.0) mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=2, - n_cells_max=10_000) - + initial_refinement_level = 2, + n_cells_max = 10_000) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver) - ############################################################################### # ODE solvers, callbacks etc. @@ -32,19 +31,19 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=10, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 10, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) cfl = 1.4 -stepsize_callback = StepsizeCallback(cfl=cfl) +stepsize_callback = StepsizeCallback(cfl = cfl) -glm_speed_callback = GlmSpeedCallback(glm_scale=0.5, cfl=cfl) +glm_speed_callback = GlmSpeedCallback(glm_scale = 0.5, cfl = cfl) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, @@ -52,11 +51,10 @@ callbacks = CallbackSet(summary_callback, stepsize_callback, glm_speed_callback) - ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/tree_3d_dgsem/elixir_mhd_ec_shockcapturing.jl b/examples/tree_3d_dgsem/elixir_mhd_ec_shockcapturing.jl index 6b4f6e310ce..f8a72b6f452 100644 --- a/examples/tree_3d_dgsem/elixir_mhd_ec_shockcapturing.jl +++ b/examples/tree_3d_dgsem/elixir_mhd_ec_shockcapturing.jl @@ -10,25 +10,26 @@ equations = IdealGlmMhdEquations3D(1.4) initial_condition = initial_condition_weak_blast_wave surface_flux = (flux_hindenlang_gassner, flux_nonconservative_powell) -volume_flux = (flux_hindenlang_gassner, flux_nonconservative_powell) +volume_flux = (flux_hindenlang_gassner, flux_nonconservative_powell) polydeg = 4 basis = LobattoLegendreBasis(polydeg) indicator_sc = IndicatorHennemannGassner(equations, basis, - alpha_max=0.5, - alpha_min=0.001, - alpha_smooth=true, - variable=density_pressure) + alpha_max = 0.5, + alpha_min = 0.001, + alpha_smooth = true, + variable = density_pressure) volume_integral = VolumeIntegralShockCapturingHG(indicator_sc; - volume_flux_dg=volume_flux, - volume_flux_fv=surface_flux) + volume_flux_dg = volume_flux, + volume_flux_fv = surface_flux) -solver = DGSEM(polydeg=polydeg, surface_flux=surface_flux, volume_integral=volume_integral) +solver = DGSEM(polydeg = polydeg, surface_flux = surface_flux, + volume_integral = volume_integral) coordinates_min = (-2.0, -2.0, -2.0) -coordinates_max = ( 2.0, 2.0, 2.0) +coordinates_max = (2.0, 2.0, 2.0) mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=3, - n_cells_max=10_000) + initial_refinement_level = 3, + n_cells_max = 10_000) # create the semi discretization object semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver) @@ -42,25 +43,24 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) cfl = 1.4 -stepsize_callback = StepsizeCallback(cfl=cfl) +stepsize_callback = StepsizeCallback(cfl = cfl) -glm_speed_callback = GlmSpeedCallback(glm_scale=0.5, cfl=cfl) +glm_speed_callback = GlmSpeedCallback(glm_scale = 0.5, cfl = cfl) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, stepsize_callback, glm_speed_callback) - ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/tree_3d_dgsem/elixir_navierstokes_convergence.jl b/examples/tree_3d_dgsem/elixir_navierstokes_convergence.jl index ebb0137a1bb..3ada9503c6a 100644 --- a/examples/tree_3d_dgsem/elixir_navierstokes_convergence.jl +++ b/examples/tree_3d_dgsem/elixir_navierstokes_convergence.jl @@ -8,213 +8,215 @@ prandtl_number() = 0.72 mu() = 0.01 equations = CompressibleEulerEquations3D(1.4) -equations_parabolic = CompressibleNavierStokesDiffusion3D(equations, mu=mu(), Prandtl=prandtl_number(), - gradient_variables=GradientVariablesPrimitive()) +equations_parabolic = CompressibleNavierStokesDiffusion3D(equations, mu = mu(), + Prandtl = prandtl_number(), + gradient_variables = GradientVariablesPrimitive()) # Create DG solver with polynomial degree = 3 and (local) Lax-Friedrichs/Rusanov flux as surface flux -solver = DGSEM(polydeg=3, surface_flux=flux_lax_friedrichs, - volume_integral=VolumeIntegralWeakForm()) +solver = DGSEM(polydeg = 3, surface_flux = flux_lax_friedrichs, + volume_integral = VolumeIntegralWeakForm()) coordinates_min = (-1.0, -1.0, -1.0) # minimum coordinates (min(x), min(y), min(z)) -coordinates_max = ( 1.0, 1.0, 1.0) # maximum coordinates (max(x), max(y), max(z)) +coordinates_max = (1.0, 1.0, 1.0) # maximum coordinates (max(x), max(y), max(z)) # Create a uniformly refined mesh with periodic boundaries mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=3, - periodicity=(true, false, true), - n_cells_max=50_000) # set maximum capacity of tree data structure + initial_refinement_level = 3, + periodicity = (true, false, true), + n_cells_max = 50_000) # set maximum capacity of tree data structure # Note: the initial condition cannot be specialized to `CompressibleNavierStokesDiffusion3D` # since it is called by both the parabolic solver (which passes in `CompressibleNavierStokesDiffusion3D`) # and by the initial condition (which passes in `CompressibleEulerEquations3D`). # This convergence test setup was originally derived by Andrew Winters (@andrewwinters5000) function initial_condition_navier_stokes_convergence_test(x, t, equations) - # Constants. OBS! Must match those in `source_terms_navier_stokes_convergence_test` - c = 2.0 - A1 = 0.5 - A2 = 1.0 - A3 = 0.5 - - # Convenience values for trig. functions - pi_x = pi * x[1] - pi_y = pi * x[2] - pi_z = pi * x[3] - pi_t = pi * t - - rho = c + A1 * sin(pi_x) * cos(pi_y) * sin(pi_z) * cos(pi_t) - v1 = A2 * sin(pi_x) * log(x[2] + 2.0) * (1.0 - exp(-A3 * (x[2] - 1.0))) * sin(pi_z) * cos(pi_t) - v2 = v1 - v3 = v1 - p = rho^2 - - return prim2cons(SVector(rho, v1, v2, v3, p), equations) + # Constants. OBS! Must match those in `source_terms_navier_stokes_convergence_test` + c = 2.0 + A1 = 0.5 + A2 = 1.0 + A3 = 0.5 + + # Convenience values for trig. functions + pi_x = pi * x[1] + pi_y = pi * x[2] + pi_z = pi * x[3] + pi_t = pi * t + + rho = c + A1 * sin(pi_x) * cos(pi_y) * sin(pi_z) * cos(pi_t) + v1 = A2 * sin(pi_x) * log(x[2] + 2.0) * (1.0 - exp(-A3 * (x[2] - 1.0))) * sin(pi_z) * + cos(pi_t) + v2 = v1 + v3 = v1 + p = rho^2 + + return prim2cons(SVector(rho, v1, v2, v3, p), equations) end @inline function source_terms_navier_stokes_convergence_test(u, x, t, equations) - # TODO: parabolic - # we currently need to hardcode these parameters until we fix the "combined equation" issue - # see also https://github.com/trixi-framework/Trixi.jl/pull/1160 - inv_gamma_minus_one = inv(equations.gamma - 1) - Pr = prandtl_number() - mu_ = mu() - - # Constants. OBS! Must match those in `initial_condition_navier_stokes_convergence_test` - c = 2.0 - A1 = 0.5 - A2 = 1.0 - A3 = 0.5 - - # Convenience values for trig. functions - pi_x = pi * x[1] - pi_y = pi * x[2] - pi_z = pi * x[3] - pi_t = pi * t - - # Define auxiliary functions for the strange function of the y variable - # to make expressions easier to read - g = log(x[2] + 2.0) * (1.0 - exp(-A3 * (x[2] - 1.0))) - g_y = ( A3 * log(x[2] + 2.0) * exp(-A3 * (x[2] - 1.0)) - + (1.0 - exp(-A3 * (x[2] - 1.0))) / (x[2] + 2.0) ) - g_yy = ( 2.0 * A3 * exp(-A3 * (x[2] - 1.0)) / (x[2] + 2.0) - - (1.0 - exp(-A3 * (x[2] - 1.0))) / ((x[2] + 2.0)^2) - - A3^2 * log(x[2] + 2.0) * exp(-A3 * (x[2] - 1.0)) ) - - # Density and its derivatives - rho = c + A1 * sin(pi_x) * cos(pi_y) * sin(pi_z) * cos(pi_t) - rho_t = -pi * A1 * sin(pi_x) * cos(pi_y) * sin(pi_z) * sin(pi_t) - rho_x = pi * A1 * cos(pi_x) * cos(pi_y) * sin(pi_z) * cos(pi_t) - rho_y = -pi * A1 * sin(pi_x) * sin(pi_y) * sin(pi_z) * cos(pi_t) - rho_z = pi * A1 * sin(pi_x) * cos(pi_y) * cos(pi_z) * cos(pi_t) - rho_xx = -pi^2 * (rho - c) - rho_yy = -pi^2 * (rho - c) - rho_zz = -pi^2 * (rho - c) - - # Velocities and their derivatives - # v1 terms - v1 = A2 * sin(pi_x) * g * sin(pi_z) * cos(pi_t) - v1_t = -pi * A2 * sin(pi_x) * g * sin(pi_z) * sin(pi_t) - v1_x = pi * A2 * cos(pi_x) * g * sin(pi_z) * cos(pi_t) - v1_y = A2 * sin(pi_x) * g_y * sin(pi_z) * cos(pi_t) - v1_z = pi * A2 * sin(pi_x) * g * cos(pi_z) * cos(pi_t) - v1_xx = -pi^2 * v1 - v1_yy = A2 * sin(pi_x) * g_yy * sin(pi_z) * cos(pi_t) - v1_zz = -pi^2 * v1 - v1_xy = pi * A2 * cos(pi_x) * g_y * sin(pi_z) * cos(pi_t) - v1_xz = pi^2 * A2 * cos(pi_x) * g * cos(pi_z) * cos(pi_t) - v1_yz = pi * A2 * sin(pi_x) * g_y * cos(pi_z) * cos(pi_t) - # v2 terms (simplifies from ansatz) - v2 = v1 - v2_t = v1_t - v2_x = v1_x - v2_y = v1_y - v2_z = v1_z - v2_xx = v1_xx - v2_yy = v1_yy - v2_zz = v1_zz - v2_xy = v1_xy - v2_yz = v1_yz - # v3 terms (simplifies from ansatz) - v3 = v1 - v3_t = v1_t - v3_x = v1_x - v3_y = v1_y - v3_z = v1_z - v3_xx = v1_xx - v3_yy = v1_yy - v3_zz = v1_zz - v3_xz = v1_xz - v3_yz = v1_yz - - # Pressure and its derivatives - p = rho^2 - p_t = 2.0 * rho * rho_t - p_x = 2.0 * rho * rho_x - p_y = 2.0 * rho * rho_y - p_z = 2.0 * rho * rho_z - - # Total energy and its derivatives; simiplifies from ansatz that v2 = v1 and v3 = v1 - E = p * inv_gamma_minus_one + 1.5 * rho * v1^2 - E_t = p_t * inv_gamma_minus_one + 1.5 * rho_t * v1^2 + 3.0 * rho * v1 * v1_t - E_x = p_x * inv_gamma_minus_one + 1.5 * rho_x * v1^2 + 3.0 * rho * v1 * v1_x - E_y = p_y * inv_gamma_minus_one + 1.5 * rho_y * v1^2 + 3.0 * rho * v1 * v1_y - E_z = p_z * inv_gamma_minus_one + 1.5 * rho_z * v1^2 + 3.0 * rho * v1 * v1_z - - # Divergence of Fick's law ∇⋅∇q = kappa ∇⋅∇T; simplifies because p = rho², so T = p/rho = rho - kappa = equations.gamma * inv_gamma_minus_one / Pr - q_xx = kappa * rho_xx # kappa T_xx - q_yy = kappa * rho_yy # kappa T_yy - q_zz = kappa * rho_zz # kappa T_zz - - # Stress tensor and its derivatives (exploit symmetry) - tau11 = 4.0 / 3.0 * v1_x - 2.0 / 3.0 * (v2_y + v3_z) - tau12 = v1_y + v2_x - tau13 = v1_z + v3_x - tau22 = 4.0 / 3.0 * v2_y - 2.0 / 3.0 * (v1_x + v3_z) - tau23 = v2_z + v3_y - tau33 = 4.0 / 3.0 * v3_z - 2.0 / 3.0 * (v1_x + v2_y) - - tau11_x = 4.0 / 3.0 * v1_xx - 2.0 / 3.0 * (v2_xy + v3_xz) - tau12_x = v1_xy + v2_xx - tau13_x = v1_xz + v3_xx - - tau12_y = v1_yy + v2_xy - tau22_y = 4.0 / 3.0 * v2_yy - 2.0 / 3.0 * (v1_xy + v3_yz) - tau23_y = v2_yz + v3_yy - - tau13_z = v1_zz + v3_xz - tau23_z = v2_zz + v3_yz - tau33_z = 4.0 / 3.0 * v3_zz - 2.0 / 3.0 * (v1_xz + v2_yz) - - # Compute the source terms - # Density equation - du1 = ( rho_t + rho_x * v1 + rho * v1_x - + rho_y * v2 + rho * v2_y - + rho_z * v3 + rho * v3_z ) - # x-momentum equation - du2 = ( rho_t * v1 + rho * v1_t + p_x + rho_x * v1^2 - + 2.0 * rho * v1 * v1_x - + rho_y * v1 * v2 - + rho * v1_y * v2 - + rho * v1 * v2_y - + rho_z * v1 * v3 - + rho * v1_z * v3 - + rho * v1 * v3_z - - mu_ * (tau11_x + tau12_y + tau13_z) ) - # y-momentum equation - du3 = ( rho_t * v2 + rho * v2_t + p_y + rho_x * v1 * v2 - + rho * v1_x * v2 - + rho * v1 * v2_x - + rho_y * v2^2 - + 2.0 * rho * v2 * v2_y - + rho_z * v2 * v3 - + rho * v2_z * v3 - + rho * v2 * v3_z - - mu_ * (tau12_x + tau22_y + tau23_z) ) - # z-momentum equation - du4 = ( rho_t * v3 + rho * v3_t + p_z + rho_x * v1 * v3 - + rho * v1_x * v3 - + rho * v1 * v3_x - + rho_y * v2 * v3 - + rho * v2_y * v3 - + rho * v2 * v3_y - + rho_z * v3^2 - + 2.0 * rho * v3 * v3_z - - mu_ * (tau13_x + tau23_y + tau33_z) ) - # Total energy equation - du5 = ( E_t + v1_x * (E + p) + v1 * (E_x + p_x) - + v2_y * (E + p) + v2 * (E_y + p_y) - + v3_z * (E + p) + v3 * (E_z + p_z) - # stress tensor and temperature gradient from x-direction - - mu_ * ( q_xx + v1_x * tau11 + v2_x * tau12 + v3_x * tau13 - + v1 * tau11_x + v2 * tau12_x + v3 * tau13_x) - # stress tensor and temperature gradient terms from y-direction - - mu_ * ( q_yy + v1_y * tau12 + v2_y * tau22 + v3_y * tau23 - + v1 * tau12_y + v2 * tau22_y + v3 * tau23_y) - # stress tensor and temperature gradient terms from z-direction - - mu_ * ( q_zz + v1_z * tau13 + v2_z * tau23 + v3_z * tau33 - + v1 * tau13_z + v2 * tau23_z + v3 * tau33_z) ) - - return SVector(du1, du2, du3, du4, du5) + # TODO: parabolic + # we currently need to hardcode these parameters until we fix the "combined equation" issue + # see also https://github.com/trixi-framework/Trixi.jl/pull/1160 + inv_gamma_minus_one = inv(equations.gamma - 1) + Pr = prandtl_number() + mu_ = mu() + + # Constants. OBS! Must match those in `initial_condition_navier_stokes_convergence_test` + c = 2.0 + A1 = 0.5 + A2 = 1.0 + A3 = 0.5 + + # Convenience values for trig. functions + pi_x = pi * x[1] + pi_y = pi * x[2] + pi_z = pi * x[3] + pi_t = pi * t + + # Define auxiliary functions for the strange function of the y variable + # to make expressions easier to read + g = log(x[2] + 2.0) * (1.0 - exp(-A3 * (x[2] - 1.0))) + g_y = (A3 * log(x[2] + 2.0) * exp(-A3 * (x[2] - 1.0)) + + (1.0 - exp(-A3 * (x[2] - 1.0))) / (x[2] + 2.0)) + g_yy = (2.0 * A3 * exp(-A3 * (x[2] - 1.0)) / (x[2] + 2.0) - + (1.0 - exp(-A3 * (x[2] - 1.0))) / ((x[2] + 2.0)^2) - + A3^2 * log(x[2] + 2.0) * exp(-A3 * (x[2] - 1.0))) + + # Density and its derivatives + rho = c + A1 * sin(pi_x) * cos(pi_y) * sin(pi_z) * cos(pi_t) + rho_t = -pi * A1 * sin(pi_x) * cos(pi_y) * sin(pi_z) * sin(pi_t) + rho_x = pi * A1 * cos(pi_x) * cos(pi_y) * sin(pi_z) * cos(pi_t) + rho_y = -pi * A1 * sin(pi_x) * sin(pi_y) * sin(pi_z) * cos(pi_t) + rho_z = pi * A1 * sin(pi_x) * cos(pi_y) * cos(pi_z) * cos(pi_t) + rho_xx = -pi^2 * (rho - c) + rho_yy = -pi^2 * (rho - c) + rho_zz = -pi^2 * (rho - c) + + # Velocities and their derivatives + # v1 terms + v1 = A2 * sin(pi_x) * g * sin(pi_z) * cos(pi_t) + v1_t = -pi * A2 * sin(pi_x) * g * sin(pi_z) * sin(pi_t) + v1_x = pi * A2 * cos(pi_x) * g * sin(pi_z) * cos(pi_t) + v1_y = A2 * sin(pi_x) * g_y * sin(pi_z) * cos(pi_t) + v1_z = pi * A2 * sin(pi_x) * g * cos(pi_z) * cos(pi_t) + v1_xx = -pi^2 * v1 + v1_yy = A2 * sin(pi_x) * g_yy * sin(pi_z) * cos(pi_t) + v1_zz = -pi^2 * v1 + v1_xy = pi * A2 * cos(pi_x) * g_y * sin(pi_z) * cos(pi_t) + v1_xz = pi^2 * A2 * cos(pi_x) * g * cos(pi_z) * cos(pi_t) + v1_yz = pi * A2 * sin(pi_x) * g_y * cos(pi_z) * cos(pi_t) + # v2 terms (simplifies from ansatz) + v2 = v1 + v2_t = v1_t + v2_x = v1_x + v2_y = v1_y + v2_z = v1_z + v2_xx = v1_xx + v2_yy = v1_yy + v2_zz = v1_zz + v2_xy = v1_xy + v2_yz = v1_yz + # v3 terms (simplifies from ansatz) + v3 = v1 + v3_t = v1_t + v3_x = v1_x + v3_y = v1_y + v3_z = v1_z + v3_xx = v1_xx + v3_yy = v1_yy + v3_zz = v1_zz + v3_xz = v1_xz + v3_yz = v1_yz + + # Pressure and its derivatives + p = rho^2 + p_t = 2.0 * rho * rho_t + p_x = 2.0 * rho * rho_x + p_y = 2.0 * rho * rho_y + p_z = 2.0 * rho * rho_z + + # Total energy and its derivatives; simiplifies from ansatz that v2 = v1 and v3 = v1 + E = p * inv_gamma_minus_one + 1.5 * rho * v1^2 + E_t = p_t * inv_gamma_minus_one + 1.5 * rho_t * v1^2 + 3.0 * rho * v1 * v1_t + E_x = p_x * inv_gamma_minus_one + 1.5 * rho_x * v1^2 + 3.0 * rho * v1 * v1_x + E_y = p_y * inv_gamma_minus_one + 1.5 * rho_y * v1^2 + 3.0 * rho * v1 * v1_y + E_z = p_z * inv_gamma_minus_one + 1.5 * rho_z * v1^2 + 3.0 * rho * v1 * v1_z + + # Divergence of Fick's law ∇⋅∇q = kappa ∇⋅∇T; simplifies because p = rho², so T = p/rho = rho + kappa = equations.gamma * inv_gamma_minus_one / Pr + q_xx = kappa * rho_xx # kappa T_xx + q_yy = kappa * rho_yy # kappa T_yy + q_zz = kappa * rho_zz # kappa T_zz + + # Stress tensor and its derivatives (exploit symmetry) + tau11 = 4.0 / 3.0 * v1_x - 2.0 / 3.0 * (v2_y + v3_z) + tau12 = v1_y + v2_x + tau13 = v1_z + v3_x + tau22 = 4.0 / 3.0 * v2_y - 2.0 / 3.0 * (v1_x + v3_z) + tau23 = v2_z + v3_y + tau33 = 4.0 / 3.0 * v3_z - 2.0 / 3.0 * (v1_x + v2_y) + + tau11_x = 4.0 / 3.0 * v1_xx - 2.0 / 3.0 * (v2_xy + v3_xz) + tau12_x = v1_xy + v2_xx + tau13_x = v1_xz + v3_xx + + tau12_y = v1_yy + v2_xy + tau22_y = 4.0 / 3.0 * v2_yy - 2.0 / 3.0 * (v1_xy + v3_yz) + tau23_y = v2_yz + v3_yy + + tau13_z = v1_zz + v3_xz + tau23_z = v2_zz + v3_yz + tau33_z = 4.0 / 3.0 * v3_zz - 2.0 / 3.0 * (v1_xz + v2_yz) + + # Compute the source terms + # Density equation + du1 = (rho_t + rho_x * v1 + rho * v1_x + + rho_y * v2 + rho * v2_y + + rho_z * v3 + rho * v3_z) + # x-momentum equation + du2 = (rho_t * v1 + rho * v1_t + p_x + rho_x * v1^2 + + 2.0 * rho * v1 * v1_x + + rho_y * v1 * v2 + + rho * v1_y * v2 + + rho * v1 * v2_y + + rho_z * v1 * v3 + + rho * v1_z * v3 + + rho * v1 * v3_z - + mu_ * (tau11_x + tau12_y + tau13_z)) + # y-momentum equation + du3 = (rho_t * v2 + rho * v2_t + p_y + rho_x * v1 * v2 + + rho * v1_x * v2 + + rho * v1 * v2_x + + rho_y * v2^2 + + 2.0 * rho * v2 * v2_y + + rho_z * v2 * v3 + + rho * v2_z * v3 + + rho * v2 * v3_z - + mu_ * (tau12_x + tau22_y + tau23_z)) + # z-momentum equation + du4 = (rho_t * v3 + rho * v3_t + p_z + rho_x * v1 * v3 + + rho * v1_x * v3 + + rho * v1 * v3_x + + rho_y * v2 * v3 + + rho * v2_y * v3 + + rho * v2 * v3_y + + rho_z * v3^2 + + 2.0 * rho * v3 * v3_z - + mu_ * (tau13_x + tau23_y + tau33_z)) + # Total energy equation + du5 = (E_t + v1_x * (E + p) + v1 * (E_x + p_x) + + v2_y * (E + p) + v2 * (E_y + p_y) + + v3_z * (E + p) + v3 * (E_z + p_z) - + # stress tensor and temperature gradient from x-direction + mu_ * (q_xx + v1_x * tau11 + v2_x * tau12 + v3_x * tau13 + + v1 * tau11_x + v2 * tau12_x + v3 * tau13_x) - + # stress tensor and temperature gradient terms from y-direction + mu_ * (q_yy + v1_y * tau12 + v2_y * tau22 + v3_y * tau23 + + v1 * tau12_y + v2 * tau22_y + v3 * tau23_y) - + # stress tensor and temperature gradient terms from z-direction + mu_ * (q_zz + v1_z * tau13 + v2_z * tau23 + v3_z * tau33 + + v1 * tau13_z + v2 * tau23_z + v3 * tau33_z)) + + return SVector(du1, du2, du3, du4, du5) end initial_condition = initial_condition_navier_stokes_convergence_test @@ -222,30 +224,33 @@ initial_condition = initial_condition_navier_stokes_convergence_test # BC types velocity_bc_top_bottom = NoSlip() do x, t, equations u = initial_condition_navier_stokes_convergence_test(x, t, equations) - return SVector(u[2], u[3], u[4]) + return SVector(u[2], u[3], u[4]) end heat_bc_top_bottom = Adiabatic((x, t, equations) -> 0.0) -boundary_condition_top_bottom = BoundaryConditionNavierStokesWall(velocity_bc_top_bottom, heat_bc_top_bottom) +boundary_condition_top_bottom = BoundaryConditionNavierStokesWall(velocity_bc_top_bottom, + heat_bc_top_bottom) # define inviscid boundary conditions boundary_conditions = (; x_neg = boundary_condition_periodic, - x_pos = boundary_condition_periodic, - y_neg = boundary_condition_slip_wall, - y_pos = boundary_condition_slip_wall, - z_neg = boundary_condition_periodic, - z_pos = boundary_condition_periodic) + x_pos = boundary_condition_periodic, + y_neg = boundary_condition_slip_wall, + y_pos = boundary_condition_slip_wall, + z_neg = boundary_condition_periodic, + z_pos = boundary_condition_periodic) # define viscous boundary conditions boundary_conditions_parabolic = (; x_neg = boundary_condition_periodic, - x_pos = boundary_condition_periodic, - y_neg = boundary_condition_top_bottom, - y_pos = boundary_condition_top_bottom, - z_neg = boundary_condition_periodic, - z_pos = boundary_condition_periodic) - -semi = SemidiscretizationHyperbolicParabolic(mesh, (equations, equations_parabolic), initial_condition, solver; - boundary_conditions=(boundary_conditions, boundary_conditions_parabolic), - source_terms=source_terms_navier_stokes_convergence_test) + x_pos = boundary_condition_periodic, + y_neg = boundary_condition_top_bottom, + y_pos = boundary_condition_top_bottom, + z_neg = boundary_condition_periodic, + z_pos = boundary_condition_periodic) + +semi = SemidiscretizationHyperbolicParabolic(mesh, (equations, equations_parabolic), + initial_condition, solver; + boundary_conditions = (boundary_conditions, + boundary_conditions_parabolic), + source_terms = source_terms_navier_stokes_convergence_test) ############################################################################### # ODE solvers, callbacks etc. @@ -255,16 +260,15 @@ tspan = (0.0, 1.0) ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() -alive_callback = AliveCallback(alive_interval=10) +alive_callback = AliveCallback(alive_interval = 10) analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) callbacks = CallbackSet(summary_callback, alive_callback, analysis_callback) ############################################################################### # run the simulation time_int_tol = 1e-8 -sol = solve(ode, RDPK3SpFSAL49(); abstol=time_int_tol, reltol=time_int_tol, dt = 1e-5, - ode_default_options()..., callback=callbacks) +sol = solve(ode, RDPK3SpFSAL49(); abstol = time_int_tol, reltol = time_int_tol, dt = 1e-5, + ode_default_options()..., callback = callbacks) summary_callback() # print the timer summary - diff --git a/examples/tree_3d_dgsem/elixir_navierstokes_taylor_green_vortex.jl b/examples/tree_3d_dgsem/elixir_navierstokes_taylor_green_vortex.jl index 5556831a59d..65bd9aa133d 100644 --- a/examples/tree_3d_dgsem/elixir_navierstokes_taylor_green_vortex.jl +++ b/examples/tree_3d_dgsem/elixir_navierstokes_taylor_green_vortex.jl @@ -10,8 +10,8 @@ prandtl_number() = 0.72 mu() = 6.25e-4 # equivalent to Re = 1600 equations = CompressibleEulerEquations3D(1.4) -equations_parabolic = CompressibleNavierStokesDiffusion3D(equations, mu=mu(), - Prandtl=prandtl_number()) +equations_parabolic = CompressibleNavierStokesDiffusion3D(equations, mu = mu(), + Prandtl = prandtl_number()) """ initial_condition_taylor_green_vortex(x, t, equations::CompressibleEulerEquations3D) @@ -22,31 +22,34 @@ The classical viscous Taylor-Green vortex, as found for instance in Simulation of the Compressible Taylor Green Vortex using High-Order Flux Reconstruction Schemes [DOI: 10.2514/6.2014-3210](https://doi.org/10.2514/6.2014-3210) """ -function initial_condition_taylor_green_vortex(x, t, equations::CompressibleEulerEquations3D) - A = 1.0 # magnitude of speed - Ms = 0.1 # maximum Mach number - - rho = 1.0 - v1 = A * sin(x[1]) * cos(x[2]) * cos(x[3]) - v2 = -A * cos(x[1]) * sin(x[2]) * cos(x[3]) - v3 = 0.0 - p = (A / Ms)^2 * rho / equations.gamma # scaling to get Ms - p = p + 1.0/16.0 * A^2 * rho * (cos(2*x[1])*cos(2*x[3]) + 2*cos(2*x[2]) + 2*cos(2*x[1]) + cos(2*x[2])*cos(2*x[3])) - - return prim2cons(SVector(rho, v1, v2, v3, p), equations) +function initial_condition_taylor_green_vortex(x, t, + equations::CompressibleEulerEquations3D) + A = 1.0 # magnitude of speed + Ms = 0.1 # maximum Mach number + + rho = 1.0 + v1 = A * sin(x[1]) * cos(x[2]) * cos(x[3]) + v2 = -A * cos(x[1]) * sin(x[2]) * cos(x[3]) + v3 = 0.0 + p = (A / Ms)^2 * rho / equations.gamma # scaling to get Ms + p = p + + 1.0 / 16.0 * A^2 * rho * + (cos(2 * x[1]) * cos(2 * x[3]) + 2 * cos(2 * x[2]) + 2 * cos(2 * x[1]) + + cos(2 * x[2]) * cos(2 * x[3])) + + return prim2cons(SVector(rho, v1, v2, v3, p), equations) end initial_condition = initial_condition_taylor_green_vortex volume_flux = flux_ranocha -solver = DGSEM(polydeg=3, surface_flux=flux_hllc, - volume_integral=VolumeIntegralFluxDifferencing(volume_flux)) +solver = DGSEM(polydeg = 3, surface_flux = flux_hllc, + volume_integral = VolumeIntegralFluxDifferencing(volume_flux)) coordinates_min = (-1.0, -1.0, -1.0) .* pi -coordinates_max = ( 1.0, 1.0, 1.0) .* pi +coordinates_max = (1.0, 1.0, 1.0) .* pi mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=3, - n_cells_max=100_000) - + initial_refinement_level = 3, + n_cells_max = 100_000) semi = SemidiscretizationHyperbolicParabolic(mesh, (equations, equations_parabolic), initial_condition, solver) @@ -60,12 +63,13 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 50 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval, save_analysis=true, - extra_analysis_integrals=(energy_kinetic, - energy_internal, - enstrophy)) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval, + save_analysis = true, + extra_analysis_integrals = (energy_kinetic, + energy_internal, + enstrophy)) -alive_callback = AliveCallback(analysis_interval=analysis_interval,) +alive_callback = AliveCallback(analysis_interval = analysis_interval) callbacks = CallbackSet(summary_callback, analysis_callback, @@ -75,6 +79,6 @@ callbacks = CallbackSet(summary_callback, # run the simulation time_int_tol = 1e-8 -sol = solve(ode, RDPK3SpFSAL49(); abstol=time_int_tol, reltol=time_int_tol, - ode_default_options()..., callback=callbacks) +sol = solve(ode, RDPK3SpFSAL49(); abstol = time_int_tol, reltol = time_int_tol, + ode_default_options()..., callback = callbacks) summary_callback() # print the timer summary diff --git a/examples/tree_3d_fdsbp/elixir_advection_extended.jl b/examples/tree_3d_fdsbp/elixir_advection_extended.jl index 241e0698649..22085a63510 100644 --- a/examples/tree_3d_fdsbp/elixir_advection_extended.jl +++ b/examples/tree_3d_fdsbp/elixir_advection_extended.jl @@ -13,22 +13,21 @@ equations = LinearScalarAdvectionEquation3D(advection_velocity) initial_condition = initial_condition_convergence_test D_SBP = derivative_operator(SummationByPartsOperators.MattssonNordström2004(), - derivative_order=1, accuracy_order=4, - xmin=0.0, xmax=1.0, N=10) + derivative_order = 1, accuracy_order = 4, + xmin = 0.0, xmax = 1.0, N = 10) solver = FDSBP(D_SBP, - surface_integral=SurfaceIntegralStrongForm(flux_lax_friedrichs), - volume_integral=VolumeIntegralStrongForm()) + surface_integral = SurfaceIntegralStrongForm(flux_lax_friedrichs), + volume_integral = VolumeIntegralStrongForm()) coordinates_min = (-1.0, -1.0, -1.0) -coordinates_max = ( 1.0, 1.0, 1.0) +coordinates_max = (1.0, 1.0, 1.0) mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=1, - n_cells_max=30_000, - periodicity=true) + initial_refinement_level = 1, + n_cells_max = 30_000, + periodicity = true) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver) - ############################################################################### # ODE solvers, callbacks etc. @@ -38,19 +37,18 @@ ode = semidiscretize(semi, tspan); summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval, - extra_analysis_integrals=(energy_total,)) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval, + extra_analysis_integrals = (energy_total,)) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback) - ############################################################################### # run the simulation -sol = solve(ode, RDPK3SpFSAL49(); abstol=1.0e-9, reltol=1.0e-9, - ode_default_options()..., callback=callbacks) +sol = solve(ode, RDPK3SpFSAL49(); abstol = 1.0e-9, reltol = 1.0e-9, + ode_default_options()..., callback = callbacks) summary_callback() diff --git a/examples/tree_3d_fdsbp/elixir_euler_convergence.jl b/examples/tree_3d_fdsbp/elixir_euler_convergence.jl index 6aafa1b5cc1..aa5b231ee13 100644 --- a/examples/tree_3d_fdsbp/elixir_euler_convergence.jl +++ b/examples/tree_3d_fdsbp/elixir_euler_convergence.jl @@ -11,24 +11,23 @@ equations = CompressibleEulerEquations3D(1.4) initial_condition = initial_condition_convergence_test D_upw = upwind_operators(SummationByPartsOperators.Mattsson2017, - derivative_order=1, - accuracy_order=4, - xmin=-1.0, xmax=1.0, - N=16) + derivative_order = 1, + accuracy_order = 4, + xmin = -1.0, xmax = 1.0, + N = 16) flux_splitting = splitting_steger_warming solver = FDSBP(D_upw, - surface_integral=SurfaceIntegralUpwind(flux_splitting), - volume_integral=VolumeIntegralUpwind(flux_splitting)) + surface_integral = SurfaceIntegralUpwind(flux_splitting), + volume_integral = VolumeIntegralUpwind(flux_splitting)) coordinates_min = (0.0, 0.0, 0.0) coordinates_max = (2.0, 2.0, 2.0) mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=2, - n_cells_max=10_000) + initial_refinement_level = 2, + n_cells_max = 10_000) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver, - source_terms=source_terms_convergence_test) - + source_terms = source_terms_convergence_test) ############################################################################### # ODE solvers, callbacks etc. @@ -39,27 +38,26 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=100, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 100, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) -stepsize_callback = StepsizeCallback(cfl=1.1) +stepsize_callback = StepsizeCallback(cfl = 1.1) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, save_solution, stepsize_callback) - ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/tree_3d_fdsbp/elixir_euler_taylor_green_vortex.jl b/examples/tree_3d_fdsbp/elixir_euler_taylor_green_vortex.jl index d2495cff5cd..0354200ae42 100644 --- a/examples/tree_3d_fdsbp/elixir_euler_taylor_green_vortex.jl +++ b/examples/tree_3d_fdsbp/elixir_euler_taylor_green_vortex.jl @@ -14,40 +14,43 @@ equations = CompressibleEulerEquations3D(1.4) The classical inviscid Taylor-Green vortex. """ -function initial_condition_taylor_green_vortex(x, t, equations::CompressibleEulerEquations3D) - A = 1.0 # magnitude of speed - Ms = 0.1 # maximum Mach number - - rho = 1.0 - v1 = A * sin(x[1]) * cos(x[2]) * cos(x[3]) - v2 = -A * cos(x[1]) * sin(x[2]) * cos(x[3]) - v3 = 0.0 - p = (A / Ms)^2 * rho / equations.gamma # scaling to get Ms - p = p + 1.0/16.0 * A^2 * rho * (cos(2*x[1])*cos(2*x[3]) + 2*cos(2*x[2]) + 2*cos(2*x[1]) + cos(2*x[2])*cos(2*x[3])) - - return prim2cons(SVector(rho, v1, v2, v3, p), equations) +function initial_condition_taylor_green_vortex(x, t, + equations::CompressibleEulerEquations3D) + A = 1.0 # magnitude of speed + Ms = 0.1 # maximum Mach number + + rho = 1.0 + v1 = A * sin(x[1]) * cos(x[2]) * cos(x[3]) + v2 = -A * cos(x[1]) * sin(x[2]) * cos(x[3]) + v3 = 0.0 + p = (A / Ms)^2 * rho / equations.gamma # scaling to get Ms + p = p + + 1.0 / 16.0 * A^2 * rho * + (cos(2 * x[1]) * cos(2 * x[3]) + 2 * cos(2 * x[2]) + 2 * cos(2 * x[1]) + + cos(2 * x[2]) * cos(2 * x[3])) + + return prim2cons(SVector(rho, v1, v2, v3, p), equations) end initial_condition = initial_condition_taylor_green_vortex D_upw = upwind_operators(SummationByPartsOperators.Mattsson2017, - derivative_order=1, - accuracy_order=4, - xmin=-1.0, xmax=1.0, - N=16) + derivative_order = 1, + accuracy_order = 4, + xmin = -1.0, xmax = 1.0, + N = 16) flux_splitting = splitting_steger_warming solver = FDSBP(D_upw, - surface_integral=SurfaceIntegralUpwind(flux_splitting), - volume_integral=VolumeIntegralUpwind(flux_splitting)) + surface_integral = SurfaceIntegralUpwind(flux_splitting), + volume_integral = VolumeIntegralUpwind(flux_splitting)) coordinates_min = (-1.0, -1.0, -1.0) .* pi -coordinates_max = ( 1.0, 1.0, 1.0) .* pi +coordinates_max = (1.0, 1.0, 1.0) .* pi mesh = TreeMesh(coordinates_min, coordinates_max, - initial_refinement_level=2, - n_cells_max=100_000) + initial_refinement_level = 2, + n_cells_max = 100_000) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver) - ############################################################################### # ODE solvers, callbacks etc. @@ -57,28 +60,27 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval, - save_analysis=true, - extra_analysis_integrals=(energy_total, - energy_kinetic, - energy_internal,)) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval, + save_analysis = true, + extra_analysis_integrals = (energy_total, + energy_kinetic, + energy_internal)) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=1000, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 1000, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, save_solution) - ############################################################################### # run the simulation -sol = solve(ode, SSPRK43(); abstol=1.0e-6, reltol=1.0e-6, - ode_default_options()..., callback=callbacks) +sol = solve(ode, SSPRK43(); abstol = 1.0e-6, reltol = 1.0e-6, + ode_default_options()..., callback = callbacks) summary_callback() # print the timer summary diff --git a/examples/unstructured_2d_dgsem/elixir_acoustics_gauss_wall.jl b/examples/unstructured_2d_dgsem/elixir_acoustics_gauss_wall.jl index 2f8228dffb8..8f8e867dca8 100644 --- a/examples/unstructured_2d_dgsem/elixir_acoustics_gauss_wall.jl +++ b/examples/unstructured_2d_dgsem/elixir_acoustics_gauss_wall.jl @@ -6,16 +6,18 @@ using Trixi ############################################################################### # semidiscretization of the acoustic perturbation equations -equations = AcousticPerturbationEquations2D(v_mean_global=(0.0, -0.5), c_mean_global=1.0, - rho_mean_global=1.0) +equations = AcousticPerturbationEquations2D(v_mean_global = (0.0, -0.5), + c_mean_global = 1.0, + rho_mean_global = 1.0) # Create DG solver with polynomial degree = 4 and (local) Lax-Friedrichs/Rusanov flux -solver = DGSEM(polydeg=4, surface_flux=flux_lax_friedrichs) +solver = DGSEM(polydeg = 4, surface_flux = flux_lax_friedrichs) # Create unstructured quadrilateral mesh from a file default_mesh_file = joinpath(@__DIR__, "mesh_five_circles_in_circle.mesh") -isfile(default_mesh_file) || download("https://gist.githubusercontent.com/andrewwinters5000/3c79baad6b4d73bb26ec6420b5d16f45/raw/22aefc4ec2107cf0bffc40e81dfbc52240c625b1/mesh_five_circles_in_circle.mesh", - default_mesh_file) +isfile(default_mesh_file) || + download("https://gist.githubusercontent.com/andrewwinters5000/3c79baad6b4d73bb26ec6420b5d16f45/raw/22aefc4ec2107cf0bffc40e81dfbc52240c625b1/mesh_five_circles_in_circle.mesh", + default_mesh_file) mesh_file = default_mesh_file mesh = UnstructuredMesh2D(mesh_file) @@ -27,27 +29,26 @@ A Gaussian pulse, used in the `gauss_wall` example elixir in combination with [`boundary_condition_wall`](@ref). Uses the global mean values from `equations`. """ function initial_condition_gauss_wall(x, t, equations::AcousticPerturbationEquations2D) - v1_prime = 0.0 - v2_prime = 0.0 - p_prime = exp(-log(2) * (x[1]^2 + (x[2] - 25)^2) / 25) + v1_prime = 0.0 + v2_prime = 0.0 + p_prime = exp(-log(2) * (x[1]^2 + (x[2] - 25)^2) / 25) - prim = SVector(v1_prime, v2_prime, p_prime, global_mean_vars(equations)...) + prim = SVector(v1_prime, v2_prime, p_prime, global_mean_vars(equations)...) - return prim2cons(prim, equations) + return prim2cons(prim, equations) end initial_condition = initial_condition_gauss_wall -boundary_conditions = Dict( :OuterCircle => boundary_condition_slip_wall, - :InnerCircle1 => boundary_condition_slip_wall, - :InnerCircle2 => boundary_condition_slip_wall, - :InnerCircle3 => boundary_condition_slip_wall, - :InnerCircle4 => boundary_condition_slip_wall, - :InnerCircle5 => boundary_condition_slip_wall ) +boundary_conditions = Dict(:OuterCircle => boundary_condition_slip_wall, + :InnerCircle1 => boundary_condition_slip_wall, + :InnerCircle2 => boundary_condition_slip_wall, + :InnerCircle3 => boundary_condition_slip_wall, + :InnerCircle4 => boundary_condition_slip_wall, + :InnerCircle5 => boundary_condition_slip_wall) # A semidiscretization collects data structures and functions for the spatial discretization semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver, - boundary_conditions=boundary_conditions) - + boundary_conditions = boundary_conditions) ############################################################################### # ODE solvers, callbacks etc. @@ -61,10 +62,10 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() # The AnalysisCallback allows to analyse the solution in regular intervals and prints the results -analysis_callback = AnalysisCallback(semi, interval=100) +analysis_callback = AnalysisCallback(semi, interval = 100) # The SaveSolutionCallback allows to save the solution to a file in regular intervals -save_solution = SaveSolutionCallback(interval=50, solution_variables=cons2state) +save_solution = SaveSolutionCallback(interval = 50, solution_variables = cons2state) # Create a CallbackSet to collect all callbacks such that they can be passed to the ODE solver callbacks = CallbackSet(summary_callback, analysis_callback, save_solution) @@ -73,7 +74,7 @@ callbacks = CallbackSet(summary_callback, analysis_callback, save_solution) # run the simulation # use a Runge-Kutta method with automatic (error based) time step size control -sol = solve(ode, RDPK3SpFSAL49(); abstol=1.0e-6, reltol=1.0e-6, - ode_default_options()..., callback=callbacks); +sol = solve(ode, RDPK3SpFSAL49(); abstol = 1.0e-6, reltol = 1.0e-6, + ode_default_options()..., callback = callbacks); # Print the timer summary summary_callback() diff --git a/examples/unstructured_2d_dgsem/elixir_advection_basic.jl b/examples/unstructured_2d_dgsem/elixir_advection_basic.jl index 274978d48b0..afef6c2c38f 100644 --- a/examples/unstructured_2d_dgsem/elixir_advection_basic.jl +++ b/examples/unstructured_2d_dgsem/elixir_advection_basic.jl @@ -12,22 +12,24 @@ equations = LinearScalarAdvectionEquation2D(advection_velocity) ############################################################################### # Get the DG approximation space -solver = DGSEM(polydeg=6, surface_flux=flux_lax_friedrichs) +solver = DGSEM(polydeg = 6, surface_flux = flux_lax_friedrichs) ############################################################################### # Get the curved quad mesh from a file (downloads the file if not available locally) default_mesh_file = joinpath(@__DIR__, "mesh_periodic_square_with_twist.mesh") -isfile(default_mesh_file) || download("https://gist.githubusercontent.com/andrewwinters5000/12ce661d7c354c3d94c74b964b0f1c96/raw/8275b9a60c6e7ebbdea5fc4b4f091c47af3d5273/mesh_periodic_square_with_twist.mesh", - default_mesh_file) +isfile(default_mesh_file) || + download("https://gist.githubusercontent.com/andrewwinters5000/12ce661d7c354c3d94c74b964b0f1c96/raw/8275b9a60c6e7ebbdea5fc4b4f091c47af3d5273/mesh_periodic_square_with_twist.mesh", + default_mesh_file) mesh_file = default_mesh_file -mesh = UnstructuredMesh2D(mesh_file, periodicity=true) +mesh = UnstructuredMesh2D(mesh_file, periodicity = true) ############################################################################### # create the semi discretization object -semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition_convergence_test, solver) +semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition_convergence_test, + solver) ############################################################################### # ODE solvers, callbacks etc. @@ -40,22 +42,23 @@ ode = semidiscretize(semi, (0.0, 1.0)); summary_callback = SummaryCallback() # The AnalysisCallback allows to analyse the solution in regular intervals and prints the results -analysis_callback = AnalysisCallback(semi, interval=100) +analysis_callback = AnalysisCallback(semi, interval = 100) # The SaveSolutionCallback allows to save the solution to a file in regular intervals -save_solution = SaveSolutionCallback(interval=100, - solution_variables=cons2prim) +save_solution = SaveSolutionCallback(interval = 100, + solution_variables = cons2prim) # The StepsizeCallback handles the re-calculation of the maximum Δt after each time step -stepsize_callback = StepsizeCallback(cfl=1.6) +stepsize_callback = StepsizeCallback(cfl = 1.6) # Create a CallbackSet to collect all callbacks such that they can be passed to the ODE solver -callbacks = CallbackSet(summary_callback, analysis_callback, save_solution, stepsize_callback) +callbacks = CallbackSet(summary_callback, analysis_callback, save_solution, + stepsize_callback) ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/unstructured_2d_dgsem/elixir_euler_basic.jl b/examples/unstructured_2d_dgsem/elixir_euler_basic.jl index 9fbea47a9d5..cd6a1995757 100644 --- a/examples/unstructured_2d_dgsem/elixir_euler_basic.jl +++ b/examples/unstructured_2d_dgsem/elixir_euler_basic.jl @@ -12,23 +12,24 @@ initial_condition = initial_condition_convergence_test source_terms = source_terms_convergence_test boundary_condition_convergence_test = BoundaryConditionDirichlet(initial_condition) -boundary_conditions = Dict( :Slant => boundary_condition_convergence_test, - :Bezier => boundary_condition_convergence_test, - :Right => boundary_condition_convergence_test, - :Bottom => boundary_condition_convergence_test, - :Top => boundary_condition_convergence_test ) +boundary_conditions = Dict(:Slant => boundary_condition_convergence_test, + :Bezier => boundary_condition_convergence_test, + :Right => boundary_condition_convergence_test, + :Bottom => boundary_condition_convergence_test, + :Top => boundary_condition_convergence_test) ############################################################################### # Get the DG approximation space -solver = DGSEM(polydeg=8, surface_flux=flux_lax_friedrichs) +solver = DGSEM(polydeg = 8, surface_flux = flux_lax_friedrichs) ############################################################################### # Get the curved quad mesh from a file (downloads the file if not available locally) default_mesh_file = joinpath(@__DIR__, "mesh_trixi_unstructured_mesh_docs.mesh") -isfile(default_mesh_file) || download("https://gist.githubusercontent.com/andrewwinters5000/52056f1487853fab63b7f4ed7f171c80/raw/9d573387dfdbb8bce2a55db7246f4207663ac07f/mesh_trixi_unstructured_mesh_docs.mesh", - default_mesh_file) +isfile(default_mesh_file) || + download("https://gist.githubusercontent.com/andrewwinters5000/52056f1487853fab63b7f4ed7f171c80/raw/9d573387dfdbb8bce2a55db7246f4207663ac07f/mesh_trixi_unstructured_mesh_docs.mesh", + default_mesh_file) mesh_file = default_mesh_file mesh = UnstructuredMesh2D(mesh_file) @@ -37,8 +38,8 @@ mesh = UnstructuredMesh2D(mesh_file) # create the semi discretization object semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver, - source_terms=source_terms, - boundary_conditions=boundary_conditions) + source_terms = source_terms, + boundary_conditions = boundary_conditions) ############################################################################### # ODE solvers, callbacks etc. @@ -49,18 +50,18 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_restart = SaveRestartCallback(interval=50, - save_final_restart=true) +save_restart = SaveRestartCallback(interval = 50, + save_final_restart = true) -save_solution = SaveSolutionCallback(interval=10, - save_initial_solution=true, - save_final_solution=true) +save_solution = SaveSolutionCallback(interval = 10, + save_initial_solution = true, + save_final_solution = true) -stepsize_callback = StepsizeCallback(cfl=0.9) +stepsize_callback = StepsizeCallback(cfl = 0.9) callbacks = CallbackSet(summary_callback, analysis_callback, @@ -72,7 +73,7 @@ callbacks = CallbackSet(summary_callback, ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/unstructured_2d_dgsem/elixir_euler_ec.jl b/examples/unstructured_2d_dgsem/elixir_euler_ec.jl index 2725142fd17..0f53aa62a18 100644 --- a/examples/unstructured_2d_dgsem/elixir_euler_ec.jl +++ b/examples/unstructured_2d_dgsem/elixir_euler_ec.jl @@ -6,7 +6,7 @@ using Trixi ############################################################################### # semidiscretization of the compressible Euler equations -equations = CompressibleEulerEquations2D(5/3) +equations = CompressibleEulerEquations2D(5 / 3) initial_condition = initial_condition_weak_blast_wave @@ -14,18 +14,19 @@ initial_condition = initial_condition_weak_blast_wave # Get the DG approximation space volume_flux = flux_ranocha -solver = DGSEM(polydeg=6, surface_flux=flux_ranocha, - volume_integral=VolumeIntegralFluxDifferencing(volume_flux)) +solver = DGSEM(polydeg = 6, surface_flux = flux_ranocha, + volume_integral = VolumeIntegralFluxDifferencing(volume_flux)) ############################################################################### # Get the curved quad mesh from a file default_mesh_file = joinpath(@__DIR__, "mesh_periodic_square_with_twist.mesh") -isfile(default_mesh_file) || download("https://gist.githubusercontent.com/andrewwinters5000/12ce661d7c354c3d94c74b964b0f1c96/raw/8275b9a60c6e7ebbdea5fc4b4f091c47af3d5273/mesh_periodic_square_with_twist.mesh", - default_mesh_file) +isfile(default_mesh_file) || + download("https://gist.githubusercontent.com/andrewwinters5000/12ce661d7c354c3d94c74b964b0f1c96/raw/8275b9a60c6e7ebbdea5fc4b4f091c47af3d5273/mesh_periodic_square_with_twist.mesh", + default_mesh_file) mesh_file = default_mesh_file -mesh = UnstructuredMesh2D(mesh_file, periodicity=true) +mesh = UnstructuredMesh2D(mesh_file, periodicity = true) ############################################################################### # create the semi discretization object @@ -41,15 +42,15 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=100, - save_initial_solution=true, - save_final_solution=true) +save_solution = SaveSolutionCallback(interval = 100, + save_initial_solution = true, + save_final_solution = true) -stepsize_callback = StepsizeCallback(cfl=1.0) +stepsize_callback = StepsizeCallback(cfl = 1.0) callbacks = CallbackSet(summary_callback, analysis_callback, @@ -60,7 +61,7 @@ callbacks = CallbackSet(summary_callback, ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/unstructured_2d_dgsem/elixir_euler_free_stream.jl b/examples/unstructured_2d_dgsem/elixir_euler_free_stream.jl index 36e119ab794..a2fec1a320a 100644 --- a/examples/unstructured_2d_dgsem/elixir_euler_free_stream.jl +++ b/examples/unstructured_2d_dgsem/elixir_euler_free_stream.jl @@ -11,25 +11,26 @@ equations = CompressibleEulerEquations2D(1.4) initial_condition = initial_condition_constant boundary_condition_free_stream = BoundaryConditionDirichlet(initial_condition) -boundary_conditions = Dict( :Body => boundary_condition_free_stream, - :Button1 => boundary_condition_free_stream, - :Button2 => boundary_condition_free_stream, - :Eye1 => boundary_condition_free_stream, - :Eye2 => boundary_condition_free_stream, - :Smile => boundary_condition_free_stream, - :Bowtie => boundary_condition_free_stream ) +boundary_conditions = Dict(:Body => boundary_condition_free_stream, + :Button1 => boundary_condition_free_stream, + :Button2 => boundary_condition_free_stream, + :Eye1 => boundary_condition_free_stream, + :Eye2 => boundary_condition_free_stream, + :Smile => boundary_condition_free_stream, + :Bowtie => boundary_condition_free_stream) ############################################################################### # Get the DG approximation space -solver = DGSEM(polydeg=6, surface_flux=flux_hll) +solver = DGSEM(polydeg = 6, surface_flux = flux_hll) ############################################################################### # Get the curved quad mesh from a file (downloads the file if not available locally) default_mesh_file = joinpath(@__DIR__, "mesh_gingerbread_man.mesh") -isfile(default_mesh_file) || download("https://gist.githubusercontent.com/andrewwinters5000/2c6440b5f8a57db131061ad7aa78ee2b/raw/1f89fdf2c874ff678c78afb6fe8dc784bdfd421f/mesh_gingerbread_man.mesh", - default_mesh_file) +isfile(default_mesh_file) || + download("https://gist.githubusercontent.com/andrewwinters5000/2c6440b5f8a57db131061ad7aa78ee2b/raw/1f89fdf2c874ff678c78afb6fe8dc784bdfd421f/mesh_gingerbread_man.mesh", + default_mesh_file) mesh_file = default_mesh_file mesh = UnstructuredMesh2D(mesh_file) @@ -38,7 +39,7 @@ mesh = UnstructuredMesh2D(mesh_file) # create the semi discretization object semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver, - boundary_conditions=boundary_conditions) + boundary_conditions = boundary_conditions) ############################################################################### # ODE solvers, callbacks etc. @@ -49,15 +50,15 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=100, - save_initial_solution=true, - save_final_solution=true) +save_solution = SaveSolutionCallback(interval = 100, + save_initial_solution = true, + save_final_solution = true) -stepsize_callback = StepsizeCallback(cfl=1.0) +stepsize_callback = StepsizeCallback(cfl = 1.0) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, save_solution, stepsize_callback) @@ -65,7 +66,7 @@ callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, sav ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/unstructured_2d_dgsem/elixir_euler_periodic.jl b/examples/unstructured_2d_dgsem/elixir_euler_periodic.jl index 796c99987a2..afd177f0740 100644 --- a/examples/unstructured_2d_dgsem/elixir_euler_periodic.jl +++ b/examples/unstructured_2d_dgsem/elixir_euler_periodic.jl @@ -15,24 +15,25 @@ boundary_conditions = boundary_condition_periodic ############################################################################### # Get the DG approximation space -solver = DGSEM(polydeg=6, surface_flux=FluxRotated(flux_hll)) +solver = DGSEM(polydeg = 6, surface_flux = FluxRotated(flux_hll)) ############################################################################### # Get the curved quad mesh from a file (downloads the file if not available locally) default_mesh_file = joinpath(@__DIR__, "mesh_periodic_square_with_twist.mesh") -isfile(default_mesh_file) || download("https://gist.githubusercontent.com/andrewwinters5000/12ce661d7c354c3d94c74b964b0f1c96/raw/8275b9a60c6e7ebbdea5fc4b4f091c47af3d5273/mesh_periodic_square_with_twist.mesh", - default_mesh_file) +isfile(default_mesh_file) || + download("https://gist.githubusercontent.com/andrewwinters5000/12ce661d7c354c3d94c74b964b0f1c96/raw/8275b9a60c6e7ebbdea5fc4b4f091c47af3d5273/mesh_periodic_square_with_twist.mesh", + default_mesh_file) mesh_file = default_mesh_file -mesh = UnstructuredMesh2D(mesh_file, periodicity=true) +mesh = UnstructuredMesh2D(mesh_file, periodicity = true) ############################################################################### # create the semi discretization object semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver, - source_terms=source_terms, - boundary_conditions=boundary_conditions) + source_terms = source_terms, + boundary_conditions = boundary_conditions) ############################################################################### # ODE solvers, callbacks etc. @@ -43,14 +44,14 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback) ############################################################################### # run the simulation -sol = solve(ode, SSPRK43(); ode_default_options()..., callback=callbacks); +sol = solve(ode, SSPRK43(); ode_default_options()..., callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/unstructured_2d_dgsem/elixir_euler_restart.jl b/examples/unstructured_2d_dgsem/elixir_euler_restart.jl index 6653f8662d9..4d6af65b8a4 100644 --- a/examples/unstructured_2d_dgsem/elixir_euler_restart.jl +++ b/examples/unstructured_2d_dgsem/elixir_euler_restart.jl @@ -7,7 +7,6 @@ using Trixi trixi_include(@__MODULE__, joinpath(@__DIR__, "elixir_euler_basic.jl")) - ############################################################################### # adapt the parameters that have changed compared to "elixir_advection_extended.jl" @@ -18,8 +17,8 @@ restart_filename = joinpath("out", "restart_000050.h5") mesh = load_mesh(restart_filename) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver, - source_terms=source_terms, - boundary_conditions=boundary_conditions) + source_terms = source_terms, + boundary_conditions = boundary_conditions) tspan = (load_time(restart_filename), 1.0) dt = load_dt(restart_filename) @@ -28,17 +27,15 @@ ode = semidiscretize(semi, tspan, restart_filename); # Do not overwrite the initial snapshot written by elixir_advection_extended.jl. save_solution.condition.save_initial_solution = false -integrator = init(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=dt, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +integrator = init(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = dt, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); # Get the last time index and work with that. load_timestep!(integrator, restart_filename) - ############################################################################### # run the simulation sol = solve!