xref: /libCEED/examples/fluids/navierstokes.c (revision 6f7ff1d2abec09182eb41eda704e7105d824c2c2)

// Copyright (c) 2017-2022, Lawrence Livermore National Security, LLC and other CEED contributors.
// All Rights Reserved. See the top-level LICENSE and NOTICE files for details.
//
// SPDX-License-Identifier: BSD-2-Clause
//
// This file is part of CEED:  http://github.com/ceed

//                        libCEED + PETSc Example: Navier-Stokes
//
// This example demonstrates a simple usage of libCEED with PETSc to solve a Navier-Stokes problem.
//
// Build with:
//
//     make [PETSC_DIR=</path/to/petsc>] [CEED_DIR=</path/to/libceed>] navierstokes
//
// Sample runs:
//
//     ./navierstokes -ceed /cpu/self -problem density_current -degree 1
//     ./navierstokes -ceed /gpu/cuda -problem advection -degree 1
//
//TESTARGS(name="blasius_aniso_diff_filter") -ceed {ceed_resource} -test_type diff_filter -options_file examples/fluids/tests-output/blasius_test.yaml -compare_final_state_atol 5e-10 -compare_final_state_filename examples/fluids/tests-output/fluids-navierstokes-blasius_diff_filter_aniso_vandriest.bin -diff_filter_monitor -ts_max_steps 0 -state_var primitive -diff_filter_friction_length 1e-5 -diff_filter_wall_damping_function van_driest -diff_filter_ksp_rtol 1e-8 -diff_filter_grid_based_width -diff_filter_width_scaling 1,0.7,1
//TESTARGS(name="blasius_iso_diff_filter") -ceed {ceed_resource} -test_type diff_filter -options_file examples/fluids/tests-output/blasius_test.yaml -compare_final_state_atol 2e-12 -compare_final_state_filename examples/fluids/tests-output/fluids-navierstokes-blasius_diff_filter_iso.bin -diff_filter_monitor -ts_max_steps 0 -diff_filter_width_scaling 4.2e-5,4.2e-5,4.2e-5 -diff_filter_ksp_atol 1e-14 -diff_filter_ksp_rtol 1e-16
//TESTARGS(name="blasius_SGS_DataDriven") -ceed {ceed_resource} -test_type solver -options_file examples/fluids/tests-output/blasius_stgtest.yaml -sgs_model_type data_driven -sgs_model_dd_leakyrelu_alpha 0.3 -sgs_model_dd_parameter_dir examples/fluids/dd_sgs_data -ts_dt 1e-9 -compare_final_state_atol 2e-12 -compare_final_state_filename examples/fluids/tests-output/fluids-navierstokes-blasius-sgs-data-driven.bin -state_var primitive
//TESTARGS(name="gaussianwave_idl") -ceed {ceed_resource} -test_type solver -options_file examples/fluids/gaussianwave.yaml -compare_final_state_atol 2e-11 -compare_final_state_filename examples/fluids/tests-output/fluids-navierstokes-gaussianwave-IDL.bin -dm_plex_box_faces 5,5,1 -ts_max_steps 5 -idl_decay_time 2e-3 -idl_length 0.25 -idl_start 0
//TESTARGS(name="turb_spanstats") -ceed {ceed_resource} -test_type turb_spanstats -options_file examples/fluids/tests-output/stats_test.yaml -compare_final_state_atol 1E-11 -compare_final_state_filename examples/fluids/tests-output/fluids-navierstokes-turb-spanstats-stats.bin
//TESTARGS(name="blasius") -ceed {ceed_resource} -test_type solver -options_file examples/fluids/tests-output/blasius_test.yaml -compare_final_state_atol 2E-11 -compare_final_state_filename examples/fluids/tests-output/fluids-navierstokes-blasius.bin
