3D support for subcell limiting

NEWS.md

@@ -6,6 +6,14 @@ used in the Julia ecosystem. Notable changes will be documented in this file
 for human readability.
 
 
+## Changes in the v0.13 lifecycle
+
+#### Added
+- Initial 3D support for subcell limiting with `P4estMesh` was added ([#2582]).
+  In the new version, positivity limiting for conservative variables (using `positivity_variables_cons`)
+  is supported. `BoundsCheckCallback` is not supported in 3D yet.
+
+
 ## Changes when updating to v0.13 from v0.12.x
 
 #### Changed

examples/p4est_3d_dgsem/elixir_euler_sedov_sc_subcell.jl

@@ -0,0 +1,103 @@
+using Trixi
+
+###############################################################################
+# semidiscretization of the compressible Euler equations
+
+equations = CompressibleEulerEquations3D(1.4)
+
+"""
+    initial_condition_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
+
+surface_flux = flux_lax_friedrichs
+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
+                  callback = callbacks);

examples/p4est_3d_dgsem/elixir_euler_source_terms_nonperiodic_hohqmesh_sc_subcell.jl

@@ -0,0 +1,75 @@
+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);

examples/p4est_3d_dgsem/elixir_mhd_shockcapturing_subcell.jl

@@ -0,0 +1,124 @@
+using Trixi
+
+###############################################################################
+# semidiscretization of the compressible ideal GLM-MHD equations
+
+equations = IdealGlmMhdEquations3D(1.4)
+
+"""
+    initial_condition_blast_wave(x, t, equations::IdealGlmMhdEquations3D)
+
+Weak magnetic blast wave setup taken from Section 6.1 of the paper:
+- A. M. Rueda-Ramírez, S. Hennemann, F. J. Hindenlang, A. R. Winters, G. J. Gassner (2021)
+  An entropy stable nodal discontinuous Galerkin method for the resistive MHD
+  equations. Part II: Subcell finite volume shock capturing
+  [doi: 10.1016/j.jcp.2021.110580](https://doi.org/10.1016/j.jcp.2021.110580)
+"""
+function initial_condition_blast_wave(x, t, equations::IdealGlmMhdEquations3D)
+    # Center of the blast wave is selected for the domain [0, 3]^3
+    inicenter = (1.5, 1.5, 1.5)
+    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)
+
+    delta_0 = 0.1
+    r_0 = 0.3
+    lambda = exp(5.0 / delta_0 * (r - r_0))
+
+    prim_inner = SVector(1.2, 0.1, 0.0, 0.1, 0.9, 1.0, 1.0, 1.0, 0.0)
+    prim_outer = SVector(1.2, 0.2, -0.4, 0.2, 0.3, 1.0, 1.0, 1.0, 0.0)
+    prim_vars = (prim_inner + lambda * prim_outer) / (1.0 + lambda)
+
+    return prim2cons(prim_vars, equations)
+end
+initial_condition = initial_condition_blast_wave
+
+surface_flux = (flux_lax_friedrichs, flux_nonconservative_powell_local_symmetric)
+volume_flux = (flux_hindenlang_gassner, flux_nonconservative_powell_local_symmetric)
+polydeg = 3
+basis = LobattoLegendreBasis(polydeg)
+limiter_idp = SubcellLimiterIDP(equations, basis;
+                                positivity_variables_cons = ["rho"],
+                                positivity_variables_nonlinear = [pressure])
+volume_integral = VolumeIntegralSubcellLimiting(limiter_idp;
+                                                volume_flux_dg = volume_flux,
+                                                volume_flux_fv = surface_flux)
+solver = DGSEM(basis, surface_flux, volume_integral)
+
+# Mapping as described in https://arxiv.org/abs/2012.12040 but with slightly less warping.
+# The mapping will be interpolated at tree level, and then refined without changing
+# the geometry interpolant.
+function mapping(xi_, eta_, zeta_)
+    # Transform input variables between -1 and 1 onto [0,3]
+    xi = 1.5 * xi_ + 1.5
+    eta = 1.5 * eta_ + 1.5
+    zeta = 1.5 * zeta_ + 1.5
+
+    y = eta +
+        3 / 11 * (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 +
+        3 / 11 * (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 +
+        3 / 11 * (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
+
+trees_per_dimension = (2, 2, 2)
+mesh = P4estMesh(trees_per_dimension,
+                 polydeg = 3,
+                 mapping = mapping,
+                 # coordinates_min = (0.0, 0.0, 0.0),
+                 # coordinates_max = (3.0, 3.0, 3.0),
+                 initial_refinement_level = 2,
+                 periodicity = true)
+
+semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver)
+
+###############################################################################
+# ODE solvers, callbacks etc.
+
+tspan = (0.0, 0.5)
+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,
+                                     extra_node_variables = (:limiting_coefficient,))
+
+cfl = 0.9
+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
+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);

src/callbacks_stage/subcell_bounds_check.jl

@@ -214,4 +214,5 @@ end
 end
 
 include("subcell_bounds_check_2d.jl")
+include("subcell_bounds_check_3d.jl")
 end # @muladd

src/callbacks_stage/subcell_bounds_check_2d.jl

@@ -5,7 +5,7 @@
 @muladd begin
 #! format: noindent
 
-@inline function check_bounds(u, equations::AbstractEquations{2}, # only works for 2D
+@inline function check_bounds(u, equations::AbstractEquations{2},
                               solver, cache, limiter::SubcellLimiterIDP)
     (; local_twosided, positivity, local_onesided) = solver.volume_integral.limiter
     (; variable_bounds) = limiter.cache.subcell_limiter_coefficients