elixir_euler_laplace_diffusion.jl

using OrdinaryDiffEqLowStorageRK
using Trixi

# Up to version 0.13.0, `max_abs_speed_naive` was used as the default wave speed estimate of
# `const flux_lax_friedrichs = FluxLaxFriedrichs(), i.e., `FluxLaxFriedrichs(max_abs_speed = max_abs_speed_naive)`.
# In the `StepsizeCallback`, though, the less diffusive `max_abs_speeds` is employed which is consistent with `max_abs_speed`.
# Thus, we exchanged in PR#2458 the default wave speed used in the LLF flux to `max_abs_speed`.
# To ensure that every example still runs we specify explicitly `FluxLaxFriedrichs(max_abs_speed_naive)`.
# We remark, however, that the now default `max_abs_speed` is in general recommended due to compliance with the
# `StepsizeCallback` (CFL-Condition) and less diffusion.
surface_flux = FluxLaxFriedrichs(max_abs_speed_naive)
volume_flux = flux_ranocha
dg = DGMulti(polydeg = 3, element_type = Tri(), approximation_type = Polynomial(),
             surface_integral = SurfaceIntegralWeakForm(surface_flux),
             volume_integral = VolumeIntegralFluxDifferencing(volume_flux))

equations = CompressibleEulerEquations2D(1.4)
equations_parabolic = LaplaceDiffusionEntropyVariables2D(0.001, equations)

initial_condition = initial_condition_weak_blast_wave

cells_per_dimension = (16, 16)
mesh = DGMultiMesh(dg, cells_per_dimension,
                   coordinates_min = (-1.0, -1.0), coordinates_max = (1.0, 1.0),
                   periodicity = true)
semi = SemidiscretizationHyperbolicParabolic(mesh, (equations, equations_parabolic),
                                             initial_condition, dg;
                                             boundary_conditions = (boundary_condition_periodic,
                                                                    boundary_condition_periodic))

tspan = (0.0, 1.1)
ode = semidiscretize(semi, tspan)

summary_callback = SummaryCallback()
alive_callback = AliveCallback(alive_interval = 10)
analysis_interval = 100
analysis_callback = AnalysisCallback(semi, interval = analysis_interval, uEltype = real(dg))
callbacks = CallbackSet(summary_callback,
                        analysis_callback,
                        alive_callback)

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

alg = RDPK3SpFSAL35()
sol = solve(ode, alg; abstol = 1.0e-6, reltol = 1.0e-6,
            ode_default_options()..., callback = callbacks);