3D subcell limiting for Io simulations

examples/p4est_2d_dgsem/elixir_euler_subsonic_constant.jl

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+using OrdinaryDiffEqSSPRK
+using Trixi
+using LinearAlgebra: norm
+
+###############################################################################
+## Semidiscretization of the compressible Euler equations
+
+equations = CompressibleEulerEquations2D(1.4)
+polydeg = 3
+solver = DGSEM(polydeg = polydeg, surface_flux = flux_lax_friedrichs)
+
+@inline function initial_condition_subsonic(x_, t, equations::CompressibleEulerEquations2D)
+    rho, v1, v2, p = (0.5313, 0.0, 0.0, 0.4)
+
+    prim = SVector(rho, v1, v2, p)
+    return prim2cons(prim, equations)
+end
+
+initial_condition = initial_condition_subsonic
+
+# Calculate the boundary flux from the inner state while using the pressure from the outer state
+# when the flow is subsonic (which is always the case in this example).
+
+# If the naive approach of only using the inner state is used, the errors increase with the
+# increase of refinement level, see https://github.com/trixi-framework/Trixi.jl/issues/2530
+# These errors arise from the corner points in this test.
+
+# See the reference below for a discussion on inflow/outflow boundary conditions. The subsonic
+# outflow boundary conditions are discussed in Section 2.3.
+#
+# - Jan-Reneé Carlson (2011)
+#   Inflow/Outflow Boundary Conditions with Application to FUN3D.
+#   [NASA TM 20110022658](https://ntrs.nasa.gov/citations/20110022658)
+@inline function boundary_condition_outflow_general(u_inner,
+                                                    normal_direction::AbstractVector, x, t,
+                                                    surface_flux_function,
+                                                    equations::CompressibleEulerEquations2D)
+
+    # This would be for the general case where we need to check the magnitude of the local Mach number
+    norm_ = norm(normal_direction)
+    # Normalize the vector without using `normalize` since we need to multiply by the `norm_` later
+    normal = normal_direction / norm_
+
+    # Rotate the internal solution state
+    u_local = Trixi.rotate_to_x(u_inner, normal, equations)
+
+    # Compute the primitive variables
+    rho_local, v_normal, v_tangent, p_local = cons2prim(u_local, equations)
+
+    # Compute local Mach number
+    a_local = sqrt(equations.gamma * p_local / rho_local)
+    Mach_local = abs(v_normal / a_local)
+    if Mach_local <= 1.0 # The `if` is not needed in this elixir but kept for generality
+        # In general, `p_local` need not be available from the initial condition
+        p_local = pressure(initial_condition_subsonic(x, t, equations), equations)
+    end
+
+    # Create the `u_surface` solution state where the local pressure is possibly set from an external value
+    prim = SVector(rho_local, v_normal, v_tangent, p_local)
+    u_boundary = prim2cons(prim, equations)
+    u_surface = Trixi.rotate_from_x(u_boundary, normal, equations)
+
+    # Compute the flux using the appropriate mixture of internal / external solution states
+    return flux(u_surface, normal_direction, equations)
+end
+
+boundary_conditions = Dict(:x_neg => boundary_condition_outflow_general,
+                           :x_pos => boundary_condition_outflow_general,
+                           :y_neg => boundary_condition_outflow_general,
+                           :y_pos => boundary_condition_outflow_general)
+
+coordinates_min = (0.0, 0.0)
+coordinates_max = (1.0, 1.0)
+
+trees_per_dimension = (1, 1)
+
+mesh = P4estMesh(trees_per_dimension, polydeg = polydeg,
+                 coordinates_min = coordinates_min, coordinates_max = coordinates_max,
+                 initial_refinement_level = 3,
+                 periodicity = false)
+
+semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver,
+                                    boundary_conditions = boundary_conditions)
+
+###############################################################################
+## ODE solvers, callbacks etc.
+
+tspan = (0.0, 0.25)
+ode = semidiscretize(semi, tspan)
+
+summary_callback = SummaryCallback()
+
+analysis_interval = 1000
+analysis_callback = AnalysisCallback(semi, interval = analysis_interval)
+
+alive_callback = AliveCallback(analysis_interval = 100)
+
+save_solution = SaveSolutionCallback(interval = 100,
+                                     save_initial_solution = true,
+                                     save_final_solution = true,
+                                     solution_variables = cons2prim)
+
+stepsize_callback = StepsizeCallback(cfl = 0.5)
+
+callbacks = CallbackSet(summary_callback,
+                        analysis_callback, alive_callback,
+                        save_solution,
+                        stepsize_callback)
+
+###############################################################################
+## Run the simulation
+sol = solve(ode, SSPRK54();
+            dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback
+            save_everystep = false, callback = callbacks);

