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trixi-framework
GitHub Repository: trixi-framework/Trixi.jl
 Path: blob/main/examples/tree_1d_dgsem/elixir_euler_laplace_diffusion.jl
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using OrdinaryDiffEqLowStorageRK

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using Trixi

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###############################################################################

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# semidiscretization of the compressible Euler equations with Laplacian

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# diffusion represented in terms of entropy variables

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equations = CompressibleEulerEquations1D(1.4)

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equations_parabolic = LaplaceDiffusionEntropyVariables1D(0.01, equations)

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initial_condition = initial_condition_weak_blast_wave

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volume_flux = flux_ranocha

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solver = DGSEM(polydeg = 3, surface_flux = flux_ranocha,

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               volume_integral = VolumeIntegralFluxDifferencing(volume_flux))

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coordinates_min = (-2.0,)

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coordinates_max = (2.0,)

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mesh = TreeMesh(coordinates_min, coordinates_max,

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                initial_refinement_level = 5,

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                n_cells_max = 10_000, periodicity = true)

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semi = SemidiscretizationHyperbolicParabolic(mesh, (equations, equations_parabolic),

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                                             initial_condition, solver;

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                                             boundary_conditions = (boundary_condition_periodic,

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                                                                    boundary_condition_periodic))

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###############################################################################

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# ODE solvers, callbacks etc.

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tspan = (0.0, 0.4)

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ode = semidiscretize(semi, tspan)

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summary_callback = SummaryCallback()

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analysis_interval = 100

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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,

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                                     save_initial_solution = true,

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                                     save_final_solution = true,

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                                     solution_variables = cons2prim)

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stepsize_callback = StepsizeCallback(cfl = 0.8)

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callbacks = CallbackSet(summary_callback,

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                        analysis_callback, alive_callback,

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                        save_solution,

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                        stepsize_callback)

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###############################################################################

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# run the simulation

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sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false);

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            dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback

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            ode_default_options()..., callback = callbacks);

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