//TESTARGS(name="blasius_STG") -ceed {ceed_resource} -test_type solver -options_file examples/fluids/tests-output/blasius_stgtest.yaml -compare_final_state_atol 2E-11 -compare_final_state_filename examples/fluids/tests-output/fluids-navierstokes-blasius_STG.bin
//TESTARGS(name="blasius_STG_weakT") -ceed {ceed_resource} -test_type solver -options_file examples/fluids/tests-output/blasius_stgtest.yaml -compare_final_state_atol 1E-11 -compare_final_state_filename examples/fluids/tests-output/fluids-navierstokes-blasius_STG_weakT.bin -weakT
//TESTARGS(name="blasius_STG_strongBC") -ceed {ceed_resource} -test_type solver -options_file examples/fluids/tests-output/blasius_stgtest.yaml -compare_final_state_atol 1E-10 -compare_final_state_filename examples/fluids/tests-output/fluids-navierstokes-blasius_STG_strongBC.bin -stg_strong true
//TESTARGS(name="channel") -ceed {ceed_resource} -test_type solver -options_file examples/fluids/channel.yaml -compare_final_state_atol 2e-11 -compare_final_state_filename examples/fluids/tests-output/fluids-navierstokes-channel.bin -dm_plex_box_faces 5,5,1 -ts_max_steps 5
//TESTARGS(name="channel-primitive") -ceed {ceed_resource} -test_type solver -options_file examples/fluids/channel.yaml -compare_final_state_atol 2e-11 -compare_final_state_filename examples/fluids/tests-output/fluids-navierstokes-channel-prim.bin -dm_plex_box_faces 5,5,1 -ts_max_steps 5 -state_var primitive
//TESTARGS(name="dc_explicit") -ceed {ceed_resource} -test_type solver -degree 3 -q_extra 2 -dm_plex_box_faces 1,1,2 -dm_plex_box_lower 0,0,0 -dm_plex_box_upper 125,125,250 -dm_plex_dim 3 -bc_slip_x 5,6 -bc_slip_y 3,4 -bc_Slip_z 1,2 -units_kilogram 1e-9 -center 62.5,62.5,187.5 -rc 100. -thetaC -35. -mu 75 -ts_dt 1e-3 -units_meter 1e-2 -units_second 1e-2 -compare_final_state_atol 1E-11 -compare_final_state_filename examples/fluids/tests-output/fluids-navierstokes-dc-explicit.bin
//TESTARGS(name="dc_implicit_stab_none") -ceed {ceed_resource} -test_type solver -degree 3 -dm_plex_box_faces 1,1,2 -dm_plex_box_lower 0,0,0 -dm_plex_box_upper 125,125,250 -dm_plex_dim 3 -bc_slip_x 5,6 -bc_slip_y 3,4 -bc_Slip_z 1,2 -units_kilogram 1e-9 -center 62.5,62.5,187.5 -rc 100. -thetaC -35. -mu 75 -units_meter 1e-2 -units_second 1e-2 -ksp_atol 1e-4 -ksp_rtol 1e-3 -ksp_type bcgs -snes_atol 1e-3 -snes_lag_jacobian 100 -snes_lag_jacobian_persists -snes_mf_operator -ts_dt 1e-3 -implicit -ts_type alpha -compare_final_state_atol 5E-4 -compare_final_state_filename examples/fluids/tests-output/fluids-navierstokes-dc-implicit-stab-none.bin
//TESTARGS(name="adv_rotation_implicit_stab_supg") -ceed {ceed_resource} -test_type solver -problem advection -CtauS .3 -stab supg -degree 3 -dm_plex_box_faces 1,1,2 -dm_plex_box_lower 0,0,0 -dm_plex_box_upper 125,125,250 -dm_plex_dim 3 -bc_wall 1,2,3,4,5,6 -wall_comps 4 -units_kilogram 1e-9 -rc 100. -ksp_atol 1e-4 -ksp_rtol 1e-3 -ksp_type bcgs -snes_atol 1e-3 -snes_lag_jacobian 100 -snes_lag_jacobian_persists -snes_mf_operator -ts_dt 1e-3 -implicit -dm_mat_preallocate_skip 0 -ts_type alpha -compare_final_state_atol 5E-4 -compare_final_state_filename examples/fluids/tests-output/fluids-navierstokes-adv-rotation-implicit-stab-supg.bin
