elixir_advection_basic.jl

using OrdinaryDiffEqLowStorageRK
using Trixi

###############################################################################
# semidiscretization of the linear advection equation

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

###############################################################################
# Get the FDSBP approximation operator

D_SBP = derivative_operator(SummationByPartsOperators.MattssonAlmquistVanDerWeide2018Accurate(),
                            derivative_order = 1, accuracy_order = 4,
                            xmin = -1.0, xmax = 1.0, N = 15)
solver = FDSBP(D_SBP,
               surface_integral = SurfaceIntegralStrongForm(flux_lax_friedrichs),
               volume_integral = VolumeIntegralStrongForm())

###############################################################################
# Get the curved quad mesh from a file (downloads the file if not available locally)
mesh_file = Trixi.download("https://gist.githubusercontent.com/andrewwinters5000/12ce661d7c354c3d94c74b964b0f1c96/raw/8275b9a60c6e7ebbdea5fc4b4f091c47af3d5273/mesh_periodic_square_with_twist.mesh",
                           joinpath(@__DIR__, "mesh_periodic_square_with_twist.mesh"))

mesh = UnstructuredMesh2D(mesh_file, periodicity = true)

###############################################################################
# create the semidiscretization object

semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition_convergence_test,
                                    solver;
                                    boundary_conditions = boundary_condition_periodic)

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

# Create ODE problem with time span from 0.0 to 1.0
ode = semidiscretize(semi, (0.0, 1.0))

# At the beginning of the main loop, the SummaryCallback prints a summary of the simulation setup
# and resets the timers
summary_callback = SummaryCallback()

# The AnalysisCallback allows to analyse the solution in regular intervals and prints the results
analysis_callback = AnalysisCallback(semi, interval = 100)

# The SaveSolutionCallback allows to save the solution to a file in regular intervals
save_solution = SaveSolutionCallback(interval = 100,
                                     solution_variables = cons2prim)

# The StepsizeCallback handles the re-calculation of the maximum Δt after each time step
stepsize_callback = StepsizeCallback(cfl = 1.6)

# Create a CallbackSet to collect all callbacks such that they can be passed to the ODE solver
callbacks = CallbackSet(summary_callback, analysis_callback, save_solution,
                        stepsize_callback)

###############################################################################
# run the simulation

sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false);
            dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback
            ode_default_options()..., callback = callbacks);