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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -1,7 +1,7 @@ | ||
| name = "Trixi" | ||
| uuid = "a7f1ee26-1774-49b1-8366-f1abc58fbfcb" | ||
| authors = ["Michael Schlottke-Lakemper <[email protected]>", "Gregor Gassner <[email protected]>", "Hendrik Ranocha <[email protected]>", "Andrew R. Winters <[email protected]>", "Jesse Chan <[email protected]>"] | ||
| version = "0.6.2-pre" | ||
| version = "0.6.3-pre" | ||
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| [deps] | ||
| CodeTracking = "da1fd8a2-8d9e-5ec2-8556-3022fb5608a2" | ||
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@@ -66,7 +66,7 @@ Makie = "0.19" | |
| MuladdMacro = "0.2.2" | ||
| Octavian = "0.3.5" | ||
| OffsetArrays = "1.3" | ||
| P4est = "0.4" | ||
| P4est = "0.4.9" | ||
| Polyester = "0.7.5" | ||
| PrecompileTools = "1.1" | ||
| Printf = "1" | ||
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@@ -84,7 +84,7 @@ StaticArrays = "1" | |
| StrideArrays = "0.1.18" | ||
| StructArrays = "0.6" | ||
| SummationByPartsOperators = "0.5.41" | ||
| T8code = "0.4.1" | ||
| T8code = "0.4.3" | ||
| TimerOutputs = "0.5" | ||
| Triangulate = "2.0" | ||
| TriplotBase = "0.1" | ||
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98 changes: 98 additions & 0 deletions
98
examples/p4est_2d_dgsem/elixir_advection_diffusion_nonperiodic_amr.jl
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,98 @@ | ||
| using OrdinaryDiffEq | ||
| using Trixi | ||
|
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| ############################################################################### | ||
| # semidiscretization of the linear advection-diffusion equation | ||
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| diffusivity() = 5.0e-2 | ||
| advection_velocity = (1.0, 0.0) | ||
| equations = LinearScalarAdvectionEquation2D(advection_velocity) | ||
| equations_parabolic = LaplaceDiffusion2D(diffusivity(), equations) | ||
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| # 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) | ||
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| coordinates_min = (-1.0, -0.5) # minimum coordinates (min(x), min(y)) | ||
| coordinates_max = (0.0, 0.5) # maximum coordinates (max(x), max(y)) | ||
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| 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) | ||
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| # Example setup taken from | ||
| # - Truman Ellis, Jesse Chan, and Leszek Demkowicz (2016). | ||
| # Robust DPG methods for transient convection-diffusion. | ||
| # In: Building bridges: connections and challenges in modern approaches | ||
| # 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) | ||
| end | ||
| initial_condition = initial_condition_eriksson_johnson | ||
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| boundary_conditions = Dict(:x_neg => BoundaryConditionDirichlet(initial_condition), | ||
| :y_neg => BoundaryConditionDirichlet(initial_condition), | ||
| :y_pos => BoundaryConditionDirichlet(initial_condition), | ||
| :x_pos => boundary_condition_do_nothing) | ||
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| boundary_conditions_parabolic = Dict(:x_neg => BoundaryConditionDirichlet(initial_condition), | ||
| :x_pos => BoundaryConditionDirichlet(initial_condition), | ||
| :y_neg => BoundaryConditionDirichlet(initial_condition), | ||
| :y_pos => BoundaryConditionDirichlet(initial_condition)) | ||
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| # 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)) | ||
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| ############################################################################### | ||
| # ODE solvers, callbacks etc. | ||
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| # Create ODE problem with time span `tspan` | ||
| tspan = (0.0, 0.5) | ||
| ode = semidiscretize(semi, tspan) | ||
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| # At the beginning of the main loop, the SummaryCallback prints a summary of the simulation setup | ||
| # and resets the timers | ||
| summary_callback = SummaryCallback() | ||
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| # The AnalysisCallback allows to analyse the solution in regular intervals and prints the results | ||
| analysis_interval = 1000 | ||
| analysis_callback = AnalysisCallback(semi, interval = analysis_interval) | ||
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| # The AliveCallback prints short status information in regular intervals | ||
| alive_callback = AliveCallback(analysis_interval = analysis_interval) | ||
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| amr_controller = ControllerThreeLevel(semi, IndicatorMax(semi, variable = first), | ||