//TESTARGS(name="adv_translation_implicit_stab_su") -ceed {ceed_resource} -test_type solver -problem advection -CtauS .3 -stab su -degree 3 -dm_plex_box_faces 1,1,2 -dm_plex_box_lower 0,0,0 -dm_plex_box_upper 125,125,250 -dm_plex_dim 3 -units_kilogram 1e-9 -rc 100. -ksp_atol 1e-4 -ksp_rtol 1e-3 -ksp_type bcgs -snes_atol 1e-3 -snes_lag_jacobian 100 -snes_lag_jacobian_persists -snes_mf_operator -ts_dt 1e-3 -implicit -dm_mat_preallocate_skip 0 -ts_type alpha -wind_type translation -wind_translation .53,-1.33,-2.65 -bc_inflow 1,2,3,4,5,6 -compare_final_state_atol 5E-4 -compare_final_state_filename examples/fluids/tests-output/fluids-navierstokes-adv-translation-implicit-stab-su.bin
//TESTARGS(name="adv2d_rotation_explicit_strong") -ceed {ceed_resource} -test_type solver -problem advection2d -strong_form 1 -degree 3 -dm_plex_box_faces 2,2 -dm_plex_box_lower 0,0 -dm_plex_box_upper 125,125 -bc_wall 1,2,3,4 -wall_comps 4 -units_kilogram 1e-9 -rc 100. -ts_dt 1e-3 -compare_final_state_atol 1E-11 -compare_final_state_filename examples/fluids/tests-output/fluids-navierstokes-adv2d-rotation-explicit-strong.bin
//TESTARGS(name="adv2d_rotation_implicit_stab_supg") -ceed {ceed_resource} -test_type solver -problem advection2d -CtauS .3 -stab supg -degree 3 -dm_plex_box_faces 1,1,2 -dm_plex_box_lower 0,0 -dm_plex_box_upper 125,125 -bc_wall 1,2,3,4 -wall_comps 4 -units_kilogram 1e-9 -rc 100. -ksp_atol 1e-4 -ksp_rtol 1e-3 -ksp_type bcgs -snes_atol 1e-3 -snes_lag_jacobian 100 -snes_lag_jacobian_persists -snes_mf_operator -ts_dt 1e-3 -implicit -dm_mat_preallocate_skip 0 -ts_type alpha -compare_final_state_atol 5E-4 -compare_final_state_filename examples/fluids/tests-output/fluids-navierstokes-adv2d-rotation-implicit-stab-supg.bin
//TESTARGS(name="euler_implicit") -ceed {ceed_resource} -test_type solver -problem euler_vortex -degree 3 -dm_plex_box_faces 1,1,2 -dm_plex_box_lower 0,0,0 -dm_plex_box_upper 125,125,250 -dm_plex_dim 3 -units_meter 1e-4 -units_second 1e-4 -mean_velocity 1.4,-2.,0 -bc_inflow 4,6 -bc_outflow 3,5 -bc_slip_z 1,2 -vortex_strength 2 -ksp_atol 1e-4 -ksp_rtol 1e-3 -ksp_type bcgs -snes_atol 1e-3 -snes_lag_jacobian 100 -snes_lag_jacobian_persists -snes_mf_operator -ts_dt 1e-3 -implicit -dm_mat_preallocate_skip 0 -ts_type alpha -compare_final_state_atol 5E-4 -compare_final_state_filename examples/fluids/tests-output/fluids-navierstokes-euler-implicit.bin
//TESTARGS(name="euler_explicit") -ceed {ceed_resource} -test_type solver -problem euler_vortex -degree 3 -q_extra 2 -dm_plex_box_faces 2,2,1 -dm_plex_box_lower 0,0,0 -dm_plex_box_upper 125,125,250 -dm_plex_dim 3 -units_meter 1e-4 -units_second 1e-4 -mean_velocity 1.4,-2.,0 -bc_inflow 4,6 -bc_outflow 3,5 -bc_slip_z 1,2 -vortex_strength 2 -ts_dt 1e-7 -ts_rk_type 5bs -ts_rtol 1e-10 -ts_atol 1e-10 -compare_final_state_atol 1E-7 -compare_final_state_filename examples/fluids/tests-output/fluids-navierstokes-euler-explicit.bin
//TESTARGS(name="shocktube_explicit_su_yzb") -ceed {ceed_resource} -test_type solver -problem shocktube -degree 1 -q_extra 2 -dm_plex_box_faces 50,1,1 -units_meter 1e-2 units_second 1e-2 -dm_plex_box_lower 0,0,0 -dm_plex_box_upper 1000,20,20 -dm_plex_dim 3 -bc_slip_x 5,6 -bc_slip_y 3,4 -bc_Slip_z 1,2 -yzb -stab su -compare_final_state_atol 1E-11 -compare_final_state_filename examples/fluids/tests-output/fluids-navierstokes-shocktube-explicit-su-yzb.bin

