elixir_advection_diffusion_amr.jl

using OrdinaryDiffEqLowStorageRK
using Trixi

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

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

diffusivity() = 5.0e-4
equations_parabolic = LaplaceDiffusion3D(diffusivity(), equations)

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

coordinates_min = (-1.0, -1.0, -1.0)
coordinates_max = (1.0, 1.0, 1.0)
mesh = TreeMesh(coordinates_min, coordinates_max,
                initial_refinement_level = 4,
                n_cells_max = 80_000)

# Define initial condition
function initial_condition_diffusive_convergence_test(x, t,
                                                      equation::LinearScalarAdvectionEquation3D)
    # Store translated coordinate for easy use of exact solution
    x_trans = x - equation.advection_velocity * t

    nu = diffusivity()
    c = 1.0
    A = 0.5
    L = 2
    f = 1 / L
    omega = 2 * pi * f
    scalar = c + A * sin(omega * sum(x_trans)) * exp(-2 * nu * omega^2 * t)
    return SVector(scalar)
end
initial_condition = initial_condition_diffusive_convergence_test

# define periodic boundary conditions everywhere
boundary_conditions = boundary_condition_periodic
boundary_conditions_parabolic = boundary_condition_periodic

# A semidiscretization collects data structures and functions for the spatial discretization
semi = SemidiscretizationHyperbolicParabolic(mesh,
                                             (equations, equations_parabolic),
                                             initial_condition, solver;
                                             solver_parabolic = ViscousFormulationBassiRebay1(),
                                             boundary_conditions = (boundary_conditions,
                                                                    boundary_conditions_parabolic))

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

tspan = (0.0, 0.2)
ode = semidiscretize(semi, tspan)

summary_callback = SummaryCallback()

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

alive_callback = AliveCallback(analysis_interval = analysis_interval)

save_solution = SaveSolutionCallback(interval = 100,
                                     save_initial_solution = true,
                                     save_final_solution = true,
                                     solution_variables = cons2prim)

amr_controller = ControllerThreeLevel(semi, IndicatorMax(semi, variable = first),
                                      base_level = 3,
                                      med_level = 4, med_threshold = 1.2,
                                      max_level = 5, max_threshold = 1.45)
amr_callback = AMRCallback(semi, amr_controller,
                           interval = 5,
                           adapt_initial_condition = true,
                           adapt_initial_condition_only_refine = true)

stepsize_callback = StepsizeCallback(cfl = 1.0)

callbacks = CallbackSet(summary_callback,
                        analysis_callback,
                        alive_callback,
                        save_solution,
                        amr_callback,
                        stepsize_callback)

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

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);