(integrator) summary_callback() # print the timer summary - diff --git a/examples/unstructured_2d_dgsem/elixir_euler_sedov.jl b/examples/unstructured_2d_dgsem/elixir_euler_sedov.jl index 570a2084691..e1cc0932969 100644 --- a/examples/unstructured_2d_dgsem/elixir_euler_sedov.jl +++ b/examples/unstructured_2d_dgsem/elixir_euler_sedov.jl @@ -14,25 +14,25 @@ The Sedov blast wave setup based on Flash - https://flash.rochester.edu/site/flashcode/user_support/flash_ug_devel/node187.html#SECTION010114000000000000000 """ function initial_condition_sedov_blast_wave(x, t, equations::CompressibleEulerEquations2D) - # Set up polar coordinates - inicenter = SVector(0.0, 0.0) - x_norm = x[1] - inicenter[1] - y_norm = x[2] - inicenter[2] - r = sqrt(x_norm^2 + y_norm^2) - - # Setup based on https://flash.rochester.edu/site/flashcode/user_support/flash_ug_devel/node187.html#SECTION010114000000000000000 - r0 = 0.21875 # = 3.5 * smallest dx (for domain length=4 and max-ref=6) - E = 1.0 - p0_inner = 3 * (equations.gamma - 1) * E / (3 * pi * r0^2) - p0_outer = 1.0e-5 # = true Sedov setup - - # Calculate primitive variables - rho = 1.0 - v1 = 0.0 - v2 = 0.0 - p = r > r0 ? p0_outer : p0_inner - - return prim2cons(SVector(rho, v1, v2, p), equations) + # Set up polar coordinates + inicenter = SVector(0.0, 0.0) + x_norm = x[1] - inicenter[1] + y_norm = x[2] - inicenter[2] + r = sqrt(x_norm^2 + y_norm^2) + + # Setup based on https://flash.rochester.edu/site/flashcode/user_support/flash_ug_devel/node187.html#SECTION010114000000000000000 + r0 = 0.21875 # = 3.5 * smallest dx (for domain length=4 and max-ref=6) + E = 1.0 + p0_inner = 3 * (equations.gamma - 1) * E / (3 * pi * r0^2) + p0_outer = 1.0e-5 # = true Sedov setup + + # Calculate primitive variables + rho = 1.0 + v1 = 0.0 + v2 = 0.0 + p = r > r0 ? p0_outer : p0_inner + + return prim2cons(SVector(rho, v1, v2, p), equations) end initial_condition = initial_condition_sedov_blast_wave @@ -43,23 +43,25 @@ volume_flux = flux_ranocha polydeg = 6 basis = LobattoLegendreBasis(polydeg) indicator_sc = IndicatorHennemannGassner(equations, basis, - alpha_max=1.0, - alpha_min=0.001, - alpha_smooth=true, - variable=density_pressure) + alpha_max = 1.0, + alpha_min = 0.001, + alpha_smooth = true, + variable = density_pressure) volume_integral = VolumeIntegralShockCapturingHG(indicator_sc; - volume_flux_dg=volume_flux, - volume_flux_fv=surface_flux) + volume_flux_dg = volume_flux, + volume_flux_fv = surface_flux) -solver = DGSEM(polydeg=polydeg, surface_flux=surface_flux, volume_integral=volume_integral) +solver = DGSEM(polydeg = polydeg, surface_flux = surface_flux, + volume_integral = volume_integral) # Get the curved quad mesh from a file default_mesh_file = joinpath(@__DIR__, "mesh_periodic_square_with_twist.mesh") -isfile(default_mesh_file) || download("https://gist.githubusercontent.com/andrewwinters5000/12ce661d7c354c3d94c74b964b0f1c96/raw/8275b9a60c6e7ebbdea5fc4b4f091c47af3d5273/mesh_periodic_square_with_twist.mesh", - default_mesh_file) +isfile(default_mesh_file) || + download("https://gist.githubusercontent.com/andrewwinters5000/12ce661d7c354c3d94c74b964b0f1c96/raw/8275b9a60c6e7ebbdea5fc4b4f091c47af3d5273/mesh_periodic_square_with_twist.mesh", + default_mesh_file) mesh_file = default_mesh_file -mesh = UnstructuredMesh2D(mesh_file, periodicity=true) +mesh = UnstructuredMesh2D(mesh_file, periodicity = true) # create the semidiscretization semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver) @@ -73,15 +75,15 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 300 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=300, - save_initial_solution=true, - save_final_solution=true) +save_solution = SaveSolutionCallback(interval = 300, + save_initial_solution = true, + save_final_solution = true) -stepsize_callback = StepsizeCallback(cfl=0.5) +stepsize_callback = StepsizeCallback(cfl = 0.5) callbacks = CallbackSet(summary_callback, analysis_callback, @@ -92,7 +94,7 @@ callbacks = CallbackSet(summary_callback, ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/unstructured_2d_dgsem/elixir_euler_wall_bc.jl b/examples/unstructured_2d_dgsem/elixir_euler_wall_bc.jl index 5bfe1ae4e0e..b2abefe7eeb 100644 --- a/examples/unstructured_2d_dgsem/elixir_euler_wall_bc.jl +++ b/examples/unstructured_2d_dgsem/elixir_euler_wall_bc.jl @@ -10,40 +10,41 @@ equations = CompressibleEulerEquations2D(1.4) @inline function uniform_flow_state(x, t, equations::CompressibleEulerEquations2D) - # set the freestream flow parameters - rho_freestream = 1.0 - u_freestream = 0.3 - p_freestream = inv(equations.gamma) - - theta = pi / 90.0 # analogous with a two degree angle of attack - si, co = sincos(theta) - v1 = u_freestream * co - v2 = u_freestream * si - - prim = SVector(rho_freestream, v1, v2, p_freestream) - return prim2cons(prim, equations) + # set the freestream flow parameters + rho_freestream = 1.0 + u_freestream = 0.3 + p_freestream = inv(equations.gamma) + + theta = pi / 90.0 # analogous with a two degree angle of attack + si, co = sincos(theta) + v1 = u_freestream * co + v2 = u_freestream * si + + prim = SVector(rho_freestream, v1, v2, p_freestream) + return prim2cons(prim, equations) end initial_condition = uniform_flow_state boundary_condition_uniform_flow = BoundaryConditionDirichlet(uniform_flow_state) -boundary_conditions = Dict( :Bottom => boundary_condition_uniform_flow, - :Top => boundary_condition_uniform_flow, - :Right => boundary_condition_uniform_flow, - :Left => boundary_condition_uniform_flow, - :Circle => boundary_condition_slip_wall ) +boundary_conditions = Dict(:Bottom => boundary_condition_uniform_flow, + :Top => boundary_condition_uniform_flow, + :Right => boundary_condition_uniform_flow, + :Left => boundary_condition_uniform_flow, + :Circle => boundary_condition_slip_wall) ############################################################################### # Get the DG approximation space -solver = DGSEM(polydeg=4, surface_flux=flux_hll) +solver = DGSEM(polydeg = 4, surface_flux = flux_hll) ############################################################################### # Get the curved quad mesh from a file default_mesh_file = joinpath(@__DIR__, "mesh_box_around_circle.mesh") -isfile(default_mesh_file) || download("https://gist.githubusercontent.com/andrewwinters5000/8b9b11a1eedfa54b215c122c3d17b271/raw/0d2b5d98c87e67a6f384693a8b8e54b4c9fcbf3d/mesh_box_around_circle.mesh", - default_mesh_file) +isfile(default_mesh_file) || + download("https://gist.githubusercontent.com/andrewwinters5000/8b9b11a1eedfa54b215c122c3d17b271/raw/0d2b5d98c87e67a6f384693a8b8e54b4c9fcbf3d/mesh_box_around_circle.mesh", + default_mesh_file) mesh_file = default_mesh_file mesh = UnstructuredMesh2D(mesh_file) @@ -52,7 +53,7 @@ mesh = UnstructuredMesh2D(mesh_file) # create the semi discretization object semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver, - boundary_conditions=boundary_conditions) + boundary_conditions = boundary_conditions) ############################################################################### # ODE solvers, callbacks etc. @@ -63,22 +64,23 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=10, - save_initial_solution=true, - save_final_solution=true) +save_solution = SaveSolutionCallback(interval = 10, + save_initial_solution = true, + save_final_solution = true) -stepsize_callback = StepsizeCallback(cfl=1.0) +stepsize_callback = StepsizeCallback(cfl = 1.0) -callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, save_solution, stepsize_callback) +callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, save_solution, + stepsize_callback) ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/unstructured_2d_dgsem/elixir_mhd_alfven_wave.jl b/examples/unstructured_2d_dgsem/elixir_mhd_alfven_wave.jl index 6b31776b297..fdafed98c8d 100644 --- a/examples/unstructured_2d_dgsem/elixir_mhd_alfven_wave.jl +++ b/examples/unstructured_2d_dgsem/elixir_mhd_alfven_wave.jl @@ -5,22 +5,23 @@ using Trixi ############################################################################### # semidiscretization of the compressible ideal GLM-MHD equations -gamma = 5/3 +gamma = 5 / 3 equations = IdealGlmMhdEquations2D(gamma) initial_condition = initial_condition_convergence_test volume_flux = (flux_central, flux_nonconservative_powell) -solver = DGSEM(polydeg=7, surface_flux=(flux_hll, flux_nonconservative_powell), - volume_integral=VolumeIntegralFluxDifferencing(volume_flux)) +solver = DGSEM(polydeg = 7, surface_flux = (flux_hll, flux_nonconservative_powell), + volume_integral = VolumeIntegralFluxDifferencing(volume_flux)) # Get the unstructured quad mesh from a file (downloads the file if not available locally) default_mesh_file = joinpath(@__DIR__, "mesh_alfven_wave_with_twist_and_flip.mesh") -isfile(default_mesh_file) || download("https://gist.githubusercontent.com/andrewwinters5000/8f8cd23df27fcd494553f2a89f3c1ba4/raw/85e3c8d976bbe57ca3d559d653087b0889535295/mesh_alfven_wave_with_twist_and_flip.mesh", - default_mesh_file) +isfile(default_mesh_file) || + download("https://gist.githubusercontent.com/andrewwinters5000/8f8cd23df27fcd494553f2a89f3c1ba4/raw/85e3c8d976bbe57ca3d559d653087b0889535295/mesh_alfven_wave_with_twist_and_flip.mesh", + default_mesh_file) mesh_file = default_mesh_file -mesh = UnstructuredMesh2D(mesh_file, periodicity=true) +mesh = UnstructuredMesh2D(mesh_file, periodicity = true) semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver) @@ -33,21 +34,24 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval, save_analysis=false, - extra_analysis_integrals=(entropy, energy_total, - energy_kinetic, energy_internal, - energy_magnetic, cross_helicity)) - -alive_callback = AliveCallback(analysis_interval=analysis_interval) - -save_solution = SaveSolutionCallback(interval=100, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval, + save_analysis = false, + extra_analysis_integrals = (entropy, energy_total, + energy_kinetic, + energy_internal, + energy_magnetic, + cross_helicity)) + +alive_callback = AliveCallback(analysis_interval = analysis_interval) + +save_solution = SaveSolutionCallback(interval = 100, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) cfl = 0.9 -stepsize_callback = StepsizeCallback(cfl=cfl) +stepsize_callback = StepsizeCallback(cfl = cfl) -glm_speed_callback = GlmSpeedCallback(glm_scale=0.5, cfl=cfl) +glm_speed_callback = GlmSpeedCallback(glm_scale = 0.5, cfl = cfl) callbacks = CallbackSet(summary_callback, analysis_callback, @@ -56,11 +60,10 @@ callbacks = CallbackSet(summary_callback, stepsize_callback, glm_speed_callback) - ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/unstructured_2d_dgsem/elixir_mhd_ec.jl b/examples/unstructured_2d_dgsem/elixir_mhd_ec.jl index d75079bb8d7..a40f92cac02 100644 --- a/examples/unstructured_2d_dgsem/elixir_mhd_ec.jl +++ b/examples/unstructured_2d_dgsem/elixir_mhd_ec.jl @@ -6,40 +6,42 @@ using Trixi ############################################################################### # semidiscretization of the compressible ideal GLM-MHD equations -equations = IdealGlmMhdEquations2D(5/3) +equations = IdealGlmMhdEquations2D(5 / 3) function initial_condition_shifted_weak_blast_wave(x, t, equations::IdealGlmMhdEquations2D) - # Adapted MHD version of the weak blast wave from Hennemann & Gassner JCP paper 2020 (Sec. 6.3) - # Shift blastwave to center of domain - inicenter = (sqrt(2)/2, sqrt(2)/2) - x_norm = x[1] - inicenter[1] - y_norm = x[2] - inicenter[2] - r = sqrt(x_norm^2 + y_norm^2) - phi = atan(y_norm, x_norm) - - # Calculate primitive variables - rho = r > 0.5 ? 1.0 : 1.1691 - v1 = r > 0.5 ? 0.0 : 0.1882 * cos(phi) - v2 = r > 0.5 ? 0.0 : 0.1882 * sin(phi) - p = r > 0.5 ? 1.0 : 1.245 - - return prim2cons(SVector(rho, v1, v2, 0.0, p, 1.0, 1.0, 1.0, 0.0), equations) + # Adapted MHD version of the weak blast wave from Hennemann & Gassner JCP paper 2020 (Sec. 6.3) + # Shift blastwave to center of domain + inicenter = (sqrt(2) / 2, sqrt(2) / 2) + x_norm = x[1] - inicenter[1] + y_norm = x[2] - inicenter[2] + r = sqrt(x_norm^2 + y_norm^2) + phi = atan(y_norm, x_norm) + + # Calculate primitive variables + rho = r > 0.5 ? 1.0 : 1.1691 + v1 = r > 0.5 ? 0.0 : 0.1882 * cos(phi) + v2 = r > 0.5 ? 0.0 : 0.1882 * sin(phi) + p = r > 0.5 ? 1.0 : 1.245 + + return prim2cons(SVector(rho, v1, v2, 0.0, p, 1.0, 1.0, 1.0, 0.0), equations) end initial_condition = initial_condition_shifted_weak_blast_wave # Get the DG approximation space volume_flux = (flux_hindenlang_gassner, flux_nonconservative_powell) -solver = DGSEM(polydeg=6, surface_flux=(flux_hindenlang_gassner, flux_nonconservative_powell), - volume_integral=VolumeIntegralFluxDifferencing(volume_flux)) +solver = DGSEM(polydeg = 6, + surface_flux = (flux_hindenlang_gassner, flux_nonconservative_powell), + volume_integral = VolumeIntegralFluxDifferencing(volume_flux)) # Get the unstructured quad mesh from a file (downloads the file if not available locally) default_mesh_file = joinpath(@__DIR__, "mesh_alfven_wave_with_twist_and_flip.mesh") -isfile(default_mesh_file) || download("https://gist.githubusercontent.com/andrewwinters5000/8f8cd23df27fcd494553f2a89f3c1ba4/raw/85e3c8d976bbe57ca3d559d653087b0889535295/mesh_alfven_wave_with_twist_and_flip.mesh", - default_mesh_file) +isfile(default_mesh_file) || + download("https://gist.githubusercontent.com/andrewwinters5000/8f8cd23df27fcd494553f2a89f3c1ba4/raw/85e3c8d976bbe57ca3d559d653087b0889535295/mesh_alfven_wave_with_twist_and_flip.mesh", + default_mesh_file) mesh_file = default_mesh_file -mesh = UnstructuredMesh2D(mesh_file, periodicity=true) +mesh = UnstructuredMesh2D(mesh_file, periodicity = true) # create the semi discretization object semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver) @@ -53,21 +55,24 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval, save_analysis=false, - extra_analysis_integrals=(entropy, energy_total, - energy_kinetic, energy_internal, - energy_magnetic, cross_helicity)) - -alive_callback = AliveCallback(analysis_interval=analysis_interval) - -save_solution = SaveSolutionCallback(interval=100, - save_initial_solution=true, - save_final_solution=true, - solution_variables=cons2prim) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval, + save_analysis = false, + extra_analysis_integrals = (entropy, energy_total, + energy_kinetic, + energy_internal, + energy_magnetic, + cross_helicity)) + +alive_callback = AliveCallback(analysis_interval = analysis_interval) + +save_solution = SaveSolutionCallback(interval = 100, + save_initial_solution = true, + save_final_solution = true, + solution_variables = cons2prim) cfl = 1.0 -stepsize_callback = StepsizeCallback(cfl=cfl) +stepsize_callback = StepsizeCallback(cfl = cfl) -glm_speed_callback = GlmSpeedCallback(glm_scale=0.5, cfl=cfl) +glm_speed_callback = GlmSpeedCallback(glm_scale = 0.5, cfl = cfl) callbacks = CallbackSet(summary_callback, analysis_callback, @@ -79,7 +84,7 @@ callbacks = CallbackSet(summary_callback, ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/unstructured_2d_dgsem/elixir_shallowwater_dirichlet.jl b/examples/unstructured_2d_dgsem/elixir_shallowwater_dirichlet.jl index 044b2549b01..1148f25fae3 100644 --- a/examples/unstructured_2d_dgsem/elixir_shallowwater_dirichlet.jl +++ b/examples/unstructured_2d_dgsem/elixir_shallowwater_dirichlet.jl @@ -7,47 +7,48 @@ using Trixi # semidiscretization of the shallow water equations with a continuous # bottom topography function (set in the initial conditions) -equations = ShallowWaterEquations2D(gravity_constant=1.0, H0=3.0) +equations = ShallowWaterEquations2D(gravity_constant = 1.0, H0 = 3.0) # An initial condition with constant total water height and zero velocities to test well-balancedness. function initial_condition_well_balancedness(x, t, equations::ShallowWaterEquations2D) - # Set the background values - H = equations.H0 - v1 = 0.0 - v2 = 0.0 - # bottom topography taken from Pond.control in [HOHQMesh](https://github.com/trixi-framework/HOHQMesh) - x1, x2 = x - b = ( 1.5 / exp( 0.5 * ((x1 - 1.0)^2 + (x2 - 1.0)^2) ) - + 0.75 / exp( 0.5 * ((x1 + 1.0)^2 + (x2 + 1.0)^2) ) ) - return prim2cons(SVector(H, v1, v2, b), equations) + # Set the background values + H = equations.H0 + v1 = 0.0 + v2 = 0.0 + # bottom topography taken from Pond.control in [HOHQMesh](https://github.com/trixi-framework/HOHQMesh) + x1, x2 = x + b = (1.5 / exp(0.5 * ((x1 - 1.0)^2 + (x2 - 1.0)^2)) + + 0.75 / exp(0.5 * ((x1 + 1.0)^2 + (x2 + 1.0)^2))) + return prim2cons(SVector(H, v1, v2, b), equations) end initial_condition = initial_condition_well_balancedness boundary_condition_constant = BoundaryConditionDirichlet(initial_condition) -boundary_condition = Dict( :OuterCircle => boundary_condition_constant ) +boundary_condition = Dict(:OuterCircle => boundary_condition_constant) ############################################################################### # Get the DG approximation space volume_flux = (flux_wintermeyer_etal, flux_nonconservative_wintermeyer_etal) -solver = DGSEM(polydeg=4, surface_flux=(flux_hll, flux_nonconservative_fjordholm_etal), - volume_integral=VolumeIntegralFluxDifferencing(volume_flux)) +solver = DGSEM(polydeg = 4, surface_flux = (flux_hll, flux_nonconservative_fjordholm_etal), + volume_integral = VolumeIntegralFluxDifferencing(volume_flux)) ############################################################################### # This setup is for the curved, split form well-balancedness testing # Get the unstructured quad mesh from a file (downloads the file if not available locally) default_mesh_file = joinpath(@__DIR__, "mesh_outer_circle.mesh") -isfile(default_mesh_file) || download("https://gist.githubusercontent.com/andrewwinters5000/9beddd9cd00e2a0a15865129eeb24928/raw/be71e67fa48bc4e1e97f5f6cd77c3ed34c6ba9be/mesh_outer_circle.mesh", - default_mesh_file) +isfile(default_mesh_file) || + download("https://gist.githubusercontent.com/andrewwinters5000/9beddd9cd00e2a0a15865129eeb24928/raw/be71e67fa48bc4e1e97f5f6cd77c3ed34c6ba9be/mesh_outer_circle.mesh", + default_mesh_file) mesh_file = default_mesh_file mesh = UnstructuredMesh2D(mesh_file) # Create the semi discretization object semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver, - boundary_conditions=boundary_condition) + boundary_conditions = boundary_condition) ############################################################################### # ODE solvers, callbacks, etc. @@ -58,15 +59,15 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 1000 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval, - save_analysis=true, - extra_analysis_integrals=(lake_at_rest_error,)) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval, + save_analysis = true, + extra_analysis_integrals = (lake_at_rest_error,)) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=1000, - save_initial_solution=true, - save_final_solution=true) +save_solution = SaveSolutionCallback(interval = 1000, + save_initial_solution = true, + save_final_solution = true) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, save_solution) @@ -74,6 +75,6 @@ callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, sav # run the simulation # use a Runge-Kutta method with automatic (error based) time step size control -sol = solve(ode, RDPK3SpFSAL49(); abstol=1.0e-11, reltol=1.0e-11, - ode_default_options()..., callback=callbacks); +sol = solve(ode, RDPK3SpFSAL49(); abstol = 1.0e-11, reltol = 1.0e-11, + ode_default_options()..., callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/unstructured_2d_dgsem/elixir_shallowwater_ec.jl b/examples/unstructured_2d_dgsem/elixir_shallowwater_ec.jl index 138b256c08b..8e9d396d826 100644 --- a/examples/unstructured_2d_dgsem/elixir_shallowwater_ec.jl +++ b/examples/unstructured_2d_dgsem/elixir_shallowwater_ec.jl @@ -7,7 +7,7 @@ using Trixi # semidiscretization of the shallow water equations with a discontinuous # bottom topography function -equations = ShallowWaterEquations2D(gravity_constant=9.81) +equations = ShallowWaterEquations2D(gravity_constant = 9.81) # Note, this initial condition is used to compute errors in the analysis callback but the initialization is # overwritten by `initial_condition_ec_discontinuous_bottom` below. @@ -17,19 +17,21 @@ initial_condition = initial_condition_weak_blast_wave # Get the DG approximation space volume_flux = (flux_wintermeyer_etal, flux_nonconservative_wintermeyer_etal) -solver = DGSEM(polydeg=6, surface_flux=(flux_fjordholm_etal, flux_nonconservative_fjordholm_etal), - volume_integral=VolumeIntegralFluxDifferencing(volume_flux)) +solver = DGSEM(polydeg = 6, + surface_flux = (flux_fjordholm_etal, flux_nonconservative_fjordholm_etal), + volume_integral = VolumeIntegralFluxDifferencing(volume_flux)) ############################################################################### # This setup is for the curved, split form entropy conservation testing (needs periodic BCs) # Get the unstructured quad mesh from a file (downloads the file if not available locally) default_mesh_file = joinpath(@__DIR__, "mesh_alfven_wave_with_twist_and_flip.mesh") -isfile(default_mesh_file) || download("https://gist.githubusercontent.com/andrewwinters5000/8f8cd23df27fcd494553f2a89f3c1ba4/raw/85e3c8d976bbe57ca3d559d653087b0889535295/mesh_alfven_wave_with_twist_and_flip.mesh", - default_mesh_file) +isfile(default_mesh_file) || + download("https://gist.githubusercontent.com/andrewwinters5000/8f8cd23df27fcd494553f2a89f3c1ba4/raw/85e3c8d976bbe57ca3d559d653087b0889535295/mesh_alfven_wave_with_twist_and_flip.mesh", + default_mesh_file) mesh_file = default_mesh_file -mesh = UnstructuredMesh2D(mesh_file, periodicity=true) +mesh = UnstructuredMesh2D(mesh_file, periodicity = true) # Create the semi discretization object semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver) @@ -49,45 +51,48 @@ ode = semidiscretize(semi, tspan) # In contrast to the usual signature of initial conditions, this one get passed the # `element_id` explicitly. In particular, this initial conditions works as intended # only for the specific mesh loaded above! -function initial_condition_ec_discontinuous_bottom(x, t, element_id, equations::ShallowWaterEquations2D) - # Set up polar coordinates - inicenter = SVector(0.7, 0.7) - x_norm = x[1] - inicenter[1] - y_norm = x[2] - inicenter[2] - r = sqrt(x_norm^2 + y_norm^2) - phi = atan(y_norm, x_norm) - sin_phi, cos_phi = sincos(phi) - - # Set the background values - H = 3.25 - v1 = 0.0 - v2 = 0.0 - b = 0.0 - - # setup the discontinuous water height and velocities - if element_id == 10 - H = 4.0 - v1 = 0.1882 * cos_phi - v2 = 0.1882 * sin_phi - end - - # Setup a discontinuous bottom topography using the element id number - if element_id == 7 - b = 2.0 + 0.5 * sin(2.0 * pi * x[1]) + 0.5 * cos(2.0 * pi * x[2]) - end - - return prim2cons(SVector(H, v1, v2, b), equations) +function initial_condition_ec_discontinuous_bottom(x, t, element_id, + equations::ShallowWaterEquations2D) + # Set up polar coordinates + inicenter = SVector(0.7, 0.7) + x_norm = x[1] - inicenter[1] + y_norm = x[2] - inicenter[2] + r = sqrt(x_norm^2 + y_norm^2) + phi = atan(y_norm, x_norm) + sin_phi, cos_phi = sincos(phi) + + # Set the background values + H = 3.25 + v1 = 0.0 + v2 = 0.0 + b = 0.0 + + # setup the discontinuous water height and velocities + if element_id == 10 + H = 4.0 + v1 = 0.1882 * cos_phi + v2 = 0.1882 * sin_phi + end + + # Setup a discontinuous bottom topography using the element id number + if element_id == 7 + b = 2.0 + 0.5 * sin(2.0 * pi * x[1]) + 0.5 * cos(2.0 * pi * x[2]) + end + + return prim2cons(SVector(H, v1, v2, b), equations) end # point to the data we want to augment u = Trixi.wrap_array(ode.u0, semi) # reset the initial condition for element in eachelement(semi.solver, semi.cache) - for j in eachnode(semi.solver), i in eachnode(semi.solver) - x_node = Trixi.get_node_coords(semi.cache.elements.node_coordinates, equations, semi.solver, i, j, element) - u_node = initial_condition_ec_discontinuous_bottom(x_node, first(tspan), element, equations) - Trixi.set_node_vars!(u, u_node, equations, semi.solver, i, j, element) - end + for j in eachnode(semi.solver), i in eachnode(semi.solver) + x_node = Trixi.get_node_coords(semi.cache.elements.node_coordinates, equations, + semi.solver, i, j, element) + u_node = initial_condition_ec_discontinuous_bottom(x_node, first(tspan), element, + equations) + Trixi.set_node_vars!(u, u_node, equations, semi.solver, i, j, element) + end end ############################################################################### @@ -96,15 +101,15 @@ end summary_callback = SummaryCallback() analysis_interval = 1000 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=1000, - save_initial_solution=true, - save_final_solution=true) +save_solution = SaveSolutionCallback(interval = 1000, + save_initial_solution = true, + save_final_solution = true) -stepsize_callback = StepsizeCallback(cfl=3.0) +stepsize_callback = StepsizeCallback(cfl = 3.0) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, save_solution, stepsize_callback) @@ -112,7 +117,7 @@ callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, sav ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/unstructured_2d_dgsem/elixir_shallowwater_ec_shockcapturing.jl b/examples/unstructured_2d_dgsem/elixir_shallowwater_ec_shockcapturing.jl index ee3650f3bb5..94202b81df0 100644 --- a/examples/unstructured_2d_dgsem/elixir_shallowwater_ec_shockcapturing.jl +++ b/examples/unstructured_2d_dgsem/elixir_shallowwater_ec_shockcapturing.jl @@ -7,7 +7,7 @@ using Trixi # semidiscretization of the shallow water equations with a discontinuous # bottom topography function -equations = ShallowWaterEquations2D(gravity_constant=9.81) +equations = ShallowWaterEquations2D(gravity_constant = 9.81) # Note, this initial condition is used to compute errors in the analysis callback but the initialization is # overwritten by `initial_condition_ec_discontinuous_bottom` below. @@ -17,17 +17,17 @@ initial_condition = initial_condition_weak_blast_wave # Get the DG approximation space surface_flux = (flux_fjordholm_etal, flux_nonconservative_fjordholm_etal) -volume_flux = (flux_wintermeyer_etal, flux_nonconservative_wintermeyer_etal) +volume_flux = (flux_wintermeyer_etal, flux_nonconservative_wintermeyer_etal) polydeg = 6 basis = LobattoLegendreBasis(polydeg) indicator_sc = IndicatorHennemannGassner(equations, basis, - alpha_max=0.5, - alpha_min=0.001, - alpha_smooth=true, - variable=waterheight_pressure) + alpha_max = 0.5, + alpha_min = 0.001, + alpha_smooth = true, + variable = waterheight_pressure) volume_integral = VolumeIntegralShockCapturingHG(indicator_sc; - volume_flux_dg=volume_flux, - volume_flux_fv=surface_flux) + volume_flux_dg = volume_flux, + volume_flux_fv = surface_flux) solver = DGSEM(basis, surface_flux, volume_integral) ############################################################################### @@ -35,11 +35,12 @@ solver = DGSEM(basis, surface_flux, volume_integral) # Get the unstructured quad mesh from a file (downloads the file if not available locally) default_mesh_file = joinpath(@__DIR__, "mesh_alfven_wave_with_twist_and_flip.mesh") -isfile(default_mesh_file) || download("https://gist.githubusercontent.com/andrewwinters5000/8f8cd23df27fcd494553f2a89f3c1ba4/raw/85e3c8d976bbe57ca3d559d653087b0889535295/mesh_alfven_wave_with_twist_and_flip.mesh", - default_mesh_file) +isfile(default_mesh_file) || + download("https://gist.githubusercontent.com/andrewwinters5000/8f8cd23df27fcd494553f2a89f3c1ba4/raw/85e3c8d976bbe57ca3d559d653087b0889535295/mesh_alfven_wave_with_twist_and_flip.mesh", + default_mesh_file) mesh_file = default_mesh_file -mesh = UnstructuredMesh2D(mesh_file, periodicity=true) +mesh = UnstructuredMesh2D(mesh_file, periodicity = true) # Create the semi discretization object semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver) @@ -59,45 +60,48 @@ ode = semidiscretize(semi, tspan) # In contrast to the usual signature of initial conditions, this one get passed the # `element_id` explicitly. In particular, this initial conditions works as intended # only for the specific mesh loaded above! -function initial_condition_ec_discontinuous_bottom(x, t, element_id, equations::ShallowWaterEquations2D) - # Set up polar coordinates - inicenter = SVector(0.7, 0.7) - x_norm = x[1] - inicenter[1] - y_norm = x[2] - inicenter[2] - r = sqrt(x_norm^2 + y_norm^2) - phi = atan(y_norm, x_norm) - sin_phi, cos_phi = sincos(phi) - - # Set the background values - H = 3.25 - v1 = 0.0 - v2 = 0.0 - b = 0.0 - - # setup the discontinuous water height and velocities - if element_id == 10 - H = 4.0 - v1 = 0.1882 * cos_phi - v2 = 0.1882 * sin_phi - end - - # Setup a discontinuous bottom topography using the element id number - if element_id == 7 - b = 2.0 + 0.5 * sin(2.0 * pi * x[1]) + 0.5 * cos(2.0 * pi * x[2]) - end - - return prim2cons(SVector(H, v1, v2, b), equations) +function initial_condition_ec_discontinuous_bottom(x, t, element_id, + equations::ShallowWaterEquations2D) + # Set up polar coordinates + inicenter = SVector(0.7, 0.7) + x_norm = x[1] - inicenter[1] + y_norm = x[2] - inicenter[2] + r = sqrt(x_norm^2 + y_norm^2) + phi = atan(y_norm, x_norm) + sin_phi, cos_phi = sincos(phi) + + # Set the background values + H = 3.25 + v1 = 0.0 + v2 = 0.0 + b = 0.0 + + # setup the discontinuous water height and velocities + if element_id == 10 + H = 4.0 + v1 = 0.1882 * cos_phi + v2 = 0.1882 * sin_phi + end + + # Setup a discontinuous bottom topography using the element id number + if element_id == 7 + b = 2.0 + 0.5 * sin(2.0 * pi * x[1]) + 0.5 * cos(2.0 * pi * x[2]) + end + + return prim2cons(SVector(H, v1, v2, b), equations) end # point to the data we want to augment u = Trixi.wrap_array(ode.u0, semi) # reset the initial condition for element in eachelement(semi.solver, semi.cache) - for j in eachnode(semi.solver), i in eachnode(semi.solver) - x_node = Trixi.get_node_coords(semi.cache.elements.node_coordinates, equations, semi.solver, i, j, element) - u_node = initial_condition_ec_discontinuous_bottom(x_node, first(tspan), element, equations) - Trixi.set_node_vars!(u, u_node, equations, semi.solver, i, j, element) - end + for j in eachnode(semi.solver), i in eachnode(semi.solver) + x_node = Trixi.get_node_coords(semi.cache.elements.node_coordinates, equations, + semi.solver, i, j, element) + u_node = initial_condition_ec_discontinuous_bottom(x_node, first(tspan), element, + equations) + Trixi.set_node_vars!(u, u_node, equations, semi.solver, i, j, element) + end end ############################################################################### @@ -106,11 +110,11 @@ end summary_callback = SummaryCallback() analysis_interval = 1000 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -stepsize_callback = StepsizeCallback(cfl=3.0) +stepsize_callback = StepsizeCallback(cfl = 3.0) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, stepsize_callback) @@ -118,7 +122,7 @@ callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/unstructured_2d_dgsem/elixir_shallowwater_source_terms.jl b/examples/unstructured_2d_dgsem/elixir_shallowwater_source_terms.jl index e0b64802ff8..07668688406 100644 --- a/examples/unstructured_2d_dgsem/elixir_shallowwater_source_terms.jl +++ b/examples/unstructured_2d_dgsem/elixir_shallowwater_source_terms.jl @@ -7,7 +7,7 @@ using Trixi # semidiscretization of the shallow water equations with a periodic # bottom topography function (set in the initial conditions) -equations = ShallowWaterEquations2D(gravity_constant=9.81) +equations = ShallowWaterEquations2D(gravity_constant = 9.81) initial_condition = initial_condition_convergence_test @@ -16,23 +16,24 @@ initial_condition = initial_condition_convergence_test volume_flux = (flux_wintermeyer_etal, flux_nonconservative_wintermeyer_etal) surface_flux = (flux_fjordholm_etal, flux_nonconservative_fjordholm_etal) -solver = DGSEM(polydeg=6, surface_flux=surface_flux, - volume_integral=VolumeIntegralFluxDifferencing(volume_flux)) +solver = DGSEM(polydeg = 6, surface_flux = surface_flux, + volume_integral = VolumeIntegralFluxDifferencing(volume_flux)) ############################################################################### # This setup is for the curved, split form convergence test on a periodic domain # Get the unstructured quad mesh from a file (downloads the file if not available locally) default_mesh_file = joinpath(@__DIR__, "mesh_alfven_wave_with_twist_and_flip.mesh") -isfile(default_mesh_file) || download("https://gist.githubusercontent.com/andrewwinters5000/8f8cd23df27fcd494553f2a89f3c1ba4/raw/85e3c8d976bbe57ca3d559d653087b0889535295/mesh_alfven_wave_with_twist_and_flip.mesh", - default_mesh_file) +isfile(default_mesh_file) || + download("https://gist.githubusercontent.com/andrewwinters5000/8f8cd23df27fcd494553f2a89f3c1ba4/raw/85e3c8d976bbe57ca3d559d653087b0889535295/mesh_alfven_wave_with_twist_and_flip.mesh", + default_mesh_file) mesh_file = default_mesh_file -mesh = UnstructuredMesh2D(mesh_file, periodicity=true) +mesh = UnstructuredMesh2D(mesh_file, periodicity = true) # Create the semi discretization object semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver, - source_terms=source_terms_convergence_test) + source_terms = source_terms_convergence_test) ############################################################################### # ODE solvers, callbacks etc. @@ -43,15 +44,15 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=100, - save_initial_solution=true, - save_final_solution=true) +save_solution = SaveSolutionCallback(interval = 100, + save_initial_solution = true, + save_final_solution = true) -stepsize_callback = StepsizeCallback(cfl=1.0) +stepsize_callback = StepsizeCallback(cfl = 1.0) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, save_solution, stepsize_callback) @@ -59,7 +60,7 @@ callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, sav ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/unstructured_2d_dgsem/elixir_shallowwater_three_mound_dam_break.jl b/examples/unstructured_2d_dgsem/elixir_shallowwater_three_mound_dam_break.jl index 65b0fcae462..6164f9d4a55 100644 --- a/examples/unstructured_2d_dgsem/elixir_shallowwater_three_mound_dam_break.jl +++ b/examples/unstructured_2d_dgsem/elixir_shallowwater_three_mound_dam_break.jl @@ -8,10 +8,8 @@ using Trixi # # TODO: TrixiShallowWater: wet/dry example elixir - -equations = ShallowWaterEquations2D(gravity_constant=9.81, H0=1.875, - threshold_limiter=1e-12, threshold_wet=1e-14) - +equations = ShallowWaterEquations2D(gravity_constant = 9.81, H0 = 1.875, + threshold_limiter = 1e-12, threshold_wet = 1e-14) """ initial_condition_three_mounds(x, t, equations::ShallowWaterEquations2D) @@ -28,66 +26,68 @@ The initial conditions is taken from Section 6.3 of the paper: """ function initial_condition_three_mounds(x, t, equations::ShallowWaterEquations2D) - # Set the background values - v1 = 0.0 - v2 = 0.0 + # Set the background values + v1 = 0.0 + v2 = 0.0 - x1, x2 = x - M_1 = 1 - 0.1 * sqrt( (x1 - 30.0)^2 + (x2 - 22.5)^2 ) - M_2 = 1 - 0.1 * sqrt( (x1 - 30.0)^2 + (x2 - 7.5)^2 ) - M_3 = 2.8 - 0.28 * sqrt( (x1 - 47.5)^2 + (x2 - 15.0)^2 ) + x1, x2 = x + M_1 = 1 - 0.1 * sqrt((x1 - 30.0)^2 + (x2 - 22.5)^2) + M_2 = 1 - 0.1 * sqrt((x1 - 30.0)^2 + (x2 - 7.5)^2) + M_3 = 2.8 - 0.28 * sqrt((x1 - 47.5)^2 + (x2 - 15.0)^2) - b = max(0.0, M_1, M_2, M_3) + b = max(0.0, M_1, M_2, M_3) - # use a logistic function to transfer water height value smoothly - L = equations.H0 # maximum of function - x0 = 8 # center point of function - k = -75.0 # sharpness of transfer + # use a logistic function to transfer water height value smoothly + L = equations.H0 # maximum of function + x0 = 8 # center point of function + k = -75.0 # sharpness of transfer - H = max(b, L / (1.0 + exp(-k * (x1 - x0)))) + H = max(b, L / (1.0 + exp(-k * (x1 - x0)))) - # Avoid division by zero by adjusting the initial condition with a small dry state threshold - # that defaults to 500*eps() ≈ 1e-13 in double precision and is set in the constructor above - # for the ShallowWaterEquations struct. - H = max(H, b + equations.threshold_limiter) - return prim2cons(SVector(H, v1, v2, b), equations) + # Avoid division by zero by adjusting the initial condition with a small dry state threshold + # that defaults to 500*eps() ≈ 1e-13 in double precision and is set in the constructor above + # for the ShallowWaterEquations struct. + H = max(H, b + equations.threshold_limiter) + return prim2cons(SVector(H, v1, v2, b), equations) end initial_condition = initial_condition_three_mounds function boundary_condition_outflow(u_inner, normal_direction::AbstractVector, x, t, - surface_flux_function, equations::ShallowWaterEquations2D) - # Impulse and bottom from inside, height from external state - u_outer = SVector(equations.threshold_wet, u_inner[2], u_inner[3], u_inner[4]) + surface_flux_function, + equations::ShallowWaterEquations2D) + # Impulse and bottom from inside, height from external state + u_outer = SVector(equations.threshold_wet, u_inner[2], u_inner[3], u_inner[4]) - # calculate the boundary flux - flux = surface_flux_function(u_inner, u_outer, normal_direction, equations) + # calculate the boundary flux + flux = surface_flux_function(u_inner, u_outer, normal_direction, equations) - return flux + return flux end -boundary_conditions = Dict( :Bottom => boundary_condition_slip_wall, - :Top => boundary_condition_slip_wall, - :Right => boundary_condition_outflow, - :Left => boundary_condition_slip_wall ) +boundary_conditions = Dict(:Bottom => boundary_condition_slip_wall, + :Top => boundary_condition_slip_wall, + :Right => boundary_condition_outflow, + :Left => boundary_condition_slip_wall) ############################################################################### # Get