elixir_burgers_linear_stability.jl

using OrdinaryDiffEqLowStorageRK
using Trixi

###############################################################################
# semidiscretization of the (inviscid) Burgers' equation

equations = InviscidBurgersEquation1D()

function initial_condition_linear_stability(x, t, equation::InviscidBurgersEquation1D)
    RealT = eltype(x)
    k = 1
    return SVector(2 + sinpi(k * (x[1] - convert(RealT, 0.7))))
end

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

coordinates_min = -1.0
coordinates_max = 1.0
mesh = TreeMesh(coordinates_min, coordinates_max,
                initial_refinement_level = 4,
                n_cells_max = 10_000, periodicity = true)

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

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

tspan = (0.0, 2.0)
ode = semidiscretize(semi, tspan)

summary_callback = SummaryCallback()

analysis_interval = 100
analysis_callback = AnalysisCallback(semi, interval = analysis_interval,
                                     extra_analysis_errors = (:l2_error_primitive,
                                                              :linf_error_primitive))

alive_callback = AliveCallback(analysis_interval = analysis_interval)

stepsize_callback = StepsizeCallback(cfl = 0.8)

callbacks = CallbackSet(summary_callback,
                        analysis_callback, alive_callback,
                        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);