/// @file
/// Navier-Stokes example using PETSc

#include "petscsf.h"
const char help[] = "Solve Navier-Stokes using PETSc and libCEED\n";

#include <petscdevice.h>
#include "navierstokes.h"

#include <ceed.h>
#include <petscdmplex.h>
#include <petscts.h>

int main(int argc, char **argv) {
  // ---------------------------------------------------------------------------
  // Initialize PETSc
  // ---------------------------------------------------------------------------
  PetscCall(PetscInitialize(&argc, &argv, NULL, help));

  // ---------------------------------------------------------------------------
  // Create structs
  // ---------------------------------------------------------------------------
  AppCtx app_ctx;
  PetscCall(PetscCalloc1(1, &app_ctx));

  ProblemData *problem = NULL;
  PetscCall(PetscCalloc1(1, &problem));

  User user;
  PetscCall(PetscCalloc1(1, &user));

  CeedData ceed_data;
  PetscCall(PetscCalloc1(1, &ceed_data));

  SimpleBC bc;
  PetscCall(PetscCalloc1(1, &bc));

  Physics phys_ctx;
  PetscCall(PetscCalloc1(1, &phys_ctx));

  Units units;
  PetscCall(PetscCalloc1(1, &units));

  user->app_ctx        = app_ctx;
  user->units          = units;
  user->phys           = phys_ctx;
  problem->bc_from_ics = PETSC_TRUE;

  PetscCall(RegisterLogEvents());

  // ---------------------------------------------------------------------------
  // Process command line options
  // ---------------------------------------------------------------------------
  // -- Register problems to be available on the command line
  PetscCall(RegisterProblems_NS(app_ctx));

  // -- Process general command line options
  MPI_Comm comm = PETSC_COMM_WORLD;
  user->comm    = comm;
  PetscCall(ProcessCommandLineOptions(comm, app_ctx, bc));

  // ---------------------------------------------------------------------------
  // Initialize libCEED
  // ---------------------------------------------------------------------------
  // -- Initialize backend
  Ceed ceed;
  CeedInit(app_ctx->ceed_resource, &ceed);
  user->ceed = ceed;

  // -- Check preferred MemType
  CeedMemType mem_type_backend;
  CeedGetPreferredMemType(ceed, &mem_type_backend);

  {
    const char *resource;
    CeedGetResource(ceed, &resource);
    if (strstr(resource, "/gpu/sycl")) {
      PetscDeviceContext dctx;
      PetscCall(PetscDeviceContextGetCurrentContext(&dctx));
      void *stream_handle;
      PetscCall(PetscDeviceContextGetStreamHandle(dctx, &stream_handle));
      CeedSetStream(ceed, stream_handle);
    }
  }

  // ---------------------------------------------------------------------------
  // Set up global mesh
  // ---------------------------------------------------------------------------
  // -- Create DM
  DM      dm;
  VecType vec_type = NULL;
  MatType mat_type = NULL;
  switch (mem_type_backend) {
    case CEED_MEM_HOST:
      vec_type = VECSTANDARD;
      break;
    case CEED_MEM_DEVICE: {
      const char *resolved;
      CeedGetResource(ceed, &resolved);
      if (strstr(resolved, "/gpu/cuda")) vec_type = VECCUDA;
      else if (strstr(resolved, "/gpu/hip")) vec_type = VECKOKKOS;
      else if (strstr(resolved, "/gpu/sycl")) vec_type = VECKOKKOS;
      else vec_type = VECSTANDARD;
    }
  }
  if (strstr(vec_type, VECCUDA)) mat_type = MATAIJCUSPARSE;
  else if (strstr(vec_type, VECKOKKOS)) mat_type = MATAIJKOKKOS;
  else mat_type = MATAIJ;
  PetscCall(CreateDM(comm, problem, mat_type, vec_type, &dm));
  user->dm = dm;
  PetscCall(DMSetApplicationContext(dm, user));

  // ---------------------------------------------------------------------------
  // Choose the problem from the list of registered problems
  // ---------------------------------------------------------------------------
  {
    PetscErrorCode (*p)(ProblemData *, DM, void *, SimpleBC);
    PetscCall(PetscFunctionListFind(app_ctx->problems, app_ctx->problem_name, &p));
    PetscCheck(p, PETSC_COMM_SELF, 1, "Problem '%s' not found", app_ctx->problem_name);
    PetscCall((*p)(problem, dm, &user, bc));
  }