examples/p4est_3d_dgsem/elixir_euler_sedov_sc_subcell.jl

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+using OrdinaryDiffEqLowStorageRK
+using Trixi
+
+###############################################################################
+# semidiscretization of the compressible Euler equations
+
+equations = CompressibleEulerEquations3D(1.4)
+
+"""
+    initial_condition_medium_sedov_blast_wave(x, t, equations::CompressibleEulerEquations3D)
+
+The Sedov blast wave setup based on Flash
+- https://flash.rochester.edu/site/flashcode/user_support/flash_ug_devel/node187.html#SECTION010114000000000000000
+with smaller strength of the initial discontinuity.
+"""
+function initial_condition_sedov_blast_wave(x, t,
+                                            equations::CompressibleEulerEquations3D)
+    # Set up polar coordinates
+    inicenter = SVector(0.0, 0.0, 0.0)
+    x_norm = x[1] - inicenter[1]
+    y_norm = x[2] - inicenter[2]
+    z_norm = x[3] - inicenter[3]
+    r = sqrt(x_norm^2 + y_norm^2 + z_norm^2)
+
+    # Setup based on https://flash.rochester.edu/site/flashcode/user_support/flash_ug_devel/node187.html#SECTION010114000000000000000
+    r0 = 0.21875 # = 3.5 * smallest dx (for domain length=4 and max-ref=6)
+    E = 1.0
+    p0_inner = 3 * (equations.gamma - 1) * E / (4 * pi * r0^2)
+    p0_outer = 1.0e-5
+
+    # Calculate primitive variables
+    rho = 1.0
+    v1 = 0.0
+    v2 = 0.0
+    v3 = 0.0
+    p = r > r0 ? p0_outer : p0_inner
+
+    return prim2cons(SVector(rho, v1, v2, v3, p), equations)
+end
+
+initial_condition = initial_condition_sedov_blast_wave
+
+# Up to version 0.13.0, `max_abs_speed_naive` was used as the default wave speed estimate of
+# `const flux_lax_friedrichs = FluxLaxFriedrichs(), i.e., `FluxLaxFriedrichs(max_abs_speed = max_abs_speed_naive)`.
+# In the `StepsizeCallback`, though, the less diffusive `max_abs_speeds` is employed which is consistent with `max_abs_speed`.
+# Thus, we exchanged in PR#2458 the default wave speed used in the LLF flux to `max_abs_speed`.
+# To ensure that every example still runs we specify explicitly `FluxLaxFriedrichs(max_abs_speed_naive)`.
+# We remark, however, that the now default `max_abs_speed` is in general recommended due to compliance with the
+# `StepsizeCallback` (CFL-Condition) and less diffusion.
+surface_flux = FluxLaxFriedrichs(max_abs_speed_naive)
+volume_flux = flux_ranocha
+polydeg = 3
+basis = LobattoLegendreBasis(polydeg)
+limiter_idp = SubcellLimiterIDP(equations, basis;
+                                positivity_variables_cons = ["rho"],
+                                positivity_variables_nonlinear = [pressure],
+                                local_twosided_variables_cons = [],
+                                local_onesided_variables_nonlinear = [],
+                                max_iterations_newton = 40, # Default parameters are not sufficient to fulfill bounds properly.
+                                newton_tolerances = (1.0e-14, 1.0e-15))
+volume_integral = VolumeIntegralSubcellLimiting(limiter_idp;
+                                                volume_flux_dg = volume_flux,
+                                                volume_flux_fv = surface_flux)
+solver = DGSEM(basis, surface_flux, volume_integral)
+
+coordinates_min = (-1.0, -1.0, -1.0)
+coordinates_max = (1.0, 1.0, 1.0)
+
+trees_per_dimension = (8, 8, 8)
+mesh = P4estMesh(trees_per_dimension,
+                 polydeg = 1, initial_refinement_level = 0,
+                 coordinates_min = coordinates_min, coordinates_max = coordinates_max,
+                 periodicity = true)
+
+# create the semi discretization object
+semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver)
+
+###############################################################################
+# ODE solvers, callbacks etc.
+
+tspan = (0.0, 3.0)
+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 = 10,
+                                     save_initial_solution = true,
+                                     save_final_solution = true,
+                                     extra_node_variables = (:limiting_coefficient,))
+
+stepsize_callback = StepsizeCallback(cfl = 0.5)
+
+callbacks = CallbackSet(summary_callback,
+                        analysis_callback,
+                        alive_callback,
+                        save_solution,
+                        stepsize_callback)
+
+###############################################################################
+# run the simulation
+
+stage_callbacks = (SubcellLimiterIDPCorrection(), BoundsCheckCallback())
+
+sol = Trixi.solve(ode, Trixi.SimpleSSPRK33(stage_callbacks = stage_callbacks);
+                  dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback
+                  ode_default_options()..., callback = callbacks);

