elixir_linearizedeuler_convergence.jl

using OrdinaryDiffEqLowStorageRK
using Trixi

###############################################################################
# semidiscretization of the linearized Euler equations

equations = LinearizedEulerEquations1D(v_mean_global = 0.0, c_mean_global = 1.0,
                                       rho_mean_global = 1.0)

initial_condition = initial_condition_convergence_test

# 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)
coordinates_max = (1.0)

# Create a uniformly refined mesh with periodic boundaries
mesh = TreeMesh(coordinates_min, coordinates_max,
                initial_refinement_level = 4,
                n_cells_max = 30_000)

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

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

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()

analysis_interval = 100

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

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

# The StepsizeCallback handles the re-calculation of the maximum Δt after each time step
stepsize_callback = StepsizeCallback(cfl = 0.8)

# 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,
                        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);