  // -- Set up DM
  PetscCall(SetUpDM(dm, problem, app_ctx->degree, bc, phys_ctx));

  // -- Refine DM for high-order viz
  if (app_ctx->viz_refine) PetscCall(VizRefineDM(dm, user, problem, bc, phys_ctx));

  // ---------------------------------------------------------------------------
  // Create solution vectors
  // ---------------------------------------------------------------------------
  // -- Set up global state vector Q
  Vec Q;
  PetscCall(DMCreateGlobalVector(dm, &Q));
  PetscCall(VecZeroEntries(Q));

  // -- Set up local state vectors Q_loc, Q_dot_loc
  PetscCall(DMCreateLocalVector(dm, &user->Q_loc));
  PetscCall(DMCreateLocalVector(dm, &user->Q_dot_loc));
  PetscCall(VecZeroEntries(user->Q_dot_loc));

  // ---------------------------------------------------------------------------
  // Set up libCEED
  // ---------------------------------------------------------------------------
  // -- Set up libCEED objects
  PetscCall(SetupLibceed(ceed, ceed_data, dm, user, app_ctx, problem, bc));

  // ---------------------------------------------------------------------------
  // Set up ICs
  // ---------------------------------------------------------------------------
  // -- Fix multiplicity for ICs
  PetscCall(ICs_FixMultiplicity(dm, ceed_data, user, user->Q_loc, Q, 0.0));

  // ---------------------------------------------------------------------------
  // Set up lumped mass matrix
  // ---------------------------------------------------------------------------
  // -- Set up global mass vector
  PetscCall(VecDuplicate(Q, &user->M_inv));

  // -- Compute lumped mass matrix
  PetscCall(ComputeLumpedMassMatrix(ceed, dm, ceed_data, user->M_inv));

  // ---------------------------------------------------------------------------
  // Record boundary values from initial condition
  // ---------------------------------------------------------------------------
  // -- This overrides DMPlexInsertBoundaryValues().
  //    We use this for the main simulation DM because the reference DMPlexInsertBoundaryValues() is very slow on the GPU due to extra device-to-host
  //    communication. If we disable this, we should still get the same results due to the problem->bc function, but with potentially much slower
  //    execution.
  if (problem->bc_from_ics) {
    PetscCall(SetBCsFromICs_NS(dm, Q, user->Q_loc));
  }

  // ---------------------------------------------------------------------------
  // Create output directory
  // ---------------------------------------------------------------------------
  PetscMPIInt rank;
  MPI_Comm_rank(comm, &rank);
  if (!rank) {
    PetscCall(PetscMkdir(app_ctx->output_dir));
  }

  // ---------------------------------------------------------------------------
  // Gather initial Q values in case of continuation of simulation
  // ---------------------------------------------------------------------------
  // -- Set up initial values from binary file
  if (app_ctx->cont_steps) {
    PetscCall(SetupICsFromBinary(comm, app_ctx, Q));
  }

  // ---------------------------------------------------------------------------
  // Print problem summary
  // ---------------------------------------------------------------------------
  if (app_ctx->test_type == TESTTYPE_NONE) {
    // Header and rank
    char host_name[PETSC_MAX_PATH_LEN];
    int  comm_size;
    PetscCall(PetscGetHostName(host_name, sizeof host_name));
    PetscCall(MPI_Comm_size(comm, &comm_size));
    PetscCall(PetscPrintf(comm,
                          "\n-- Navier-Stokes solver - libCEED + PETSc --\n"
                          "  MPI:\n"
                          "    Host Name                          : %s\n"
                          "    Total ranks                        : %d\n",
                          host_name, comm_size));

    // Problem specific info
    PetscCall(problem->print_info(problem, app_ctx));