examples/p4est_3d_dgsem/elixir_euler_source_terms_nonperiodic_hohqmesh_sc_subcell.jl

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+using OrdinaryDiffEqLowStorageRK
+using Trixi
+
+###############################################################################
+# semidiscretization of the compressible Euler equations
+
+equations = CompressibleEulerEquations3D(1.4)
+
+initial_condition = initial_condition_convergence_test
+
+boundary_condition = BoundaryConditionDirichlet(initial_condition)
+boundary_conditions = Dict(:Bottom => boundary_condition,
+                           :Top => boundary_condition,
+                           :Circle => boundary_condition,
+                           :Cut => boundary_condition)
+
+surface_flux = flux_lax_friedrichs
+volume_flux = flux_ranocha
+polydeg = 4
+basis = LobattoLegendreBasis(polydeg)
+limiter_idp = SubcellLimiterIDP(equations, basis;
+                                positivity_variables_cons = ["rho"],
+                                positivity_variables_nonlinear = [pressure],
+                                local_twosided_variables_cons = [],
+                                local_onesided_variables_nonlinear = [])
+volume_integral = VolumeIntegralSubcellLimiting(limiter_idp;
+                                                volume_flux_dg = volume_flux,
+                                                volume_flux_fv = surface_flux)
+solver = DGSEM(basis, surface_flux, volume_integral)
+
+# Unstructured 3D half circle mesh from HOHQMesh
+mesh_file = Trixi.download("https://gist.githubusercontent.com/andrewwinters5000/11461efbfb02c42e06aca338b3d0b645/raw/81deeb1ebc4945952c30af5bb75fe222a18d975c/abaqus_half_circle_3d.inp",
+                           joinpath(@__DIR__, "abaqus_half_circle_3d.inp"))
+
+mesh = P4estMesh{3}(mesh_file, initial_refinement_level = 0)
+
+semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver,
+                                    source_terms = source_terms_convergence_test,
+                                    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_solution = SaveSolutionCallback(interval = 1,
+                                     save_initial_solution = true,
+                                     save_final_solution = true,
+                                     solution_variables = cons2prim,
+                                     extra_node_variables = (:limiting_coefficient,))
+
+stepsize_callback = StepsizeCallback(cfl = 0.5)
+
+callbacks = CallbackSet(summary_callback,
+                        analysis_callback, alive_callback,
+                        save_solution,
+                        stepsize_callback)
+
+###############################################################################
+# run the simulation
+
+stage_callbacks = (SubcellLimiterIDPCorrection(), BoundsCheckCallback())
+
+sol = Trixi.solve(ode, Trixi.SimpleSSPRK33(stage_callbacks = stage_callbacks);
+                  dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback
+                  ode_default_options()..., callback = callbacks);