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trixi-framework
GitHub Repository: trixi-framework/Trixi.jl
 Path: blob/main/examples/tree_2d_fdsbp/elixir_advection_extended.jl
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# !!! warning "Experimental implementation (upwind SBP)"

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#     This is an experimental feature and may change in future releases.

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using OrdinaryDiffEqLowStorageRK

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using Trixi

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###############################################################################

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# semidiscretization of the linear advection equation

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advection_velocity = (0.2, -0.7)

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equations = LinearScalarAdvectionEquation2D(advection_velocity)

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initial_condition = initial_condition_convergence_test

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D_SBP = derivative_operator(SummationByPartsOperators.MattssonNordström2004(),

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                            derivative_order = 1, accuracy_order = 4,

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                            xmin = 0.0, xmax = 1.0, N = 100)

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solver = FDSBP(D_SBP,

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               surface_integral = SurfaceIntegralStrongForm(flux_lax_friedrichs),

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               volume_integral = VolumeIntegralStrongForm())

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coordinates_min = (-1.0, -1.0)

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coordinates_max = (1.0, 1.0)

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mesh = TreeMesh(coordinates_min, coordinates_max,

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                initial_refinement_level = 1,

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                n_cells_max = 30_000,

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                periodicity = true)

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

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                                    boundary_conditions = boundary_condition_periodic)

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###############################################################################

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# ODE solvers, callbacks etc.

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tspan = (0.0, 1.0)

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ode = semidiscretize(semi, tspan)

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summary_callback = SummaryCallback()

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analysis_interval = 100

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analysis_callback = AnalysisCallback(semi, interval = analysis_interval,

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                                     extra_analysis_integrals = (energy_total,))

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alive_callback = AliveCallback(analysis_interval = analysis_interval)

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callbacks = CallbackSet(summary_callback,

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                        analysis_callback,

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                        alive_callback)

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###############################################################################

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# run the simulation

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sol = solve(ode, RDPK3SpFSAL49(); abstol = 1.0e-9, reltol = 1.0e-9,

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            ode_default_options()..., callback = callbacks)

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