    // libCEED
    const char *used_resource;
    CeedGetResource(ceed, &used_resource);
    PetscCall(PetscPrintf(comm,
                          "  libCEED:\n"
                          "    libCEED Backend                    : %s\n"
                          "    libCEED Backend MemType            : %s\n",
                          used_resource, CeedMemTypes[mem_type_backend]));
    // PETSc
    char box_faces_str[PETSC_MAX_PATH_LEN] = "3,3,3";
    if (problem->dim == 2) box_faces_str[3] = '\0';
    PetscCall(PetscOptionsGetString(NULL, NULL, "-dm_plex_box_faces", box_faces_str, sizeof(box_faces_str), NULL));
    MatType mat_type;
    VecType vec_type;
    PetscCall(DMGetMatType(dm, &mat_type));
    PetscCall(DMGetVecType(dm, &vec_type));
    PetscCall(PetscPrintf(comm,
                          "  PETSc:\n"
                          "    Box Faces                          : %s\n"
                          "    DM MatType                         : %s\n"
                          "    DM VecType                         : %s\n"
                          "    Time Stepping Scheme               : %s\n",
                          box_faces_str, mat_type, vec_type, phys_ctx->implicit ? "implicit" : "explicit"));
    if (app_ctx->cont_steps) {
      PetscCall(PetscPrintf(comm,
                            "  Continue:\n"
                            "    Filename:                          : %s\n"
                            "    Step:                              : %" PetscInt_FMT "\n"
                            "    Time:                              : %g\n",
                            app_ctx->cont_file, app_ctx->cont_steps, app_ctx->cont_time));
    }
    // Mesh
    const PetscInt num_comp_q = 5;
    PetscInt       glob_dofs, owned_dofs, local_dofs;
    const CeedInt  num_P = app_ctx->degree + 1, num_Q = num_P + app_ctx->q_extra;
    // -- Get global size
    PetscCall(DMGetGlobalVectorInfo(user->dm, &owned_dofs, &glob_dofs, NULL));
    // -- Get local size
    PetscCall(DMGetLocalVectorInfo(user->dm, &local_dofs, NULL, NULL));
    PetscCall(PetscPrintf(comm,
                          "  Mesh:\n"
                          "    Number of 1D Basis Nodes (P)       : %" CeedInt_FMT "\n"
                          "    Number of 1D Quadrature Points (Q) : %" CeedInt_FMT "\n"
                          "    Global DoFs                        : %" PetscInt_FMT "\n"
                          "    DoFs per node                      : %" PetscInt_FMT "\n"
                          "    Global nodes                       : %" PetscInt_FMT "\n",
                          num_P, num_Q, glob_dofs, num_comp_q, glob_dofs / num_comp_q));
    // -- Get Partition Statistics
    PetscCall(PetscPrintf(comm, "  Partition:                             (min,max,median,ratio)\n"));
    {
      PetscInt    *gather_buffer = NULL;
      PetscInt     part_owned_dofs[3], part_local_dofs[3], part_shared_dofs[3];
      PetscInt     median_index = comm_size % 2 ? comm_size / 2 : comm_size / 2 - 1;
      MPI_Datatype PetscInt_MPI;
      PetscCall(PetscDataTypeToMPIDataType(PETSC_INT, &PetscInt_MPI));
      if (!rank) PetscCall(PetscMalloc1(comm_size, &gather_buffer));

      PetscCallMPI(MPI_Gather(&owned_dofs, 1, PetscInt_MPI, gather_buffer, 1, PetscInt_MPI, 0, comm));
      if (!rank) {
        PetscCall(PetscSortInt(comm_size, gather_buffer));
        part_owned_dofs[0]             = gather_buffer[0];              // min
        part_owned_dofs[1]             = gather_buffer[comm_size - 1];  // max
        part_owned_dofs[2]             = gather_buffer[median_index];   // median
        PetscReal part_owned_dof_ratio = (PetscReal)part_owned_dofs[1] / (PetscReal)part_owned_dofs[2];
        PetscCall(PetscPrintf(comm, "    Owned free nodes                   : %" PetscInt_FMT ", %" PetscInt_FMT ", %" PetscInt_FMT ", %f\n",
                              part_owned_dofs[0] / num_comp_q, part_owned_dofs[1] / num_comp_q, part_owned_dofs[2] / num_comp_q,
                              part_owned_dof_ratio));
      }

      PetscCallMPI(MPI_Gather(&local_dofs, 1, PetscInt_MPI, gather_buffer, 1, PetscInt_MPI, 0, comm));
      if (!rank) {
        PetscCall(PetscSortInt(comm_size, gather_buffer));
        part_local_dofs[0]             = gather_buffer[0];              // min
        part_local_dofs[1]             = gather_buffer[comm_size - 1];  // max
        part_local_dofs[2]             = gather_buffer[median_index];   // median
        PetscReal part_local_dof_ratio = (PetscReal)part_local_dofs[1] / (PetscReal)part_local_dofs[2];
        PetscCall(PetscPrintf(comm, "    Local nodes                        : %" PetscInt_FMT ", %" PetscInt_FMT ", %" PetscInt_FMT ", %f\n",
                              part_local_dofs[0] / num_comp_q, part_local_dofs[1] / num_comp_q, part_local_dofs[2] / num_comp_q,
                              part_local_dof_ratio));
      }

