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trixi-framework
GitHub Repository: trixi-framework/Trixi.jl
 Path: blob/main/examples/dgmulti_2d/elixir_advection_diffusion_periodic.jl
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using OrdinaryDiffEqLowStorageRK

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using Trixi

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dg = DGMulti(polydeg = 1, element_type = Tri(), approximation_type = Polynomial(),

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             surface_integral = SurfaceIntegralWeakForm(flux_lax_friedrichs),

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             volume_integral = VolumeIntegralWeakForm())

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equations = LinearScalarAdvectionEquation2D(0.0, 0.0)

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equations_parabolic = LaplaceDiffusion2D(5.0e-1, equations)

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function initial_condition_sharp_gaussian(x, t, equations::LinearScalarAdvectionEquation2D)

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    return SVector(exp(-100 * (x[1]^2 + x[2]^2)))

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end

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initial_condition = initial_condition_sharp_gaussian

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cells_per_dimension = (16, 16)

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mesh = DGMultiMesh(dg, cells_per_dimension, periodicity = true)

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semi = SemidiscretizationHyperbolicParabolic(mesh, (equations, equations_parabolic),

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                                             initial_condition, dg)

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tspan = (0.0, 0.1)

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ode = semidiscretize(semi, tspan)

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summary_callback = SummaryCallback()

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alive_callback = AliveCallback(alive_interval = 10)

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analysis_interval = 100

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analysis_callback = AnalysisCallback(semi, interval = analysis_interval, uEltype = real(dg))

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save_solution = SaveSolutionCallback(interval = analysis_interval,

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                                     solution_variables = cons2prim)

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

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

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# run the simulation

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time_int_tol = 1e-6

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sol = solve(ode, RDPK3SpFSAL49(); abstol = time_int_tol, reltol = time_int_tol,

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            dt = time_int_tol, ode_default_options()..., callback = callbacks)

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