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63 changes: 63 additions & 0 deletions
63
examples/structured_2d_dgsem/elixir_eulerpolytropic_convergence.jl
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using OrdinaryDiffEq | ||
using Trixi | ||
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############################################################################### | ||
# semidiscretization of the polytropic Euler equations | ||
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gamma = 1.4 | ||
kappa = 0.5 # Scaling factor for the pressure. | ||
equations = PolytropicEulerEquations2D(gamma, kappa) | ||
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initial_condition = initial_condition_convergence_test | ||
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volume_flux = flux_winters_etal | ||
solver = DGSEM(polydeg = 3, surface_flux = flux_hll, | ||
volume_integral = VolumeIntegralFluxDifferencing(volume_flux)) | ||
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coordinates_min = (0.0, 0.0) | ||
coordinates_max = (1.0, 1.0) | ||
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cells_per_dimension = (4, 4) | ||
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mesh = StructuredMesh(cells_per_dimension, | ||
coordinates_min, | ||
coordinates_max) | ||
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semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver, | ||
source_terms = source_terms_convergence_test) | ||
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############################################################################### | ||
# ODE solvers, callbacks etc. | ||
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tspan = (0.0, 0.1) | ||
ode = semidiscretize(semi, tspan) | ||
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summary_callback = SummaryCallback() | ||
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analysis_interval = 100 | ||
analysis_callback = AnalysisCallback(semi, interval = analysis_interval, | ||
extra_analysis_errors = (:l2_error_primitive, | ||
:linf_error_primitive)) | ||
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alive_callback = AliveCallback(analysis_interval = analysis_interval) | ||
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save_solution = SaveSolutionCallback(interval = 100, | ||
save_initial_solution = true, | ||
save_final_solution = true, | ||
solution_variables = cons2prim) | ||
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stepsize_callback = StepsizeCallback(cfl = 0.1) | ||
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callbacks = CallbackSet(summary_callback, | ||
analysis_callback, alive_callback, | ||
save_solution, | ||
stepsize_callback) | ||
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############################################################################### | ||
# run the simulation | ||
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sol = solve(ode, CarpenterKennedy2N54(williamson_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 |
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using OrdinaryDiffEq | ||
using Trixi | ||
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############################################################################### | ||
# semidiscretization of the polytropic Euler equations | ||
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gamma = 1.4 | ||
kappa = 0.5 # Scaling factor for the pressure. | ||
equations = PolytropicEulerEquations2D(gamma, kappa) | ||
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initial_condition = initial_condition_weak_blast_wave | ||
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############################################################################### | ||
# Get the DG approximation space | ||
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volume_flux = flux_winters_etal | ||
solver = DGSEM(polydeg=4, surface_flux=flux_winters_etal, | ||
volume_integral=VolumeIntegralFluxDifferencing(volume_flux)) | ||
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############################################################################### | ||
# Get the curved quad mesh from a mapping function | ||
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# 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 | ||
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y = eta + 3/8 * (cos(1.5 * pi * (2 * xi - 3)/3) * | ||
cos(0.5 * pi * (2 * eta - 3)/3)) | ||
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x = xi + 3/8 * (cos(0.5 * pi * (2 * xi - 3)/3) * | ||
cos(2 * pi * (2 * y - 3)/3)) | ||
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return SVector(x, y) | ||
end | ||
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cells_per_dimension = (16, 16) | ||
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# Create curved mesh with 16 x 16 elements | ||
mesh = StructuredMesh(cells_per_dimension, mapping) | ||
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############################################################################### | ||
# create the semi discretization object | ||
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semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver) | ||
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############################################################################### | ||
# ODE solvers, callbacks etc. | ||
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tspan = (0.0, 2.0) | ||
ode = semidiscretize(semi, tspan) | ||
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summary_callback = SummaryCallback() | ||
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analysis_interval = 100 | ||
analysis_callback = AnalysisCallback(semi, interval=analysis_interval) | ||
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alive_callback = AliveCallback(analysis_interval=analysis_interval) | ||
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save_solution = SaveSolutionCallback(interval=100, | ||
save_initial_solution=true, | ||
save_final_solution=true) | ||
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stepsize_callback = StepsizeCallback(cfl=1.0) | ||
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callbacks = CallbackSet(summary_callback, | ||
analysis_callback, | ||
alive_callback, | ||
save_solution, | ||
stepsize_callback) | ||
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############################################################################### | ||
# run the simulation | ||
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sol = solve(ode, CarpenterKennedy2N54(williamson_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 |
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examples/structured_2d_dgsem/elixir_eulerpolytropic_isothermal_wave.jl
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using OrdinaryDiffEq | ||
using Trixi | ||
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############################################################################### | ||
# semidiscretization of the polytropic Euler equations | ||
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gamma = 1.0 # With gamma = 1 the system is isothermal. | ||
kappa = 1.0 # Scaling factor for the pressure. | ||
equations = PolytropicEulerEquations2D(gamma, kappa) | ||