      PetscInt num_remote_roots_total = 0;
      {
        PetscSF            sf;
        PetscInt           nrranks;
        const PetscInt    *roffset, *rmine, *rremote;
        const PetscMPIInt *rranks;
        PetscCall(DMGetSectionSF(user->dm, &sf));
        PetscCall(PetscSFGetRootRanks(sf, &nrranks, &rranks, &roffset, &rmine, &rremote));
        for (PetscInt i = 0; i < nrranks; i++) {
          if (rranks[i] == rank) continue;  // Ignore same-part global->local transfers
          num_remote_roots_total += roffset[i + 1] - roffset[i];
        }
      }
      PetscCallMPI(MPI_Gather(&num_remote_roots_total, 1, PetscInt_MPI, gather_buffer, 1, PetscInt_MPI, 0, comm));
      if (!rank) {
        PetscCall(PetscSortInt(comm_size, gather_buffer));
        part_shared_dofs[0]             = gather_buffer[0];              // min
        part_shared_dofs[1]             = gather_buffer[comm_size - 1];  // max
        part_shared_dofs[2]             = gather_buffer[median_index];   // median
        PetscReal part_shared_dof_ratio = (PetscReal)part_shared_dofs[1] / (PetscReal)part_shared_dofs[2];
        PetscCall(PetscPrintf(comm, "    Shared nodes                       : %" PetscInt_FMT ", %" PetscInt_FMT ", %" PetscInt_FMT ", %f\n",
                              part_shared_dofs[0] / num_comp_q, part_shared_dofs[1] / num_comp_q, part_shared_dofs[2] / num_comp_q,
                              part_shared_dof_ratio));
      }

      if (!rank) PetscCall(PetscFree(gather_buffer));
    }

    PetscCall(PetscPrintf(comm, "(nodes == DoFs / %" PetscInt_FMT ")\n", num_comp_q));
  }
  // -- Zero Q_loc
  PetscCall(VecZeroEntries(user->Q_loc));

  // ---------------------------------------------------------------------------
  // TS: Create, setup, and solve
  // ---------------------------------------------------------------------------
  TS          ts;
  PetscScalar final_time;
  PetscCall(TSSolve_NS(dm, user, app_ctx, phys_ctx, &Q, &final_time, &ts));

  // ---------------------------------------------------------------------------
  // Post-processing
  // ---------------------------------------------------------------------------
  PetscCall(PostProcess_NS(ts, ceed_data, dm, problem, user, Q, final_time));

  // ---------------------------------------------------------------------------
  // Destroy libCEED objects
  // ---------------------------------------------------------------------------

  PetscCall(TurbulenceStatisticsDestroy(user, ceed_data));
  PetscCall(NodalProjectionDataDestroy(user->grad_velo_proj));
  PetscCall(SGS_DD_DataDestroy(user->sgs_dd_data));
  PetscCall(DifferentialFilterDataDestroy(user->diff_filter));

  // -- Vectors
  CeedVectorDestroy(&ceed_data->x_coord);
  CeedVectorDestroy(&ceed_data->q_data);
  CeedVectorDestroy(&user->q_ceed);
  CeedVectorDestroy(&user->q_dot_ceed);
  CeedVectorDestroy(&user->g_ceed);
  CeedVectorDestroy(&user->coo_values_amat);
  CeedVectorDestroy(&user->coo_values_pmat);

  // -- Bases
  CeedBasisDestroy(&ceed_data->basis_q);
  CeedBasisDestroy(&ceed_data->basis_x);
  CeedBasisDestroy(&ceed_data->basis_xc);
  CeedBasisDestroy(&ceed_data->basis_q_sur);
  CeedBasisDestroy(&ceed_data->basis_x_sur);

  // -- Restrictions
  CeedElemRestrictionDestroy(&ceed_data->elem_restr_q);
  CeedElemRestrictionDestroy(&ceed_data->elem_restr_x);
  CeedElemRestrictionDestroy(&ceed_data->elem_restr_qd_i);

