elixir_euler_density_pulse.jl

using OrdinaryDiffEqLowStorageRK
using Trixi

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

equations = CompressibleEulerEquations3D(1.4)

"""
    initial_condition_density_pulse(x, t, equations::CompressibleEulerEquations3D)

A Gaussian pulse in the density with constant velocity and pressure; reduces the
compressible Euler equations to the linear advection equations.
"""
function initial_condition_density_pulse(x, t, equations::CompressibleEulerEquations3D)
    rho = 1 + exp(-(x[1]^2 + x[2]^2 + x[3]^2)) / 2
    v1 = 1
    v2 = 1
    v3 = 1
    rho_v1 = rho * v1
    rho_v2 = rho * v2
    rho_v3 = rho * v3
    p = 1
    rho_e_total = p / (equations.gamma - 1) + 1 / 2 * rho * (v1^2 + v2^2 + v3^2)
    return SVector(rho, rho_v1, rho_v2, rho_v3, rho_e_total)
end
initial_condition = initial_condition_density_pulse

volume_flux = flux_ranocha
solver = DGSEM(polydeg = 3, surface_flux = flux_ranocha,
               volume_integral = VolumeIntegralFluxDifferencing(volume_flux))

coordinates_min = (-2.0, -2.0, -2.0)
coordinates_max = (2.0, 2.0, 2.0)
mesh = TreeMesh(coordinates_min, coordinates_max,
                initial_refinement_level = 3,
                n_cells_max = 100_000, periodicity = true)

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

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

tspan = (0.0, 0.4)
ode = semidiscretize(semi, tspan)

summary_callback = SummaryCallback()

analysis_interval = 100
analysis_callback = AnalysisCallback(semi, interval = analysis_interval)

alive_callback = AliveCallback(analysis_interval = analysis_interval)

save_restart = SaveRestartCallback(interval = 100,
                                   save_final_restart = true)

save_solution = SaveSolutionCallback(interval = 100,
                                     save_initial_solution = true,
                                     save_final_solution = true,
                                     solution_variables = cons2prim)

stepsize_callback = StepsizeCallback(cfl = 1.1)

callbacks = CallbackSet(summary_callback,
                        analysis_callback, alive_callback,
                        save_restart, save_solution,
                        stepsize_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);