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trixi-framework
GitHub Repository: trixi-framework/Trixi.jl
 Path: blob/main/examples/p4est_2d_dgsem/elixir_advection_diffusion_rotated.jl
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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-diffusion equation

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diffusivity() = 1.0e-2

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advection_velocity = (-1.0, 1.0)

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equations = LinearScalarAdvectionEquation2D(advection_velocity)

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equations_parabolic = LaplaceDiffusion2D(diffusivity(), equations)

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function initial_condition_gauss_damped(x, t, equations)

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    damping_factor = 1 + 4 * diffusivity() * t

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    return SVector(exp(-(x[1]^2 + x[2]^2) / damping_factor) / damping_factor)

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end

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initial_condition = initial_condition_gauss_damped

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solver = DGSEM(polydeg = 3, surface_flux = flux_lax_friedrichs)

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# This maps the domain [-1, 1]^2 to a 45-degree rotated increased square

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square_size() = 5.0

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function mapping(xi, eta)

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    x = square_size() * xi

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    y = square_size() * eta

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    return SVector((x - y) / sqrt(2), (x + y) / sqrt(2))

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end

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trees_per_dimension = (23, 23)

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mesh = P4estMesh(trees_per_dimension,

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                 polydeg = 3, initial_refinement_level = 0,

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                 mapping = mapping, periodicity = true)

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

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                                             initial_condition, solver;

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                                             solver_parabolic = ParabolicFormulationLocalDG(),

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                                             boundary_conditions = (boundary_condition_periodic,

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                                                                    boundary_condition_periodic))

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

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# ODE solvers, callbacks etc.

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n_passes = 2

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tspan = (0.0, n_passes * square_size() * sqrt(2))

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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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alive_callback = AliveCallback(analysis_interval = analysis_interval)

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callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback)

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

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# run the simulation

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time_int_tol = 1.0e-6

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

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            ode_default_options()..., callback = callbacks)

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