elixir_advection_extended.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 advection equation

advection_velocity = (0.2, -0.7)
equations = LinearScalarAdvectionEquation2D(advection_velocity)

initial_condition = initial_condition_convergence_test

D_SBP = derivative_operator(SummationByPartsOperators.MattssonNordström2004(),
                            derivative_order = 1, accuracy_order = 4,
                            xmin = 0.0, xmax = 1.0, N = 100)
solver = FDSBP(D_SBP,
               surface_integral = SurfaceIntegralStrongForm(flux_lax_friedrichs),
               volume_integral = VolumeIntegralStrongForm())

coordinates_min = (-1.0, -1.0)
coordinates_max = (1.0, 1.0)
mesh = TreeMesh(coordinates_min, coordinates_max,
                initial_refinement_level = 1,
                n_cells_max = 30_000,
                periodicity = true)

semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver)

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

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

summary_callback = SummaryCallback()

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

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-9, reltol = 1.0e-9,
            ode_default_options()..., callback = callbacks)