elixir_advection_extended.jl

using OrdinaryDiffEqLowStorageRK
using Trixi

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

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

initial_condition = initial_condition_convergence_test

# you can either use a single function to impose the BCs weakly in all
# 1*ndims == 2 directions or you can pass a tuple containing BCs for
# each direction
boundary_conditions = boundary_condition_periodic

# Create DG solver with polynomial degree = 3 and (local) Lax-Friedrichs/Rusanov flux as surface flux
solver = DGSEM(polydeg = 3, surface_flux = flux_lax_friedrichs)

coordinates_min = (-1.0, -1.0) # minimum coordinates (min(x), min(y))
coordinates_max = (1.0, 1.0) # maximum coordinates (max(x), max(y))

# Create a uniformly refined mesh with periodic boundaries
mesh = TreeMesh(coordinates_min, coordinates_max,
                initial_refinement_level = 4,
                n_cells_max = 30_000, # set maximum capacity of tree data structure
                periodicity = true)

# A semidiscretization collects data structures and functions for the spatial discretization
semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver;
                                    boundary_conditions = boundary_conditions)

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

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

# 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_interval = 100
analysis_callback = AnalysisCallback(semi, interval = analysis_interval,
                                     extra_analysis_integrals = (entropy, energy_total))

# The AliveCallback prints short status information in regular intervals
alive_callback = AliveCallback(analysis_interval = analysis_interval)

# The SaveRestartCallback allows to save a file from which a Trixi.jl simulation can be restarted
save_restart = SaveRestartCallback(interval = 40,
                                   save_final_restart = true)

# The SaveSolutionCallback allows to save the solution to a file in regular intervals
save_solution = SaveSolutionCallback(interval = 100,
                                     save_initial_solution = true,
                                     save_final_solution = true,
                                     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, alive_callback,
                        save_restart, save_solution,
                        stepsize_callback)

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

# OrdinaryDiffEq's `solve` method evolves the solution in time and executes the passed callbacks
alg = CarpenterKennedy2N54(williamson_condition = false)
sol = solve(ode, alg;
            dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback
            callback = callbacks,
            ode_default_options()...);