elixir_advection_nonuniform.jl

using OrdinaryDiffEqLowStorageRK
using Trixi

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

advection_velocity = 1.0
equations = LinearScalarAdvectionEquation1D(advection_velocity)

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

cells_per_dimension = (24,)

# This mapping converts [-1, 1] to [1, 9] with a non-uniform distribution of cells
mapping(xi) = (xi + 2)^2

mesh = StructuredMesh(cells_per_dimension, mapping, 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, 0.5))

summary_callback = SummaryCallback()

analysis_callback = AnalysisCallback(semi, interval = 100)

stepsize_callback = StepsizeCallback(cfl = 1.6)

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);