  // Destroy QFunction contexts after using
  // ToDo: Simplify tracked libCEED objects, smaller struct
  {
    CeedQFunctionContextDestroy(&problem->apply_inflow_jacobian.qfunction_context);
    CeedQFunctionContextDestroy(&problem->apply_inflow_jacobian.qfunction_context);
    CeedQFunctionContextDestroy(&problem->apply_outflow_jacobian.qfunction_context);
    CeedQFunctionContextDestroy(&problem->apply_outflow_jacobian.qfunction_context);
    CeedQFunctionContextDestroy(&problem->apply_freestream_jacobian.qfunction_context);
    CeedQFunctionContextDestroy(&problem->apply_freestream_jacobian.qfunction_context);
    CeedQFunctionContextDestroy(&problem->setup_sur.qfunction_context);
    CeedQFunctionContextDestroy(&problem->setup_vol.qfunction_context);
    CeedQFunctionContextDestroy(&problem->ics.qfunction_context);
    CeedQFunctionContextDestroy(&problem->apply_vol_rhs.qfunction_context);
    CeedQFunctionContextDestroy(&problem->apply_vol_ifunction.qfunction_context);
    CeedQFunctionContextDestroy(&problem->apply_vol_ijacobian.qfunction_context);
  }

  // -- QFunctions
  CeedQFunctionDestroy(&ceed_data->qf_setup_vol);
  CeedQFunctionDestroy(&ceed_data->qf_ics);
  CeedQFunctionDestroy(&ceed_data->qf_rhs_vol);
  CeedQFunctionDestroy(&ceed_data->qf_ifunction_vol);
  CeedQFunctionDestroy(&ceed_data->qf_setup_sur);
  CeedQFunctionDestroy(&ceed_data->qf_apply_inflow);
  CeedQFunctionDestroy(&ceed_data->qf_apply_inflow_jacobian);
  CeedQFunctionDestroy(&ceed_data->qf_apply_freestream);
  CeedQFunctionDestroy(&ceed_data->qf_apply_freestream_jacobian);

  // -- Operators
  CeedOperatorDestroy(&ceed_data->op_setup_vol);
  PetscCall(OperatorApplyContextDestroy(ceed_data->op_ics_ctx));
  CeedOperatorDestroy(&user->op_rhs_vol);
  CeedOperatorDestroy(&user->op_ifunction_vol);
  PetscCall(OperatorApplyContextDestroy(user->op_rhs_ctx));
  CeedOperatorDestroy(&user->op_ifunction);
  CeedOperatorDestroy(&user->op_ijacobian);

  // -- Ceed
  CeedDestroy(&ceed);

  if (app_ctx->test_type != TESTTYPE_NONE) {
    PetscInt num_options_left = 0;
    PetscCall(PetscOptionsLeftGet(NULL, &num_options_left, NULL, NULL));
    PetscCheck(num_options_left == 0, PETSC_COMM_WORLD, -1,
               "There are unused options. This is not allowed. See error message for the unused options (or use -options_left directly)");
  }

  // ---------------------------------------------------------------------------
  // Clean up PETSc
  // ---------------------------------------------------------------------------
  // -- Vectors
  PetscCall(VecDestroy(&Q));
  PetscCall(VecDestroy(&user->M_inv));
  PetscCall(VecDestroy(&user->Q_loc));
  PetscCall(VecDestroy(&user->Q_dot_loc));

  // -- Matrices
  PetscCall(MatDestroy(&user->interp_viz));

  // -- DM
  PetscCall(DMDestroy(&dm));
  PetscCall(DMDestroy(&user->dm_viz));

  // -- TS
  PetscCall(TSDestroy(&ts));

  // -- Function list
  PetscCall(PetscFunctionListDestroy(&app_ctx->problems));

  PetscCall(PetscFree(app_ctx->amat_type));
  PetscCall(PetscFree(app_ctx->wall_forces.walls));
  PetscCall(PetscViewerDestroy(&app_ctx->wall_forces.viewer));

  // -- Structs
  PetscCall(PetscFree(units));
  PetscCall(PetscFree(user));
  PetscCall(PetscFree(problem));
  PetscCall(PetscFree(bc));
  PetscCall(PetscFree(phys_ctx));
  PetscCall(PetscFree(app_ctx));
  PetscCall(PetscFree(ceed_data));

  return PetscFinalize();
}