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# Linear pressure wave in the negative x-direction. | ||
function initial_condition_wave(x, t, equations::PolytropicEulerEquations2D) | ||
rho = 1.0 | ||
v1 = 0.0 | ||
if x[1] > 0.0 | ||
rho = ((1.0 + 0.01 * sin(x[1] * 2 * pi)) / equations.kappa)^(1 / equations.gamma) | ||
v1 = ((0.01 * sin((x[1] - 1 / 2) * 2 * pi)) / equations.kappa) | ||
end | ||
v2 = 0.0 | ||
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return prim2cons(SVector(rho, v1, v2), equations) | ||
end | ||
initial_condition = initial_condition_wave | ||
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volume_flux = flux_winters_etal | ||
solver = DGSEM(polydeg = 2, surface_flux = flux_hll, | ||
volume_integral = VolumeIntegralFluxDifferencing(volume_flux)) | ||
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coordinates_min = (-2.0, -1.0) | ||
coordinates_max = (2.0, 1.0) | ||
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cells_per_dimension = (64, 32) | ||
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boundary_conditions = (x_neg = boundary_condition_periodic, | ||
x_pos = boundary_condition_periodic, | ||
y_neg = boundary_condition_periodic, | ||
y_pos = boundary_condition_periodic) | ||
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mesh = StructuredMesh(cells_per_dimension, | ||
coordinates_min, | ||
coordinates_max) | ||
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semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver, | ||
boundary_conditions = boundary_conditions) | ||
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############################################################################### | ||
# ODE solvers, callbacks etc. | ||
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tspan = (0.0, 1.0) | ||
ode = semidiscretize(semi, tspan) | ||
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summary_callback = SummaryCallback() | ||
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analysis_interval = 200 | ||
analysis_callback = AnalysisCallback(semi, interval = analysis_interval) | ||
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alive_callback = AliveCallback(analysis_interval = analysis_interval) | ||
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save_solution = SaveSolutionCallback(interval = 50, | ||
save_initial_solution = true, | ||
save_final_solution = true, | ||
solution_variables = cons2prim) | ||
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stepsize_callback = StepsizeCallback(cfl = 1.7) | ||
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callbacks = CallbackSet(summary_callback, | ||
analysis_callback, alive_callback, | ||
save_solution, | ||
stepsize_callback) | ||
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stage_limiter! = PositivityPreservingLimiterZhangShu(thresholds = (1.0e-4, 1.0e-4), | ||
variables = (Trixi.density, pressure)) | ||
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############################################################################### | ||
# run the simulation | ||
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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); | ||
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# Print the timer summary | ||
summary_callback() |
80 changes: 80 additions & 0 deletions
80
examples/structured_2d_dgsem/elixir_eulerpolytropic_wave.jl
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Original file line number | Diff line number | Diff line change |
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@@ -0,0 +1,80 @@ | ||
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using OrdinaryDiffEq | ||
using Trixi | ||
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############################################################################### | ||
# semidiscretization of the polytropic Euler equations | ||
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gamma = 2.0 # Adiabatic monatomic gas in 2d. | ||
kappa = 0.5 # Scaling factor for the pressure. | ||
equations = PolytropicEulerEquations2D(gamma, kappa) | ||
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# Linear pressure wave in the negative x-direction. | ||
function initial_condition_wave(x, t, equations::PolytropicEulerEquations2D) | ||
rho = 1.0 | ||
v1 = 0.0 | ||
if x[1] > 0.0 | ||
rho = ((1.0 + 0.01 * sin(x[1] * 2 * pi)) / equations.kappa)^(1 / equations.gamma) | ||
v1 = ((0.01 * sin((x[1] - 1 / 2) * 2 * pi)) / equations.kappa) | ||
end | ||
v2 = 0.0 | ||
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return prim2cons(SVector(rho, v1, v2), equations) | ||
end | ||
initial_condition = initial_condition_wave | ||
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volume_flux = flux_winters_etal | ||
solver = DGSEM(polydeg = 2, surface_flux = flux_hll, | ||
volume_integral = VolumeIntegralFluxDifferencing(volume_flux)) | ||
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coordinates_min = (-2.0, -1.0) | ||
coordinates_max = (2.0, 1.0) | ||
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cells_per_dimension = (64, 32) | ||
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boundary_conditions = (x_neg = boundary_condition_periodic, | ||
x_pos = boundary_condition_periodic, | ||
y_neg = boundary_condition_periodic, | ||
y_pos = boundary_condition_periodic) | ||
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mesh = StructuredMesh(cells_per_dimension, | ||
coordinates_min, | ||
coordinates_max) | ||
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semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver, | ||
boundary_conditions = boundary_conditions) | ||
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############################################################################### | ||
# ODE solvers, callbacks etc. | ||
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tspan = (0.0, 1.0) | ||
ode = semidiscretize(semi, tspan) | ||
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summary_callback = SummaryCallback() | ||
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analysis_interval = 200 | ||
analysis_callback = AnalysisCallback(semi, interval = analysis_interval) | ||
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alive_callback = AliveCallback(analysis_interval = analysis_interval) | ||
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save_solution = SaveSolutionCallback(interval = 50, | ||
save_initial_solution = true, | ||
save_final_solution = true, | ||
solution_variables = cons2prim) | ||
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stepsize_callback = StepsizeCallback(cfl = 1.7) | ||
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callbacks = CallbackSet(summary_callback, | ||
analysis_callback, alive_callback, | ||
save_solution, | ||
stepsize_callback) | ||
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############################################################################### | ||
# run the simulation | ||
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sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), | ||
dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback | ||
save_everystep = false, callback = callbacks); | ||
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# Print the timer summary | ||
summary_callback() |
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