the DG approximation space volume_flux = (flux_wintermeyer_etal, flux_nonconservative_wintermeyer_etal) -surface_flux = (FluxHydrostaticReconstruction(flux_hll_chen_noelle, hydrostatic_reconstruction_chen_noelle), +surface_flux = (FluxHydrostaticReconstruction(flux_hll_chen_noelle, + hydrostatic_reconstruction_chen_noelle), flux_nonconservative_chen_noelle) basis = LobattoLegendreBasis(4) indicator_sc = IndicatorHennemannGassnerShallowWater(equations, basis, - alpha_max=0.5, - alpha_min=0.001, - alpha_smooth=true, - variable=waterheight_pressure) + alpha_max = 0.5, + alpha_min = 0.001, + alpha_smooth = true, + variable = waterheight_pressure) volume_integral = VolumeIntegralShockCapturingHG(indicator_sc; - volume_flux_dg=volume_flux, - volume_flux_fv=surface_flux) + volume_flux_dg = volume_flux, + volume_flux_fv = surface_flux) solver = DGSEM(basis, surface_flux, volume_integral) @@ -96,8 +96,9 @@ solver = DGSEM(basis, surface_flux, volume_integral) default_meshfile = joinpath(@__DIR__, "mesh_three_mound.mesh") -isfile(default_meshfile) || download("https://gist.githubusercontent.com/svengoldberg/c3c87fecb3fc6e46be7f0d1c7cb35f83/raw/e817ecd9e6c4686581d63c46128f9b6468d396d3/mesh_three_mound.mesh", - default_meshfile) +isfile(default_meshfile) || + download("https://gist.githubusercontent.com/svengoldberg/c3c87fecb3fc6e46be7f0d1c7cb35f83/raw/e817ecd9e6c4686581d63c46128f9b6468d396d3/mesh_three_mound.mesh", + default_meshfile) meshfile = default_meshfile @@ -105,7 +106,7 @@ mesh = UnstructuredMesh2D(meshfile) # Create the semi discretization object semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver; - boundary_conditions=boundary_conditions) + boundary_conditions = boundary_conditions) ############################################################################### # ODE solver @@ -119,21 +120,21 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 1000 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=100, - save_initial_solution=true, - save_final_solution=true) +save_solution = SaveSolutionCallback(interval = 100, + save_initial_solution = true, + save_final_solution = true) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, save_solution) ############################################################################### # run the simulation -stage_limiter! = PositivityPreservingLimiterShallowWater(variables=(Trixi.waterheight,)) +stage_limiter! = PositivityPreservingLimiterShallowWater(variables = (Trixi.waterheight,)) sol = solve(ode, SSPRK43(stage_limiter!); - ode_default_options()..., callback=callbacks); + ode_default_options()..., callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/unstructured_2d_dgsem/elixir_shallowwater_twolayer_convergence.jl b/examples/unstructured_2d_dgsem/elixir_shallowwater_twolayer_convergence.jl index d9e71e4aa44..2cab68b1cb5 100644 --- a/examples/unstructured_2d_dgsem/elixir_shallowwater_twolayer_convergence.jl +++ b/examples/unstructured_2d_dgsem/elixir_shallowwater_twolayer_convergence.jl @@ -7,7 +7,8 @@ using Trixi # Semidiscretization of the two-layer shallow water equations with a periodic # bottom topography function (set in the initial conditions) -equations = ShallowWaterTwoLayerEquations2D(gravity_constant=10.0, rho_upper=0.9, rho_lower=1.0) +equations = ShallowWaterTwoLayerEquations2D(gravity_constant = 10.0, rho_upper = 0.9, + rho_lower = 1.0) initial_condition = initial_condition_convergence_test @@ -16,23 +17,24 @@ initial_condition = initial_condition_convergence_test volume_flux = (flux_wintermeyer_etal, flux_nonconservative_wintermeyer_etal) surface_flux = (flux_fjordholm_etal, flux_nonconservative_fjordholm_etal) -solver = DGSEM(polydeg=6, surface_flux=surface_flux, - volume_integral=VolumeIntegralFluxDifferencing(volume_flux)) +solver = DGSEM(polydeg = 6, surface_flux = surface_flux, + volume_integral = VolumeIntegralFluxDifferencing(volume_flux)) ############################################################################### # This setup is for the curved, split form convergence test on a periodic domain # Get the unstructured quad mesh from a file (downloads the file if not available locally) default_mesh_file = joinpath(@__DIR__, "mesh_alfven_wave_with_twist_and_flip.mesh") -isfile(default_mesh_file) || download("https://gist.githubusercontent.com/andrewwinters5000/8f8cd23df27fcd494553f2a89f3c1ba4/raw/85e3c8d976bbe57ca3d559d653087b0889535295/mesh_alfven_wave_with_twist_and_flip.mesh", - default_mesh_file) +isfile(default_mesh_file) || + download("https://gist.githubusercontent.com/andrewwinters5000/8f8cd23df27fcd494553f2a89f3c1ba4/raw/85e3c8d976bbe57ca3d559d653087b0889535295/mesh_alfven_wave_with_twist_and_flip.mesh", + default_mesh_file) mesh_file = default_mesh_file -mesh = UnstructuredMesh2D(mesh_file, periodicity=true) +mesh = UnstructuredMesh2D(mesh_file, periodicity = true) # Create the semidiscretization object semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver, - source_terms=source_terms_convergence_test) + source_terms = source_terms_convergence_test) ############################################################################### # ODE solvers, callbacks etc. @@ -43,15 +45,15 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 500 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=500, - save_initial_solution=true, - save_final_solution=true) +save_solution = SaveSolutionCallback(interval = 500, + save_initial_solution = true, + save_final_solution = true) -stepsize_callback = StepsizeCallback(cfl=1.0) +stepsize_callback = StepsizeCallback(cfl = 1.0) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, save_solution, stepsize_callback) @@ -59,7 +61,7 @@ callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, sav ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/unstructured_2d_dgsem/elixir_shallowwater_twolayer_dam_break.jl b/examples/unstructured_2d_dgsem/elixir_shallowwater_twolayer_dam_break.jl index 4295f93b342..9d70e9287cf 100644 --- a/examples/unstructured_2d_dgsem/elixir_shallowwater_twolayer_dam_break.jl +++ b/examples/unstructured_2d_dgsem/elixir_shallowwater_twolayer_dam_break.jl @@ -7,62 +7,64 @@ using Trixi # Semidiscretization of the two-layer shallow water equations for a dam break test with a # discontinuous bottom topography function to test energy conservation -equations = ShallowWaterTwoLayerEquations2D(gravity_constant=1.0, rho_upper=0.9, rho_lower=1.0) +equations = ShallowWaterTwoLayerEquations2D(gravity_constant = 1.0, rho_upper = 0.9, + rho_lower = 1.0) # This test case uses a special work around to setup a truly discontinuous bottom topography # function and initial condition for this academic testcase of entropy conservation. First, a # dummy initial_condition_dam_break is introduced to create the semidiscretization. Then the initial # condition is reset with the true discontinuous values from initial_condition_discontinuous_dam_break. -function initial_condition_dam_break(x, t,equations::ShallowWaterTwoLayerEquations2D) - if x[1] < sqrt(2)/2 - H_upper = 1.0 - H_lower = 0.6 - b = 0.1 - else - H_upper = 0.9 - H_lower = 0.5 - b = 0.0 - end - - v1_upper = 0.0 - v2_upper = 0.0 - v1_lower = 0.0 - v2_lower = 0.0 - return prim2cons(SVector(H_upper, v1_upper, v2_upper, H_lower, v1_lower, v2_lower, b), equations) +function initial_condition_dam_break(x, t, equations::ShallowWaterTwoLayerEquations2D) + if x[1] < sqrt(2) / 2 + H_upper = 1.0 + H_lower = 0.6 + b = 0.1 + else + H_upper = 0.9 + H_lower = 0.5 + b = 0.0 + end + + v1_upper = 0.0 + v2_upper = 0.0 + v1_lower = 0.0 + v2_lower = 0.0 + return prim2cons(SVector(H_upper, v1_upper, v2_upper, H_lower, v1_lower, v2_lower, b), + equations) end initial_condition = initial_condition_dam_break boundary_condition_constant = BoundaryConditionDirichlet(initial_condition_dam_break) - ############################################################################### # Get the DG approximation space volume_flux = (flux_wintermeyer_etal, flux_nonconservative_wintermeyer_etal) -surface_flux= (flux_fjordholm_etal, flux_nonconservative_fjordholm_etal) -solver = DGSEM(polydeg=6, surface_flux=surface_flux, - volume_integral=VolumeIntegralFluxDifferencing(volume_flux)) +surface_flux = (flux_fjordholm_etal, flux_nonconservative_fjordholm_etal) +solver = DGSEM(polydeg = 6, surface_flux = surface_flux, + volume_integral = VolumeIntegralFluxDifferencing(volume_flux)) ############################################################################### # Get the unstructured quad mesh from a file (downloads the file if not available locally) default_mesh_file = joinpath(@__DIR__, "mesh_alfven_wave_with_twist_and_flip.mesh") -isfile(default_mesh_file) || download("https://gist.githubusercontent.com/andrewwinters5000/8f8cd23df27fcd494553f2a89f3c1ba4/raw/85e3c8d976bbe57ca3d559d653087b0889535295/mesh_alfven_wave_with_twist_and_flip.mesh", - default_mesh_file) +isfile(default_mesh_file) || + download("https://gist.githubusercontent.com/andrewwinters5000/8f8cd23df27fcd494553f2a89f3c1ba4/raw/85e3c8d976bbe57ca3d559d653087b0889535295/mesh_alfven_wave_with_twist_and_flip.mesh", + default_mesh_file) mesh_file = default_mesh_file -mesh = UnstructuredMesh2D(mesh_file, periodicity=false) +mesh = UnstructuredMesh2D(mesh_file, periodicity = false) # Boundary conditions -boundary_condition = Dict(:Top => boundary_condition_slip_wall, - :Left => boundary_condition_slip_wall, - :Right => boundary_condition_slip_wall, +boundary_condition = Dict(:Top => boundary_condition_slip_wall, + :Left => boundary_condition_slip_wall, + :Right => boundary_condition_slip_wall, :Bottom => boundary_condition_slip_wall) # Create the semi discretization object -semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, - solver, boundary_conditions=boundary_condition) +semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, + solver, boundary_conditions = boundary_condition) ############################################################################### # ODE solver @@ -79,58 +81,63 @@ ode = semidiscretize(semi, tspan) # `element_id` explicitly. In particular, this initial conditions works as intended # only for the specific mesh loaded above! -function initial_condition_discontinuous_dam_break(x, t, element_id, +function initial_condition_discontinuous_dam_break(x, t, element_id, equations::ShallowWaterTwoLayerEquations2D) - # Constant values - v1_upper = 0.0 - v2_upper = 0.0 - v1_lower = 0.0 - v2_lower = 0.0 - - # Left side of discontinuity - IDs = [1, 2, 5, 6, 9, 10, 13, 14] - if element_id in IDs - H_upper = 1.0 - H_lower = 0.6 - b = 0.0 - # Right side of discontinuity - else - H_upper = 0.9 - H_lower = 0.5 - b = 0.1 - end - - return prim2cons(SVector(H_upper, v1_upper, v2_upper, H_lower, v1_lower, v2_lower, b), equations) + # Constant values + v1_upper = 0.0 + v2_upper = 0.0 + v1_lower = 0.0 + v2_lower = 0.0 + + # Left side of discontinuity + IDs = [1, 2, 5, 6, 9, 10, 13, 14] + if element_id in IDs + H_upper = 1.0 + H_lower = 0.6 + b = 0.0 + # Right side of discontinuity + else + H_upper = 0.9 + H_lower = 0.5 + b = 0.1 + end + + return prim2cons(SVector(H_upper, v1_upper, v2_upper, H_lower, v1_lower, v2_lower, b), + equations) end # point to the data we want to augment u = Trixi.wrap_array(ode.u0, semi) # reset the initial condition for element in eachelement(semi.solver, semi.cache) - for j in eachnode(semi.solver), i in eachnode(semi.solver) - x_node = Trixi.get_node_coords(semi.cache.elements.node_coordinates, equations, semi.solver, i, j, element) - u_node = initial_condition_discontinuous_dam_break(x_node, first(tspan), element, equations) - Trixi.set_node_vars!(u, u_node, equations, semi.solver, i, j, element) - end + for j in eachnode(semi.solver), i in eachnode(semi.solver) + x_node = Trixi.get_node_coords(semi.cache.elements.node_coordinates, equations, + semi.solver, i, j, element) + u_node = initial_condition_discontinuous_dam_break(x_node, first(tspan), element, + equations) + Trixi.set_node_vars!(u, u_node, equations, semi.solver, i, j, element) + end end - ############################################################################### # Callbacks summary_callback = SummaryCallback() analysis_interval = 500 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval,save_analysis=false, - extra_analysis_integrals=(energy_total, energy_kinetic, energy_internal,)) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval, + save_analysis = false, + extra_analysis_integrals = (energy_total, + energy_kinetic, + energy_internal)) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=500, - save_initial_solution=true, - save_final_solution=true) +save_solution = SaveSolutionCallback(interval = 500, + save_initial_solution = true, + save_final_solution = true) -stepsize_callback = StepsizeCallback(cfl=1.0) +stepsize_callback = StepsizeCallback(cfl = 1.0) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, save_solution, stepsize_callback) @@ -138,7 +145,7 @@ callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, sav ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/unstructured_2d_dgsem/elixir_shallowwater_twolayer_well_balanced.jl b/examples/unstructured_2d_dgsem/elixir_shallowwater_twolayer_well_balanced.jl index 40bc9f2ab42..35b027c3a81 100644 --- a/examples/unstructured_2d_dgsem/elixir_shallowwater_twolayer_well_balanced.jl +++ b/examples/unstructured_2d_dgsem/elixir_shallowwater_twolayer_well_balanced.jl @@ -7,22 +7,25 @@ using Trixi # Semidiscretization of the two-layer shallow water equations with a discontinuous bottom # topography to test well-balancedness -equations = ShallowWaterTwoLayerEquations2D(gravity_constant=1.0, H0=0.6, rho_upper=0.9, rho_lower=1.0) +equations = ShallowWaterTwoLayerEquations2D(gravity_constant = 1.0, H0 = 0.6, + rho_upper = 0.9, rho_lower = 1.0) # An initial condition with constant total water height, zero velocities and a bottom topography to # test well-balancedness function initial_condition_well_balanced(x, t, equations::ShallowWaterTwoLayerEquations2D) - H_lower = 0.5 - H_upper = 0.6 - v1_upper = 0.0 - v2_upper = 0.0 - v1_lower = 0.0 - v2_lower = 0.0 - - # Bottom Topography - b = (((x[1] - 0.5)^2 + (x[2] - 0.5)^2) < 0.04 ? 0.2 * (cos(4 * pi * sqrt((x[1] - 0.5)^2 + (x[2] + - -0.5)^2)) + 1) : 0.0) - return prim2cons(SVector(H_upper, v1_upper, v2_upper, H_lower, v1_lower, v2_lower, b), equations) + H_lower = 0.5 + H_upper = 0.6 + v1_upper = 0.0 + v2_upper = 0.0 + v1_lower = 0.0 + v2_lower = 0.0 + + # Bottom Topography + b = (((x[1] - 0.5)^2 + (x[2] - 0.5)^2) < 0.04 ? + 0.2 * (cos(4 * pi * sqrt((x[1] - 0.5)^2 + (x[2] + + -0.5)^2)) + 1) : 0.0) + return prim2cons(SVector(H_upper, v1_upper, v2_upper, H_lower, v1_lower, v2_lower, b), + equations) end initial_condition = initial_condition_well_balanced @@ -32,19 +35,20 @@ initial_condition = initial_condition_well_balanced volume_flux = (flux_wintermeyer_etal, flux_nonconservative_wintermeyer_etal) surface_flux = (flux_es_fjordholm_etal, flux_nonconservative_fjordholm_etal) -solver = DGSEM(polydeg=6, surface_flux=surface_flux, - volume_integral=VolumeIntegralFluxDifferencing(volume_flux)) +solver = DGSEM(polydeg = 6, surface_flux = surface_flux, + volume_integral = VolumeIntegralFluxDifferencing(volume_flux)) ############################################################################### # This setup is for the curved, split form well-balancedness testing # Get the unstructured quad mesh from a file (downloads the file if not available locally) default_mesh_file = joinpath(@__DIR__, "mesh_alfven_wave_with_twist_and_flip.mesh") -isfile(default_mesh_file) || download("https://gist.githubusercontent.com/andrewwinters5000/8f8cd23df27fcd494553f2a89f3c1ba4/raw/85e3c8d976bbe57ca3d559d653087b0889535295/mesh_alfven_wave_with_twist_and_flip.mesh", - default_mesh_file) +isfile(default_mesh_file) || + download("https://gist.githubusercontent.com/andrewwinters5000/8f8cd23df27fcd494553f2a89f3c1ba4/raw/85e3c8d976bbe57ca3d559d653087b0889535295/mesh_alfven_wave_with_twist_and_flip.mesh", + default_mesh_file) mesh_file = default_mesh_file -mesh = UnstructuredMesh2D(mesh_file, periodicity=true) +mesh = UnstructuredMesh2D(mesh_file, periodicity = true) # Create the semi discretization object semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver) @@ -58,16 +62,16 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 1000 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval, - extra_analysis_integrals=(lake_at_rest_error,)) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval, + extra_analysis_integrals = (lake_at_rest_error,)) -stepsize_callback = StepsizeCallback(cfl=1.0) +stepsize_callback = StepsizeCallback(cfl = 1.0) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=1000, - save_initial_solution=true, - save_final_solution=true) +save_solution = SaveSolutionCallback(interval = 1000, + save_initial_solution = true, + save_final_solution = true) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, save_solution, stepsize_callback) @@ -75,7 +79,7 @@ callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, sav ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/unstructured_2d_dgsem/elixir_shallowwater_wall_bc_shockcapturing.jl b/examples/unstructured_2d_dgsem/elixir_shallowwater_wall_bc_shockcapturing.jl index 4700724c520..76b9642d595 100644 --- a/examples/unstructured_2d_dgsem/elixir_shallowwater_wall_bc_shockcapturing.jl +++ b/examples/unstructured_2d_dgsem/elixir_shallowwater_wall_bc_shockcapturing.jl @@ -7,63 +7,66 @@ using Trixi # semidiscretization of the shallow water equations with a continuous # bottom topography function -equations = ShallowWaterEquations2D(gravity_constant=9.812, H0=2.0) +equations = ShallowWaterEquations2D(gravity_constant = 9.812, H0 = 2.0) function initial_condition_stone_throw(x, t, equations::ShallowWaterEquations2D) - # Set up polar coordinates - inicenter = SVector(0.15, 0.15) - x_norm = x[1] - inicenter[1] - y_norm = x[2] - inicenter[2] - r = sqrt(x_norm^2 + y_norm^2) - - # Calculate primitive variables - H = equations.H0 - v1 = r < 0.6 ? 