elixir_advection_basic.jl

# The same setup as tree_3d_dgsem/elixir_advection_basic.jl
# to verify the StructuredMesh implementation against TreeMesh

using OrdinaryDiffEqLowStorageRK
using Trixi

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

advection_velocity = (0.2, -0.7, 0.5)
equations = LinearScalarAdvectionEquation3D(advection_velocity)

# 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, -1.0) # minimum coordinates (min(x), min(y), min(z))
coordinates_max = (1.0, 1.0, 1.0) # maximum coordinates (max(x), max(y), max(z))
cells_per_dimension = (8, 8, 8)

# Create curved mesh with 8 x 8 x 8 elements
mesh = StructuredMesh(cells_per_dimension, coordinates_min, coordinates_max,
                      periodicity = true)

# A semidiscretization collects data structures and functions for the spatial discretization
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 SaveRestartCallback allows to save a file from which a Trixi.jl simulation can be restarted
save_restart = SaveRestartCallback(interval = 100,
                                   save_final_restart = true)

# The StepsizeCallback handles the re-calculation of the maximum Δt after each time step
stepsize_callback = StepsizeCallback(cfl = 1.2)

# 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, save_restart,
                        stepsize_callback)

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

# OrdinaryDiffEq's `solve` method evolves the solution in time and executes the passed callbacks
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);