elixir_advection_upwind.jl

# !!! warning "Experimental implementation (upwind SBP)"
#     This is an experimental feature and may change in future releases.

using OrdinaryDiffEqLowStorageRK
using Trixi

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

equations = LinearScalarAdvectionEquation1D(1.0)

function initial_condition_sin(x, t, equation::LinearScalarAdvectionEquation1D)
    return SVector(sinpi(x[1] - equations.advection_velocity[1] * t))
end

D_upw = upwind_operators(SummationByPartsOperators.Mattsson2017,
                         derivative_order = 1,
                         accuracy_order = 4,
                         xmin = -1.0, xmax = 1.0,
                         N = 16)
flux_splitting = splitting_lax_friedrichs
solver = FDSBP(D_upw,
               surface_integral = SurfaceIntegralUpwind(flux_splitting),
               volume_integral = VolumeIntegralUpwind(flux_splitting))

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_sin, solver;
                                    boundary_conditions = boundary_condition_periodic)

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

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

summary_callback = SummaryCallback()

analysis_interval = 1000
analysis_callback = AnalysisCallback(semi, interval = analysis_interval)

alive_callback = AliveCallback(analysis_interval = analysis_interval)

callbacks = CallbackSet(summary_callback,
                        analysis_callback, alive_callback)

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

sol = solve(ode, RDPK3SpFSAL49(); abstol = 1.0e-6, reltol = 1.0e-6,
            ode_default_options()..., callback = callbacks);