elixir_advection_gauss_legendre.jl

using OrdinaryDiffEqLowStorageRK
using Trixi

###############################################################################
# semidiscretization of the linear advection equation

advection_velocity = 1.0
equations = LinearScalarAdvectionEquation1D(advection_velocity)

solver = DGSEM(polydeg = 3,
               basis_type = GaussLegendreBasis,
               surface_flux = flux_godunov)

coordinates_min = -1.0
coordinates_max = 1.0

mesh = TreeMesh(coordinates_min, coordinates_max,
                initial_refinement_level = 4,
                n_cells_max = 30_000, periodicity = true)

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

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

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

summary_callback = SummaryCallback()

analysis_callback = AnalysisCallback(semi, interval = 100)

stepsize_callback = StepsizeCallback(cfl = 0.8)

callbacks = CallbackSet(summary_callback, analysis_callback,
                        stepsize_callback)

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

sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false); dt = 1.0,
            ode_default_options()..., callback = callbacks);