
using OrdinaryDiffEq
using Trixi

###############################################################################
# semidiscretization of the compressible ideal GLM-MHD equations

equations = IdealGlmMhdEquations3D(5/3)

initial_condition = initial_condition_convergence_test

volume_flux = flux_central
solver = DGSEM(polydeg=5, surface_flux=flux_hll,
               volume_integral=VolumeIntegralFluxDifferencing(volume_flux))

##############################################################################
# Create the mesh

# Note, we use the domain [-1, 1]^3 for the Alfvén wave convergence test case so the
# warped mapping simplifies (quite a bit)

# Mapping as described in https://arxiv.org/abs/2012.12040
function mapping(xi, eta, zeta)
  y = eta + 0.125 * (cos(1.5 * pi * xi) * cos(0.5 * pi * eta) * cos(0.5 * pi * zeta))

  x = xi + 0.125 * (cos(0.5 * pi * xi) * cos(2 * pi * y) * cos(0.5 * pi * zeta))

  z = zeta + 0.125 * (cos(0.5 * pi * x) * cos(pi * y) * cos(0.5 * pi * zeta))

  return SVector(x, y, z)
end

cells_per_dimension = (4, 4, 4)
mesh = CurvedMesh(cells_per_dimension, mapping)

###############################################################################
# create the semi discretization object

semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver)

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

tspan = (0.0, 1.0)
ode = semidiscretize(semi, tspan)

summary_callback = SummaryCallback()

analysis_interval = 100
analysis_callback = AnalysisCallback(semi, interval=analysis_interval)
alive_callback = AliveCallback(analysis_interval=analysis_interval)

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

cfl = 1.2
stepsize_callback = StepsizeCallback(cfl=cfl)

glm_speed_callback = GlmSpeedCallback(glm_scale=0.5, cfl=cfl)

callbacks = CallbackSet(summary_callback,
                        analysis_callback, alive_callback,
                        save_solution,
                        stepsize_callback,
                        glm_speed_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
            save_everystep=false, callback=callbacks);
summary_callback() # print the timer summary
