
using OrdinaryDiffEq
using Trixi

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

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

initial_condition = initial_condition_convergence_test
boundary_conditions = BoundaryConditionDirichlet(initial_condition)

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

# Mapping as described in https://arxiv.org/abs/2012.12040 but with less warping.
function mapping(xi, eta, zeta)
  # Don't transform input variables between -1 and 1 onto [0,3] to obtain curved boundaries
  # xi = 1.5 * xi_ + 1.5
  # eta = 1.5 * eta_ + 1.5
  # zeta = 1.5 * zeta_ + 1.5

  y = eta + 1/6 * (cos(1.5 * pi * (2 * xi - 3)/3) *
                   cos(0.5 * pi * (2 * eta - 3)/3) *
                   cos(0.5 * pi * (2 * zeta - 3)/3))

  x = xi + 1/6 * (cos(0.5 * pi * (2 * xi - 3)/3) *
                  cos(2 * pi * (2 * y - 3)/3) *
                  cos(0.5 * pi * (2 * zeta - 3)/3))

  z = zeta + 1/6 * (cos(0.5 * pi * (2 * x - 3)/3) *
                    cos(pi * (2 * y - 3)/3) *
                    cos(0.5 * pi * (2 * zeta - 3)/3))

  return SVector(x, y, z)
end

cells_per_dimension = (4, 4, 4)
mesh = StructuredMesh(cells_per_dimension, mapping, periodicity=false)

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


###############################################################################
# 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,
                                     extra_analysis_integrals=(entropy,))

alive_callback = AliveCallback(analysis_interval=analysis_interval)

save_restart = SaveRestartCallback(interval=100,
                                   save_final_restart=true)

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

stepsize_callback = StepsizeCallback(cfl=1.2)

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