elixir_mhd_alfven_wave.jl

using OrdinaryDiffEqLowStorageRK
using Trixi

###############################################################################
# semidiscretization of the compressible ideal GLM-MHD equations
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_hlle,
                               flux_nonconservative_powell),
               volume_integral = VolumeIntegralFluxDifferencing(volume_flux))

# Get the unstructured quad mesh from a file (downloads the file if not available locally)
mesh_file = Trixi.download("https://gist.githubusercontent.com/andrewwinters5000/8f8cd23df27fcd494553f2a89f3c1ba4/raw/85e3c8d976bbe57ca3d559d653087b0889535295/mesh_alfven_wave_with_twist_and_flip.mesh",
                           joinpath(@__DIR__, "mesh_alfven_wave_with_twist_and_flip.mesh"))

mesh = UnstructuredMesh2D(mesh_file, periodicity = true)

semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver;
                                    boundary_conditions = boundary_condition_periodic)

###############################################################################
# ODE solvers, callbacks etc.

tspan = (0.0, 2.0)
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)
cfl = 0.9
stepsize_callback = StepsizeCallback(cfl = cfl)

glm_speed_callback = GlmSpeedCallback(glm_scale = 0.5, cfl = cfl)

callbacks = CallbackSet(summary_callback,
                        analysis_callback,
                        alive_callback,
                        save_solution,
                        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
            ode_default_options()..., callback = callbacks);