WIP: Sc/flux ruedaramirez etal normal direction

examples/structured_2d_dgsem/elixir_mhdmultiion_ec.jl

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+using OrdinaryDiffEqLowStorageRK
+using Trixi
+
+###############################################################################
+# semidiscretization of the ideal multi-ion MHD equations
+equations = IdealGlmMhdMultiIonEquations2D(gammas = (1.4, 1.667),
+                                           charge_to_mass = (1.0, 2.0))
+
+initial_condition = initial_condition_weak_blast_wave
+
+# Entropy conservative numerical fluxes
+volume_flux = (flux_ruedaramirez_etal, flux_nonconservative_ruedaramirez_etal)
+surface_flux = (flux_ruedaramirez_etal, flux_nonconservative_ruedaramirez_etal)
+# For provably entropy-stable surface fluxes, use
+# surface_flux = (FluxPlusDissipation(flux_ruedaramirez_etal, DissipationLaxFriedrichsEntropyVariables()),
+#                 flux_nonconservative_ruedaramirez_etal)
+# For a standard local Lax-Friedrichs surface flux, use
+# surface_flux = (flux_lax_friedrichs, flux_nonconservative_central)
+
+solver = DGSEM(polydeg = 3, surface_flux = surface_flux,
+               volume_integral = VolumeIntegralFluxDifferencing(volume_flux))
+
+coordinates_min = (-2.0, -2.0)
+coordinates_max = (2.0, 2.0)
+cells_per_dimension = (100, 100)
+mesh = StructuredMesh(cells_per_dimension, coordinates_min, coordinates_max)
+
+# The multi-ion GLM-MHD equations require the inclusion of source_terms_lorentz 
+# whenever multiple ion species are present
+semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver,
+                                    source_terms = source_terms_lorentz)
+
+###############################################################################
+# ODE solvers, callbacks etc.
+
+tspan = (0.0, 0.4)
+ode = semidiscretize(semi, tspan)
+
+summary_callback = SummaryCallback()
+
+analysis_interval = 10
+analysis_callback = AnalysisCallback(semi, interval = analysis_interval)
+alive_callback = AliveCallback(analysis_interval = analysis_interval)
+
+save_solution = SaveSolutionCallback(dt = 0.1, # interval=100,
+                                     save_initial_solution = true,
+                                     save_final_solution = true,
+                                     solution_variables = cons2prim)
+
+cfl = 0.5
+
+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
+            ode_default_options()..., callback = callbacks);