2.0 : 0.0 - v2 = r < 0.6 ? -2.0 : 0.0 - # bottom topography taken from Pond.control in [HOHQMesh](https://github.com/trixi-framework/HOHQMesh) - x1, x2 = x - b = ( 1.5 / exp( 0.5 * ((x1 - 1.0)^2 + (x2 - 1.0)^2) ) - + 0.75 / exp( 0.5 * ((x1 + 1.0)^2 + (x2 + 1.0)^2) ) ) - - return prim2cons(SVector(H, v1, v2, b), equations) + # Set up polar coordinates + inicenter = SVector(0.15, 0.15) + x_norm = x[1] - inicenter[1] + y_norm = x[2] - inicenter[2] + r = sqrt(x_norm^2 + y_norm^2) + + # Calculate primitive variables + H = equations.H0 + v1 = r < 0.6 ? 2.0 : 0.0 + v2 = r < 0.6 ? -2.0 : 0.0 + # bottom topography taken from Pond.control in [HOHQMesh](https://github.com/trixi-framework/HOHQMesh) + x1, x2 = x + b = (1.5 / exp(0.5 * ((x1 - 1.0)^2 + (x2 - 1.0)^2)) + + 0.75 / exp(0.5 * ((x1 + 1.0)^2 + (x2 + 1.0)^2))) + + return prim2cons(SVector(H, v1, v2, b), equations) end initial_condition = initial_condition_stone_throw -boundary_condition = Dict( :OuterCircle => boundary_condition_slip_wall ) +boundary_condition = Dict(:OuterCircle => boundary_condition_slip_wall) ############################################################################### # Get the DG approximation space -surface_flux=(FluxHydrostaticReconstruction(flux_hll, hydrostatic_reconstruction_audusse_etal), - flux_nonconservative_audusse_etal) +surface_flux = (FluxHydrostaticReconstruction(flux_hll, + hydrostatic_reconstruction_audusse_etal), + flux_nonconservative_audusse_etal) volume_flux = (flux_wintermeyer_etal, flux_nonconservative_wintermeyer_etal) polydeg = 6 basis = LobattoLegendreBasis(polydeg) indicator_sc = IndicatorHennemannGassner(equations, basis, - alpha_max=0.5, - alpha_min=0.001, - alpha_smooth=true, - variable=Trixi.waterheight) + alpha_max = 0.5, + alpha_min = 0.001, + alpha_smooth = true, + variable = Trixi.waterheight) volume_integral = VolumeIntegralShockCapturingHG(indicator_sc; - volume_flux_dg=volume_flux, - volume_flux_fv=surface_flux) + volume_flux_dg = volume_flux, + volume_flux_fv = surface_flux) -solver = DGSEM(polydeg=polydeg, surface_flux=surface_flux, volume_integral=volume_integral) +solver = DGSEM(polydeg = polydeg, surface_flux = surface_flux, + volume_integral = volume_integral) ############################################################################### # Get the unstructured quad mesh from a file (downloads the file if not available locally) default_mesh_file = joinpath(@__DIR__, "mesh_outer_circle.mesh") -isfile(default_mesh_file) || download("https://gist.githubusercontent.com/andrewwinters5000/9beddd9cd00e2a0a15865129eeb24928/raw/be71e67fa48bc4e1e97f5f6cd77c3ed34c6ba9be/mesh_outer_circle.mesh", - default_mesh_file) +isfile(default_mesh_file) || + download("https://gist.githubusercontent.com/andrewwinters5000/9beddd9cd00e2a0a15865129eeb24928/raw/be71e67fa48bc4e1e97f5f6cd77c3ed34c6ba9be/mesh_outer_circle.mesh", + default_mesh_file) mesh_file = default_mesh_file mesh = UnstructuredMesh2D(mesh_file) # Create the semi discretization object semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver, - boundary_conditions=boundary_condition) + boundary_conditions = boundary_condition) ############################################################################### # ODE solvers, callbacks, etc. @@ -74,15 +77,16 @@ ode = semidiscretize(semi, tspan) summary_callback = SummaryCallback() analysis_interval = 100 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval, save_analysis=false, - extra_analysis_integrals=(energy_kinetic, - energy_internal)) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval, + save_analysis = false, + extra_analysis_integrals = (energy_kinetic, + energy_internal)) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=100, - save_initial_solution=true, - save_final_solution=true) +save_solution = SaveSolutionCallback(interval = 100, + save_initial_solution = true, + save_final_solution = true) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, save_solution) @@ -90,6 +94,6 @@ callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, sav # run the simulation # use a Runge-Kutta method with automatic (error based) time step size control -sol = solve(ode, RDPK3SpFSAL49(); abstol=1.0e-8, reltol=1.0e-8, - ode_default_options()..., callback=callbacks); +sol = solve(ode, RDPK3SpFSAL49(); abstol = 1.0e-8, reltol = 1.0e-8, + ode_default_options()..., callback = callbacks); summary_callback() # print the timer summary diff --git a/examples/unstructured_2d_dgsem/elixir_shallowwater_well_balanced.jl b/examples/unstructured_2d_dgsem/elixir_shallowwater_well_balanced.jl index 645f985d10d..bf4d0be682a 100644 --- a/examples/unstructured_2d_dgsem/elixir_shallowwater_well_balanced.jl +++ b/examples/unstructured_2d_dgsem/elixir_shallowwater_well_balanced.jl @@ -7,21 +7,21 @@ using Trixi # semidiscretization of the shallow water equations with a discontinuous # bottom topography function (set in the initial conditions) -equations = ShallowWaterEquations2D(gravity_constant=9.81, H0=3.0) +equations = ShallowWaterEquations2D(gravity_constant = 9.81, H0 = 3.0) # An initial condition with constant total water height and zero velocities to test well-balancedness. # Note, this routine is used to compute errors in the analysis callback but the initialization is # overwritten by `initial_condition_discontinuous_well_balancedness` below. function initial_condition_well_balancedness(x, t, equations::ShallowWaterEquations2D) - # Set the background values - H = equations.H0 - v1 = 0.0 - v2 = 0.0 - # bottom topography taken from Pond.control in [HOHQMesh](https://github.com/trixi-framework/HOHQMesh) - x1, x2 = x - b = ( 1.5 / exp( 0.5 * ((x1 - 1.0)^2 + (x2 - 1.0)^2) ) - + 0.75 / exp( 0.5 * ((x1 + 1.0)^2 + (x2 + 1.0)^2) ) ) - return prim2cons(SVector(H, v1, v2, b), equations) + # Set the background values + H = equations.H0 + v1 = 0.0 + v2 = 0.0 + # bottom topography taken from Pond.control in [HOHQMesh](https://github.com/trixi-framework/HOHQMesh) + x1, x2 = x + b = (1.5 / exp(0.5 * ((x1 - 1.0)^2 + (x2 - 1.0)^2)) + + 0.75 / exp(0.5 * ((x1 + 1.0)^2 + (x2 + 1.0)^2))) + return prim2cons(SVector(H, v1, v2, b), equations) end initial_condition = initial_condition_well_balancedness @@ -30,20 +30,21 @@ initial_condition = initial_condition_well_balancedness # Get the DG approximation space volume_flux = (flux_wintermeyer_etal, flux_nonconservative_wintermeyer_etal) -surface_flux=(flux_fjordholm_etal, flux_nonconservative_fjordholm_etal) -solver = DGSEM(polydeg=6, surface_flux=surface_flux, - volume_integral=VolumeIntegralFluxDifferencing(volume_flux)) +surface_flux = (flux_fjordholm_etal, flux_nonconservative_fjordholm_etal) +solver = DGSEM(polydeg = 6, surface_flux = surface_flux, + volume_integral = VolumeIntegralFluxDifferencing(volume_flux)) ############################################################################### # This setup is for the curved, split form well-balancedness testing # Get the unstructured quad mesh from a file (downloads the file if not available locally) default_mesh_file = joinpath(@__DIR__, "mesh_alfven_wave_with_twist_and_flip.mesh") -isfile(default_mesh_file) || download("https://gist.githubusercontent.com/andrewwinters5000/8f8cd23df27fcd494553f2a89f3c1ba4/raw/85e3c8d976bbe57ca3d559d653087b0889535295/mesh_alfven_wave_with_twist_and_flip.mesh", - default_mesh_file) +isfile(default_mesh_file) || + download("https://gist.githubusercontent.com/andrewwinters5000/8f8cd23df27fcd494553f2a89f3c1ba4/raw/85e3c8d976bbe57ca3d559d653087b0889535295/mesh_alfven_wave_with_twist_and_flip.mesh", + default_mesh_file) mesh_file = default_mesh_file -mesh = UnstructuredMesh2D(mesh_file, periodicity=true) +mesh = UnstructuredMesh2D(mesh_file, periodicity = true) # Create the semi discretization object semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver) @@ -64,30 +65,33 @@ ode = semidiscretize(semi, tspan) # In contrast to the usual signature of initial conditions, this one get passed the # `element_id` explicitly. In particular, this initial conditions works as intended # only for the specific mesh loaded above! -function initial_condition_discontinuous_well_balancedness(x, t, element_id, equations::ShallowWaterEquations2D) - # Set the background values - H = equations.H0 - v1 = 0.0 - v2 = 0.0 - b = 0.0 - - # Setup a discontinuous bottom topography using the element id number - if element_id == 7 - b = 2.0 + 0.5 * sin(2.0 * pi * x[1]) + 0.5 * cos(2.0 * pi * x[2]) - end - - return prim2cons(SVector(H, v1, v2, b), equations) +function initial_condition_discontinuous_well_balancedness(x, t, element_id, + equations::ShallowWaterEquations2D) + # Set the background values + H = equations.H0 + v1 = 0.0 + v2 = 0.0 + b = 0.0 + + # Setup a discontinuous bottom topography using the element id number + if element_id == 7 + b = 2.0 + 0.5 * sin(2.0 * pi * x[1]) + 0.5 * cos(2.0 * pi * x[2]) + end + + return prim2cons(SVector(H, v1, v2, b), equations) end # point to the data we want to augment u = Trixi.wrap_array(ode.u0, semi) # reset the initial condition for element in eachelement(semi.solver, semi.cache) - for j in eachnode(semi.solver), i in eachnode(semi.solver) - x_node = Trixi.get_node_coords(semi.cache.elements.node_coordinates, equations, semi.solver, i, j, element) - u_node = initial_condition_discontinuous_well_balancedness(x_node, first(tspan), element, equations) - Trixi.set_node_vars!(u, u_node, equations, semi.solver, i, j, element) - end + for j in eachnode(semi.solver), i in eachnode(semi.solver) + x_node = Trixi.get_node_coords(semi.cache.elements.node_coordinates, equations, + semi.solver, i, j, element) + u_node = initial_condition_discontinuous_well_balancedness(x_node, first(tspan), + element, equations) + Trixi.set_node_vars!(u, u_node, equations, semi.solver, i, j, element) + end end ############################################################################### @@ -96,16 +100,16 @@ end summary_callback = SummaryCallback() analysis_interval = 1000 -analysis_callback = AnalysisCallback(semi, interval=analysis_interval, - extra_analysis_integrals=(lake_at_rest_error,)) +analysis_callback = AnalysisCallback(semi, interval = analysis_interval, + extra_analysis_integrals = (lake_at_rest_error,)) -alive_callback = AliveCallback(analysis_interval=analysis_interval) +alive_callback = AliveCallback(analysis_interval = analysis_interval) -save_solution = SaveSolutionCallback(interval=1000, - save_initial_solution=true, - save_final_solution=true) +save_solution = SaveSolutionCallback(interval = 1000, + save_initial_solution = true, + save_final_solution = true) -stepsize_callback = StepsizeCallback(cfl=3.0) +stepsize_callback = StepsizeCallback(cfl = 3.0) callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, save_solution, stepsize_callback) @@ -113,7 +117,7 @@ callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, sav ############################################################################### # run the simulation -sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), - dt=1.0, # solve needs some value here but it will be overwritten by the stepsize_callback - save_everystep=false, callback=callbacks); +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); summary_callback() # print the timer summary diff --git a/src/callbacks_stage/subcell_bounds_check.jl b/src/callbacks_stage/subcell_bounds_check.jl index 0722e77d730..527bcb0750a 100644 --- a/src/callbacks_stage/subcell_bounds_check.jl +++ b/src/callbacks_stage/subcell_bounds_check.jl @@ -118,8 +118,6 @@ function init_callback(callback::BoundsCheckCallback, semi, limiter::SubcellLimi return nothing end - # TODO: Revise Bounds Check for MCL - @unpack output_directory = callback mkpath(output_directory) open("$output_directory/deviations.txt", "a") do f @@ -128,7 +126,7 @@ function init_callback(callback::BoundsCheckCallback, semi, limiter::SubcellLimi if limiter.PressurePositivityLimiterKuzmin print(f, ", pressure_min") end - # No check for entropy limiting rn + # TODO: Bounds check for entropy limiting println(f) end @@ -192,21 +190,23 @@ end @inline function finalize_callback(callback::BoundsCheckCallback, semi, limiter::SubcellLimiterMCL) - @unpack idp_bounds_delta = limiter.cache - - # TODO: Revise bounds check for MCL + @unpack mcl_bounds_delta = limiter.cache println("─"^100) println("Maximum deviation from bounds:") println("─"^100) variables = varnames(cons2cons, semi.equations) for v in eachvariable(semi.equations) - println(variables[v], ":\n- lower bound: ", idp_bounds_delta[1, v], - "\n- upper bound: ", idp_bounds_delta[2, v]) + println(variables[v], ":\n- lower bound: ", mcl_bounds_delta[2, 1, v], + "\n- upper bound: ", mcl_bounds_delta[2, 2, v]) end if limiter.PressurePositivityLimiterKuzmin - println("pressure:\n- lower bound: ", - idp_bounds_delta[1, nvariables(semi.equations) + 1]) + println("pressure:\n- positivity: ", + mcl_bounds_delta[2, 1, nvariables(semi.equations) + 1]) + end + if limiter.SemiDiscEntropyLimiter + # TODO: Bounds check for entropy limiting + println("\nWARNING: No bounds check for the entropy limiter.") end println("─"^100 * "\n") diff --git a/src/callbacks_stage/subcell_bounds_check_2d.jl b/src/callbacks_stage/subcell_bounds_check_2d.jl index 963f9a938ab..cf47c0fc534 100644 --- a/src/callbacks_stage/subcell_bounds_check_2d.jl +++ b/src/callbacks_stage/subcell_bounds_check_2d.jl @@ -131,24 +131,21 @@ end time, iter, output_directory, save_errors) (; var_min, var_max) = limiter.cache.subcell_limiter_coefficients (; bar_states1, bar_states2, lambda1, lambda2) = limiter.cache.container_bar_states - (; idp_bounds_delta) = limiter.cache + (; mcl_bounds_delta) = limiter.cache (; antidiffusive_flux1_L, antidiffusive_flux2_L) = cache.antidiffusive_fluxes - # TODO: Revise Bounds Check for MCL - n_vars = nvariables(equations) - deviation_min = zeros(eltype(u), n_vars + limiter.PressurePositivityLimiterKuzmin) - deviation_max = zeros(eltype(u), n_vars) - if limiter.DensityLimiter # New solution u^{n+1} for element in eachelement(solver, cache) for j in eachnode(solver), i in eachnode(solver) - deviation_min[1] = max(deviation_min[1], - var_min[1, i, j, element] - u[1, i, j, element]) - deviation_max[1] = max(deviation_max[1], - u[1, i, j, element] - var_max[1, i, j, element]) + mcl_bounds_delta[1, 1, 1] = max(mcl_bounds_delta[1, 1, 1], + var_min[1, i, j, element] - + u[1, i, j, element]) + mcl_bounds_delta[1, 2, 1] = max(mcl_bounds_delta[1, 2, 1], + u[1, i, j, element] - + var_max[1, i, j, element]) end end @@ -162,34 +159,34 @@ end rho_limited = bar_states1[1, i, j, element] - antidiffusive_flux1_L[1, i, j, element] / lambda1[i, j, element] - deviation_min[1] = max(deviation_min[1], - var_min[1, i, j, element] - rho_limited) - deviation_max[1] = max(deviation_max[1], - rho_limited - var_max[1, i, j, element]) + mcl_bounds_delta[1, 1, 1] = max(mcl_bounds_delta[1, 1, 1], + var_min[1, i, j, element] - rho_limited) + mcl_bounds_delta[1, 2, 1] = max(mcl_bounds_delta[1, 2, 1], + rho_limited - var_max[1, i, j, element]) # +x rho_limited = bar_states1[1, i + 1, j, element] + antidiffusive_flux1_L[1, i + 1, j, element] / lambda1[i + 1, j, element] - deviation_min[1] = max(deviation_min[1], - var_min[1, i, j, element] - rho_limited) - deviation_max[1] = max(deviation_max[1], - rho_limited - var_max[1, i, j, element]) + mcl_bounds_delta[1, 1, 1] = max(mcl_bounds_delta[1, 1, 1], + var_min[1, i, j, element] - rho_limited) + mcl_bounds_delta[1, 2, 1] = max(mcl_bounds_delta[1, 2, 1], + rho_limited - var_max[1, i, j, element]) # -y rho_limited = bar_states2[1, i, j, element] - antidiffusive_flux2_L[1, i, j, element] / lambda2[i, j, element] - deviation_min[1] = max(deviation_min[1], - var_min[1, i, j, element] - rho_limited) - deviation_max[1] = max(deviation_max[1], - rho_limited - var_max[1, i, j, element]) + mcl_bounds_delta[1, 1, 1] = max(mcl_bounds_delta[1, 1, 1], + var_min[1, i, j, element] - rho_limited) + mcl_bounds_delta[1, 2, 1] = max(mcl_bounds_delta[1, 2, 1], + rho_limited - var_max[1, i, j, element]) # +y rho_limited = bar_states2[1, i, j + 1, element] + antidiffusive_flux2_L[1, i, j + 1, element] / lambda2[i, j + 1, element] - deviation_min[1] = max(deviation_min[1], - var_min[1, i, j, element] - rho_limited) - deviation_max[1] = max(deviation_max[1], - rho_limited - var_max[1, i, j, element]) + mcl_bounds_delta[1, 1, 1] = max(mcl_bounds_delta[1, 1, 1], + var_min[1, i, j, element] - rho_limited) + mcl_bounds_delta[1, 2, 1] = max(mcl_bounds_delta[1, 2, 1], + rho_limited - var_max[1, i, j, element]) end end end # limiter.DensityLimiter @@ -200,17 +197,20 @@ end for j in eachnode(solver), i in eachnode(solver) for v in 2:n_vars var_limited = u[v, i, j, element] / u[1, i, j, element] - deviation_min[v] = max(deviation_min[v], - var_min[v, i, j, element] - var_limited) - deviation_max[v] = max(deviation_max[v], - var_limited - var_max[v, i, j, element]) + mcl_bounds_delta[1, 1, v] = max(mcl_bounds_delta[1, 1, v], + var_min[v, i, j, element] - + var_limited) + mcl_bounds_delta[1, 2, v] = max(mcl_bounds_delta[1, 2, v], + var_limited - + var_max[v, i, j, element]) end if limiter.PressurePositivityLimiterKuzmin error_pressure = 0.5 * (u[2, i, j, element]^2 + u[3, i, j, element]^2) - u[1, i, j, element] * u[4, i, j, element] - deviation_min[n_vars + 1] = max(deviation_min[n_vars + 1], - error_pressure) + mcl_bounds_delta[1, 1, n_vars + 1] = max(mcl_bounds_delta[1, 1, + n_vars + 1], + error_pressure) end end end @@ -221,8 +221,8 @@ end # \bar{phi}^{min} <= \bar{phi}^{Lim} / \bar{rho}^{Lim} <= \bar{phi}^{max} # - pressure (p): # \bar{rho}^{Lim} \bar{rho * E}^{Lim} >= |\bar{rho * v}^{Lim}|^2 / 2 - var_limited = zero(eltype(idp_bounds_delta)) - error_pressure = zero(eltype(idp_bounds_delta)) + var_limited = zero(eltype(mcl_bounds_delta)) + error_pressure = zero(eltype(mcl_bounds_delta)) for element in eachelement(solver, cache) for j in eachnode(solver), i in eachnode(solver) # -x @@ -233,21 +233,22 @@ end var_limited = bar_states1[v, i, j, element] - antidiffusive_flux1_L[v, i, j, element] / lambda1[i, j, element] - deviation_min[v] = max(deviation_min[v], - var_min[v, i, j, element] - - var_limited / rho_limited) - deviation_max[v] = max(deviation_max[v], - var_limited / rho_limited - - var_max[v, i, j, element]) + mcl_bounds_delta[1, 1, v] = max(mcl_bounds_delta[1, 1, v], + var_min[v, i, j, element] - + var_limited / rho_limited) + mcl_bounds_delta[1, 2, v] = max(mcl_bounds_delta[1, 2, v], + var_limited / rho_limited - + var_max[v, i, j, element]) if limiter.PressurePositivityLimiterKuzmin && (v == 2 || v == 3) error_pressure += 0.5 * var_limited^2 end end if limiter.PressurePositivityLimiterKuzmin error_pressure -= var_limited * rho_limited - deviation_min[n_vars + 1] = max(deviation_min[n_vars + 1], - error_pressure) - error_pressure = zero(eltype(idp_bounds_delta)) + mcl_bounds_delta[1, 1, n_vars + 1] = max(mcl_bounds_delta[1, 1, + n_vars + 1], + error_pressure) + error_pressure = zero(eltype(mcl_bounds_delta)) end # +x rho_limited = bar_states1[1, i + 1, j, element] + @@ -257,21 +258,22 @@ end var_limited = bar_states1[v, i + 1, j, element] + antidiffusive_flux1_L[v, i + 1, j, element] / lambda1[i + 1, j, element] - deviation_min[v] = max(deviation_min[v], - var_min[v, i, j, element] - - var_limited / rho_limited) - deviation_max[v] = max(deviation_max[v], - var_limited / rho_limited - - var_max[v, i, j, element]) + mcl_bounds_delta[1, 1, v] = max(mcl_bounds_delta[1, 1, v], + var_min[v, i, j, element] - + var_limited / rho_limited) + mcl_bounds_delta[1, 2, v] = max(mcl_bounds_delta[1, 2, v], + var_limited / rho_limited - + var_max[v, i, j, element]) if limiter.PressurePositivityLimiterKuzmin && (v == 2 || v == 3) error_pressure += 0.5 * var_limited^2 end end if limiter.PressurePositivityLimiterKuzmin error_pressure -= var_limited * rho_limited - deviation_min[n_vars + 1] = max(deviation_min[n_vars + 1], - error_pressure) - error_pressure = zero(eltype(idp_bounds_delta)) + mcl_bounds_delta[1, 1, n_vars + 1] = max(mcl_bounds_delta[1, 1, + n_vars + 1], + error_pressure) + error_pressure = zero(eltype(mcl_bounds_delta)) end # -y rho_limited = bar_states2[1, i, j, element] - @@ -281,21 +283,22 @@ end var_limited = bar_states2[v, i, j, element] - antidiffusive_flux2_L[v, i, j, element] / lambda2[i, j, element] - deviation_min[v] = max(deviation_min[v], - var_min[v, i, j, element] - - var_limited / rho_limited) - deviation_max[v] = max(deviation_max[v], - var_limited / rho_limited - - var_max[v, i, j, element]) + mcl_bounds_delta[1, 1, v] = max(mcl_bounds_delta[1, 1, v], + var_min[v, i, j, element] - + var_limited / rho_limited) + mcl_bounds_delta[1, 2, v] = max(mcl_bounds_delta[1, 2, v], + var_limited / rho_limited - + var_max[v, i, j, element]) if limiter.PressurePositivityLimiterKuzmin && (v == 2 || v == 3) error_pressure += 0.5 * var_limited^2 end end if limiter.PressurePositivityLimiterKuzmin error_pressure -= var_limited * rho_limited - deviation_min[n_vars + 1] = max(deviation_min[n_vars + 1], - error_pressure) - error_pressure = zero(eltype(idp_bounds_delta)) + mcl_bounds_delta[1, 1, n_vars + 1] = max(mcl_bounds_delta[1, 1, + n_vars + 1], + error_pressure) + error_pressure = zero(eltype(mcl_bounds_delta)) end # +y rho_limited = bar_states2[1, i, j + 1, element] + @@ -305,21 +308,22 @@ end var_limited = bar_states2[v, i, j + 1, element] + antidiffusive_flux2_L[v, i, j + 1, element] / lambda2[i, j + 1, element] - deviation_min[v] = max(deviation_min[v], - var_min[v, i, j, element] - - var_limited / rho_limited) - deviation_max[v] = max(deviation_max[v], - var_limited / rho_limited - - var_max[v, i, j, element]) + mcl_bounds_delta[1, 1, v] = max(mcl_bounds_delta[1, 1, v], + var_min[v, i, j, element] - + var_limited / rho_limited) + mcl_bounds_delta[1, 2, v] = max(mcl_bounds_delta[1, 2, v], + var_limited / rho_limited - + var_max[v, i, j, element]) if limiter.PressurePositivityLimiterKuzmin && (v == 2 || v == 3) error_pressure += 0.5 * var_limited^2 end end if limiter.PressurePositivityLimiterKuzmin error_pressure -= var_limited * rho_limited - deviation_min[n_vars + 1] = max(deviation_min[n_vars + 1], - error_pressure) - error_pressure = zero(eltype(idp_bounds_delta)) + mcl_bounds_delta[1, 1, n_vars + 1] = max(mcl_bounds_delta[1, 1, + n_vars + 1], + error_pressure) + error_pressure = zero(eltype(mcl_bounds_delta)) end end end @@ -328,19 +332,20 @@ end for element in eachelement(solver, cache) for j in eachnode(solver), i in eachnode(solver) for v in 2:n_vars - deviation_min[v] = max(deviation_min[v], - var_min[v, i, j, element] - - u[v, i, j, element]) - deviation_max[v] = max(deviation_max[v], - u[v, i, j, element] - - var_max[v, i, j, element]) + mcl_bounds_delta[1, 1, v] = max(mcl_bounds_delta[1, 1, v], + var_min[v, i, j, element] - + u[v, i, j, element]) + mcl_bounds_delta[1, 2, v] = max(mcl_bounds_delta[1, 2, v], + u[v, i, j, element] - + var_max[v, i, j, element]) end if limiter.PressurePositivityLimiterKuzmin error_pressure = 0.5 * (u[2, i, j, element]^2 + u[3, i, j, element]^2) - u[1, i, j, element] * u[4, i, j, element] - deviation_min[n_vars + 1] = max(deviation_min[n_vars + 1], - error_pressure) + mcl_bounds_delta[1, 1, n_vars + 1] = max(mcl_bounds_delta[1, 1, + n_vars + 1], + error_pressure) end end end @@ -351,8 +356,8 @@ end # \bar{rho*phi}^{min} <= \bar{rho*phi}^{Lim} <= \bar{rho*phi}^{max} # - pressure (p): # \bar{rho}^{Lim} \bar{rho * E}^{Lim} >= |\bar{rho * v}^{Lim}|^2 / 2 - var_limited = zero(eltype(idp_bounds_delta)) - error_pressure = zero(eltype(idp_bounds_delta)) + var_limited = zero(eltype(mcl_bounds_delta)) + error_pressure = zero(eltype(mcl_bounds_delta)) for element in eachelement(solver, cache) for j in eachnode(solver), i in eachnode(solver) # -x @@ -363,19 +368,22 @@ end var_limited = bar_states1[v, i, j, element] - antidiffusive_flux1_L[v, i, j, element] / lambda1[i, j, element] - deviation_min[v] = max(deviation_min[v], - var_min[v, i, j, element] - var_limited) - deviation_max[v] = max(deviation_max[v], - var_limited - var_max[v, i, j, element]) + mcl_bounds_delta[1, 1, v] = max(mcl_bounds_delta[1, 1, v], + var_min[v, i, j, element] - + var_limited) + mcl_bounds_delta[1, 2, v] = max(mcl_bounds_delta[1, 2, v], + var_limited - + var_max[v, i, j, element]) if limiter.PressurePositivityLimiterKuzmin && (v == 2 || v == 3) error_pressure += 0.5 * var_limited^2 end end if limiter.PressurePositivityLimiterKuzmin error_pressure -= var_limited * rho_limited - deviation_min[n_vars + 1] = max(deviation_min[n_vars + 1], - error_pressure) - error_pressure = zero(eltype(idp_bounds_delta)) + mcl_bounds_delta[1, 1, n_vars + 1] = max(mcl_bounds_delta[1, 1, + n_vars + 1], + error_pressure) + error_pressure = zero(eltype(mcl_bounds_delta)) end # +x rho_limited = bar_states1[1, i + 1, j, element] + @@ -385,19 +393,22 @@ end var_limited = bar_states1[v, i + 1, j, element] + antidiffusive_flux1_L[v, i + 1, j, element] / lambda1[i + 1, j, element] - deviation_min[v] = max(deviation_min[v], - var_min[v, i, j, element] - var_limited) - deviation_max[v] = max(deviation_max[v], - var_limited - var_max[v, i, j, element]) + mcl_bounds_delta[1, 1, v] = max(mcl_bounds_delta[1, 1, v], + var_min[v, i, j, element] - + var_limited) + mcl_bounds_delta[1, 2, v] = max(mcl_bounds_delta[1, 2, v], + var_limited - + var_max[v, i, j, element]) if limiter.PressurePositivityLimiterKuzmin && (v == 2 || v == 3) error_pressure += 0.5 * var_limited^2 end end if limiter.PressurePositivityLimiterKuzmin error_pressure -= var_limited * rho_limited - deviation_min[n_vars + 1] = max(deviation_min[n_vars + 1], - error_pressure) - error_pressure = zero(eltype(idp_bounds_delta)) + mcl_bounds_delta[1, 1, n_vars + 1] = max(mcl_bounds_delta[1, 1, + n_vars + 1], + error_pressure) + error_pressure = zero(eltype(mcl_bounds_delta)) end # -y rho_limited = bar_states2[1, i, j, element] - @@ -407,19 +418,22 @@ end var_limited = bar_states2[v, i, j, element] - antidiffusive_flux2_L[v, i, j, element] / lambda2[i, j, element] - deviation_min[v] = max(deviation_min[v], - var_min[v, i, j, element] - var_limited) - deviation_max[v] = max(deviation_max[v], - var_limited - var_max[v, i, j, element]) + mcl_bounds_delta[1, 1, v] = max(mcl_bounds_delta[1, 1, v], + var_min[v, i, j, element] - + var_limited) + mcl_bounds_delta[1, 2, v] = max(mcl_bounds_delta[1, 2, v], + var_limited - + var_max[v, i, j, element]) if limiter.PressurePositivityLimiterKuzmin && (v == 2 || v == 3) error_pressure += 0.5 * var_limited^2 end end if limiter.PressurePositivityLimiterKuzmin error_pressure -= var_limited * rho_limited - deviation_min[n_vars + 1] = max(deviation_min[n_vars + 1], - error_pressure) - error_pressure = zero(eltype(idp_bounds_delta)) + mcl_bounds_delta[1, 1, n_vars + 1] = max(mcl_bounds_delta[1, 1, + n_vars + 1], + error_pressure) + error_pressure = zero(eltype(mcl_bounds_delta)) end # +y rho_limited = bar_states2[1, i, j + 1, element] + @@ -429,19 +443,22 @@ end var_limited = bar_states2[v, i, j + 1, element] + antidiffusive_flux2_L[v, i, j + 1, element] / lambda2[i, j + 1, element] - deviation_min[v] = max(deviation_min[v], - var_min[v, i, j, element] - var_limited) - deviation_max[v] = max(deviation_max[v], - var_limited - var_max[v, i, j, element]) + mcl_bounds_delta[1, 1, v] = max(mcl_bounds_delta[1, 1, v], + var_min[v, i, j, element] - + var_limited) + mcl_bounds_delta[1, 2, v] = max(mcl_bounds_delta[1, 2, v], + var_limited - + var_max[v, i, j, element]) if limiter.PressurePositivityLimiterKuzmin && (v == 2 || v == 3) error_pressure += 0.5 * var_limited^2 end end if limiter.PressurePositivityLimiterKuzmin error_pressure -= var_limited * rho_limited - deviation_min[n_vars + 1] = max(deviation_min[n_vars + 1], - error_pressure) - error_pressure = zero(eltype(idp_bounds_delta)) + mcl_bounds_delta[1, 1, n_vars + 1] = max(mcl_bounds_delta[1, 1, + n_vars + 1], + error_pressure) + error_pressure = zero(eltype(mcl_bounds_delta)) end end end @@ -451,8 +468,9 @@ end for j in eachnode(solver), i in eachnode(solver) error_pressure = 0.5 * (u[2, i, j, element]^2 + u[3, i, j, element]^2) - u[1, i, j, element] * u[4, i, j, element] - deviation_min[n_vars + 1] = max(deviation_min[n_vars + 1], - error_pressure) + mcl_bounds_delta[1, 1, n_vars + 1] = max(mcl_bounds_delta[1, 1, + n_vars + 1], + error_pressure) end end @@ -477,8 +495,9 @@ end (bar_states1[4, i, j, element] - antidiffusive_flux1_L[4, i, j, element] / lambda1[i, j, element]) * rho_limited - deviation_min[n_vars + 1] = max(deviation_min[n_vars + 1], - error_pressure) + mcl_bounds_delta[1, 1, n_vars + 1] = max(mcl_bounds_delta[1, 1, + n_vars + 1], + error_pressure) # +x rho_limited = bar_states1[1, i + 1, j, element] + antidiffusive_flux1_L[1, i + 1, j, element] / @@ -494,8 +513,9 @@ end (bar_states1[4, i + 1, j, element] + antidiffusive_flux1_L[4, i + 1, j, element] / lambda1[i + 1, j, element]) * rho_limited - deviation_min[n_vars + 1] = max(deviation_min[n_vars + 1], - error_pressure) + mcl_bounds_delta[1, 1, n_vars + 1] = max(mcl_bounds_delta[1, 1, + n_vars + 1], + error_pressure) # -y rho_limited = bar_states2[1, i, j, element] - antidiffusive_flux2_L[1, i, j, element] / @@ -511,8 +531,9 @@ end (bar_states2[4, i, j, element] - antidiffusive_flux2_L[4, i, j, element] / lambda2[i, j, element]) * rho_limited - deviation_min[n_vars + 1] = max(deviation_min[n_vars + 1], - error_pressure) + mcl_bounds_delta[1, 1, n_vars + 1] = max(mcl_bounds_delta[1, 1, + n_vars + 1], + error_pressure) # +y rho_limited = bar_states2[1, i, j + 1, element] + antidiffusive_flux2_L[1, i, j + 1, element] / @@ -528,8 +549,9 @@ end (bar_states2[4, i, j + 1, element] + antidiffusive_flux2_L[4, i, j + 1, element] / lambda2[i, j + 1, element]) * rho_limited - deviation_min[n_vars + 1] = max(deviation_min[n_vars + 1], - error_pressure) + mcl_bounds_delta[1, 1, n_vars + 1] = max(mcl_bounds_delta[1, 1, + n_vars + 1], + error_pressure) end end end # limiter.PressurePositivityLimiterKuzmin @@ -538,7 +560,8 @@ end # New solution u^{n+1} for element in eachelement(solver, cache) for j in eachnode(solver), i in eachnode(solver) - deviation_min[1] = max(deviation_min[1], -u[1, i, j, element]) + mcl_bounds_delta[1, 1, 1] = max(mcl_bounds_delta[1, 1, 1], + -u[1, i, j, element]) end end @@ -553,33 +576,35 @@ end rho_limited = (1 - beta) * bar_states1[1, i, j, element] - antidiffusive_flux1_L[1, i, j, element] / lambda1[i, j, element] - deviation_min[1] = max(deviation_min[1], -rho_limited) + mcl_bounds_delta[1, 1, 1] = max(mcl_bounds_delta[1, 1, 1], -rho_limited) # +x rho_limited = (1 - beta) * bar_states1[1, i + 1, j, element] + antidiffusive_flux1_L[1, i + 1, j, element] / lambda1[i + 1, j, element] - deviation_min[1] = max(deviation_min[1], -rho_limited) + mcl_bounds_delta[1, 1, 1] = max(mcl_bounds_delta[1, 1, 1], -rho_limited) # -y rho_limited = (1 - beta) * bar_states2[1, i, j, element] - antidiffusive_flux2_L[1, i, j, element] / lambda2[i, j, element] - deviation_min[1] = max(deviation_min[1], -rho_limited) + mcl_bounds_delta[1, 1, 1] = max(mcl_bounds_delta[1, 1, 1], -rho_limited) # +y rho_limited = (1 - beta) * bar_states2[1, i, j + 1, element] + antidiffusive_flux2_L[1, i, j + 1, element] / lambda2[i, j + 1, element] - deviation_min[1] = max(deviation_min[1], -rho_limited) + mcl_bounds_delta[1, 1, 1] = max(mcl_bounds_delta[1, 1, 1], -rho_limited) end end end # limiter.DensityPositivityLimiter for v in eachvariable(equations) - idp_bounds_delta[1, v] = max(idp_bounds_delta[1, v], deviation_min[v]) - idp_bounds_delta[2, v] = max(idp_bounds_delta[2, v], deviation_max[v]) + mcl_bounds_delta[2, 1, v] = max(mcl_bounds_delta[2, 1, v], + mcl_bounds_delta[1, 1, v]) + mcl_bounds_delta[2, 2, v] = max(mcl_bounds_delta[2, 2, v], + mcl_bounds_delta[1, 2, v]) end if limiter.PressurePositivityLimiterKuzmin - idp_bounds_delta[1, n_vars + 1] = max(idp_bounds_delta[1, n_vars + 1], - deviation_min[n_vars + 1]) + mcl_bounds_delta[2, 1, n_vars + 1] = max(mcl_bounds_delta[2, 1, n_vars + 1], + mcl_bounds_delta[1, 1, n_vars + 1]) end if !save_errors @@ -588,13 +613,20 @@ end open("$output_directory/deviations.txt", "a") do f print(f, iter, ", ", time) for v in eachvariable(equations) - print(f, ", ", deviation_min[v], ", ", deviation_max[v]) + print(f, ", ", mcl_bounds_delta[1, 1, v], ", ", mcl_bounds_delta[1, 2, v]) end if limiter.PressurePositivityLimiterKuzmin - print(f, ", ", deviation_min[n_vars + 1]) + print(f, ", ", mcl_bounds_delta[1, 1, n_vars + 1]) end println(f) end + for v in eachvariable(equations) + mcl_bounds_delta[1, 1, v] = zero(eltype(mcl_bounds_delta)) + mcl_bounds_delta[1, 2, v] = zero(eltype(mcl_bounds_delta)) + end + if limiter.PressurePositivityLimiterKuzmin + mcl_bounds_delta[1, 1, n_vars + 1] = zero(eltype(mcl_bounds_delta)) + end return nothing end diff --git a/src/solvers/dgsem_tree/subcell_limiters_2d.jl b/src/solvers/dgsem_tree/subcell_limiters_2d.jl index 1c27a5d5dcd..c724ada5041 100644 --- a/src/solvers/dgsem_tree/subcell_limiters_2d.jl +++ b/src/solvers/dgsem_tree/subcell_limiters_2d.jl @@ -725,9 +725,11 @@ function create_cache(limiter::Type{SubcellLimiterMCL}, equations::AbstractEquat nvariables(equations), nnodes(basis)) - idp_bounds_delta = zeros(real(basis), 2, + # Memory for bounds checking routine with `BoundsCheckCallback`. + # [maximum since the last export / total maximum, min / max, variable] + mcl_bounds_delta = zeros(real(basis), 2, 2, nvariables(equations) + PressurePositivityLimiterKuzmin) - return (; subcell_limiter_coefficients, container_bar_states, idp_bounds_delta) + return (; subcell_limiter_coefficients, container_bar_states, mcl_bounds_delta) end end # @muladd diff --git a/test/test_tree_2d_euler.jl b/test/test_tree_2d_euler.jl index 9944e45e120..77df1ba45bf 100644 --- a/test/test_tree_2d_euler.jl +++ b/test/test_tree_2d_euler.jl @@ -525,6 +525,32 @@ end end end +@trixi_testset "elixir_euler_sedov_blast_wave.jl (HLLE)" begin + @test_trixi_include(joinpath(EXAMPLES_DIR, "elixir_euler_sedov_blast_wave.jl"), + l2=[ + 0.35267161504176747, + 0.17218309138797958, + 0.17218307467125854, + 0.6236143054619037, + ], + linf=[ + 2.77484045816607, + 1.8281111268370718, + 1.8281110470490887, + 6.24263735888126, + ], + tspan=(0.0, 0.5), + surface_flux=flux_hlle) + # Ensure that we do not have excessive memory allocations + # (e.g., from type instabilities) + let + t = sol.t[end] + u_ode = sol.u[end] + du_ode = similar(u_ode) + @test (@allocated Trixi.rhs!(du_ode, u_ode, semi, t)) < 1000 + end +end + @trixi_testset "elixir_euler_sedov_blast_wave_sc_subcell.jl" begin @test_trixi_include(joinpath(EXAMPLES_DIR, "elixir_euler_sedov_blast_wave_sc_subcell.jl"), @@ -554,6 +580,7 @@ end end @trixi_testset "elixir_euler_sedov_blast_wave_MCL.jl" begin + rm("out/deviations.txt", force = true) @test_trixi_include(joinpath(EXAMPLES_DIR, "elixir_euler_sedov_blast_wave_MCL.jl"), l2=[ 0.4740321851943766, @@ -570,6 +597,10 @@ end tspan=(0.0, 1.0), initial_refinement_level=4, coverage_override=(maxiters = 6,)) + lines = readlines("out/deviations.txt") + @test lines[1] == + "# iter, simu_time, rho_min, rho_max, rho_v1_min, rho_v1_max, rho_v2_min, rho_v2_max, rho_e_min, rho_e_max, pressure_min" + @test startswith(lines[end], "349") || startswith(lines[end], "1") # Ensure that we do not have excessive memory allocations # (e.g., from type instabilities) let