elixir_advection_finite_volume.jl

using OrdinaryDiffEqLowOrderRK
using Trixi

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

advection_velocity = 1.0
equations = LinearScalarAdvectionEquation1D(advection_velocity)

# Create DG solver with polynomial degree = 0, i.e., a first order finite volume solver,
# with (local) Lax-Friedrichs/Rusanov flux as surface flux
solver = DGSEM(polydeg = 0, surface_flux = flux_lax_friedrichs)

coordinates_min = -1.0 # minimum coordinate
coordinates_max = 1.0 # maximum coordinate

# Create a uniformly refined mesh with periodic boundaries
mesh = TreeMesh(coordinates_min, coordinates_max,
                initial_refinement_level = 5,
                n_cells_max = 30_000) # set maximum capacity of tree data structure

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

###############################################################################
# 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 StepsizeCallback handles the re-calculation of the maximum Δt after each time step
stepsize_callback = StepsizeCallback(cfl = 0.9)

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

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

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