elixir_linearizedeuler_convergence.jl

using OrdinaryDiffEqLowStorageRK
using Trixi

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

equations = LinearizedEulerEquations3D(v_mean_global = (0.0, 0.0, 0.0), c_mean_global = 1.0,
                                       rho_mean_global = 1.0)

initial_condition = initial_condition_convergence_test

solver = DGSEM(polydeg = 3, surface_flux = flux_hll)

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))

# `initial_refinement_level` is provided here to allow for a
# convenient convergence test, see
# https://trixi-framework.github.io/TrixiDocumentation/stable/#Performing-a-convergence-analysis
trees_per_dimension = (4, 4, 4)
mesh = P4estMesh(trees_per_dimension, polydeg = 3,
                 coordinates_min = coordinates_min,
                 coordinates_max = coordinates_max,
                 initial_refinement_level = 0,
                 periodicity = true)

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

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

# Create ODE problem with time span from 0.0 to 0.2
tspan = (0.0, 0.2)
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);