elixir_euler_vortex_mortar_shockcapturing.jl

using OrdinaryDiffEq
using Trixi

###############################################################################
# semidiscretization of the compressible Euler equations

equations = CompressibleEulerEquations2D(1.4)

initial_conditions = initial_conditions_isentropic_vortex

surface_flux = flux_lax_friedrichs
volume_flux = flux_kennedy_gruber

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 = (-10, -10)
coordinates_max = ( 10,  10)
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,)

semi = SemidiscretizationHyperbolic(mesh, equations, initial_conditions, solver)

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

tspan = (0.0, 1.0)
ode = semidiscretize(semi, tspan)

summary_callback = SummaryCallback()

stepsize_callback = StepsizeCallback(cfl=1.4)

save_solution = SaveSolutionCallback(interval=100,
                                     save_initial_solution=true,
                                     save_final_solution=true,
                                     solution_variables=:primitive)
# TODO: Taal, restart
# restart_interval = 100

analysis_interval = 100
alive_callback = AliveCallback(analysis_interval=analysis_interval)

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))

callbacks = CallbackSet(summary_callback, stepsize_callback, save_solution, analysis_callback, alive_callback)


###############################################################################
# run the simulation

sol = solve(ode, CarpenterKennedy2N54(williamson_condition=false), dt=stepsize_callback(ode),
            save_everystep=false, callback=callbacks);
summary_callback() # print the timer summary