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trixi-framework
GitHub Repository: trixi-framework/Trixi.jl
 Path: blob/main/examples/tree_1d_fdsbp/elixir_burgers_linear_stability.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 OrdinaryDiffEqSSPRK

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using Trixi

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

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# semidiscretization of the (inviscid) Burgers' equation

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equations = InviscidBurgersEquation1D()

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function initial_condition_linear_stability(x, t, equation::InviscidBurgersEquation1D)

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    k = 1

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    return 2 + sinpi(k * (x[1] - 0.7)) |> SVector

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end

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D_upw = upwind_operators(SummationByPartsOperators.Mattsson2017,

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                         derivative_order = 1,

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                         accuracy_order = 4,

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                         xmin = -1.0, xmax = 1.0,

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                         N = 16)

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flux_splitting = splitting_lax_friedrichs

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solver = FDSBP(D_upw,

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               surface_integral = SurfaceIntegralUpwind(flux_splitting),

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               volume_integral = VolumeIntegralUpwind(flux_splitting))

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coordinates_min = -1.0

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coordinates_max = 1.0

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mesh = TreeMesh(coordinates_min, coordinates_max,

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                initial_refinement_level = 4,

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                n_cells_max = 10_000, periodicity = true)

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semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition_linear_stability,

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                                    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, 2.0)

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ode = semidiscretize(semi, tspan)

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summary_callback = SummaryCallback()

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analysis_interval = 1000

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analysis_callback = AnalysisCallback(semi, interval = analysis_interval,

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                                     extra_analysis_errors = (:l2_error_primitive,

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                                                              :linf_error_primitive))

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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, alive_callback)

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

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# run the simulation

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sol = solve(ode, SSPRK43(); abstol = 1.0e-6, reltol = 1.0e-6,

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            ode_default_options()..., callback = callbacks);

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