| base_level = 1, | ||
| med_level = 2, med_threshold = 0.9, | ||
| max_level = 3, max_threshold = 1.0) | ||
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| amr_callback = AMRCallback(semi, amr_controller, | ||
| interval = 50) | ||
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| # 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) | ||
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| ############################################################################### | ||
| # run the simulation | ||
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| # OrdinaryDiffEq's `solve` method evolves the solution in time and executes the passed callbacks | ||
| time_int_tol = 1.0e-11 | ||
| sol = solve(ode, dt = 1e-7, RDPK3SpFSAL49(); abstol = time_int_tol, reltol = time_int_tol, | ||
| ode_default_options()..., callback = callbacks) | ||
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| # Print the timer summary | ||
| summary_callback() |
83 changes: 83 additions & 0 deletions
83
examples/p4est_2d_dgsem/elixir_advection_diffusion_periodic_amr.jl
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,83 @@ | ||
| using OrdinaryDiffEq | ||
| using Trixi | ||
|
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| ############################################################################### | ||
| # semidiscretization of the linear advection-diffusion equation | ||
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| advection_velocity = (1.5, 1.0) | ||
| equations = LinearScalarAdvectionEquation2D(advection_velocity) | ||
| diffusivity() = 5.0e-2 | ||
| equations_parabolic = LaplaceDiffusion2D(diffusivity(), equations) | ||
|
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||
| # 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) | ||
|
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| coordinates_min = (-1.0, -1.0) # minimum coordinates (min(x), min(y)) | ||
| coordinates_max = (1.0, 1.0) # maximum coordinates (max(x), max(y)) | ||
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| trees_per_dimension = (4, 4) | ||
| mesh = P4estMesh(trees_per_dimension, | ||
| polydeg = 3, initial_refinement_level = 1, | ||
| coordinates_min = coordinates_min, coordinates_max = coordinates_max) | ||
|
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| # 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 | ||
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| 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 | ||
|
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| # A semidiscretization collects data structures and functions for the spatial discretization | ||
| semi = SemidiscretizationHyperbolicParabolic(mesh, | ||
| (equations, equations_parabolic), | ||
| initial_condition, solver) | ||
|
|
||
| ############################################################################### | ||
| # ODE solvers, callbacks etc. | ||
|
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||
| # Create ODE problem with time span `tspan` | ||
| tspan = (0.0, 0.5) | ||
| ode = semidiscretize(semi, tspan); | ||
|
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| # At the beginning of the main loop, the SummaryCallback prints a summary of the simulation setup | ||
| # and resets the timers | ||
| summary_callback = SummaryCallback() | ||
|
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| # The AnalysisCallback allows to analyse the solution in regular intervals and prints the results | ||
| analysis_interval = 100 | ||
| analysis_callback = AnalysisCallback(semi, interval = analysis_interval) | ||
|
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| # The AliveCallback prints short status information in regular intervals | ||
| alive_callback = AliveCallback(analysis_interval = analysis_interval) | ||
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| amr_controller = ControllerThreeLevel(semi, IndicatorMax(semi, variable = first), | ||
| base_level = 1, | ||
| med_level = 2, med_threshold = 1.25, | ||
| max_level = 3, max_threshold = 1.45) | ||
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| amr_callback = AMRCallback(semi, amr_controller, | ||
| interval = 20) | ||
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| # 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) | ||
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| ############################################################################### | ||
| # run the simulation | ||
|
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| # 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) | ||
|
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| # Print the timer summary | ||
| summary_callback() |
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