// Copyright (c) 2017-2026, 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 /// @file /// Utility functions for setting up Blasius Boundary Layer #include "../qfunctions/blasius.h" #include #include #include #include "../navierstokes.h" #include "stg_shur14.h" PetscErrorCode CompressibleBlasiusResidual(SNES snes, Vec X, Vec R, void *ctx) { const BlasiusContext blasius = (BlasiusContext)ctx; const PetscScalar *Tf, *Th; // Chebyshev coefficients PetscScalar *r, f[4], h[4]; PetscInt N = blasius->n_cheb; State S_infty = blasius->S_infty; CeedScalar U_infty = sqrt(Dot3(S_infty.Y.velocity, S_infty.Y.velocity)); PetscFunctionBeginUser; PetscScalar Ma = Mach(&blasius->newtonian_ctx, S_infty.Y.temperature, U_infty), Pr = Prandtl(&blasius->newtonian_ctx), gamma = HeatCapacityRatio(&blasius->newtonian_ctx); PetscCall(VecGetArrayRead(X, &Tf)); Th = Tf + N; PetscCall(VecGetArray(R, &r)); // Left boundary conditions f = f' = 0 ChebyshevEval(N, Tf, -1., blasius->eta_max, f); r[0] = f[0]; r[1] = f[1]; // f - right end boundary condition ChebyshevEval(N, Tf, 1., blasius->eta_max, f); r[2] = f[1] - 1.; for (int i = 0; i < N - 3; i++) { ChebyshevEval(N, Tf, blasius->X[i], blasius->eta_max, f); ChebyshevEval(N - 1, Th, blasius->X[i], blasius->eta_max, h); // mu and rho generally depend on h. // We naively assume constant mu. // For an ideal gas at constant pressure, density is inversely proportional to enthalpy. // The *_tilde values are *relative* to their freestream values, and we proved first derivatives here. const PetscScalar mu_tilde[2] = {1, 0}; const PetscScalar rho_tilde[2] = {1 / h[0], -h[1] / PetscSqr(h[0])}; const PetscScalar mu_rho_tilde[2] = { mu_tilde[0] * rho_tilde[0], mu_tilde[1] * rho_tilde[0] + mu_tilde[0] * rho_tilde[1], }; r[3 + i] = 2 * (mu_rho_tilde[0] * f[3] + mu_rho_tilde[1] * f[2]) + f[2] * f[0]; r[N + 2 + i] = (mu_rho_tilde[0] * h[2] + mu_rho_tilde[1] * h[1]) + Pr * f[0] * h[1] + Pr * (gamma - 1) * mu_rho_tilde[0] * PetscSqr(Ma * f[2]); } // h - left end boundary condition ChebyshevEval(N - 1, Th, -1., blasius->eta_max, h); r[N] = h[0] - blasius->T_wall / S_infty.Y.temperature; // h - right end boundary condition ChebyshevEval(N - 1, Th, 1., blasius->eta_max, h); r[N + 1] = h[0] - 1.; // Restore vectors PetscCall(VecRestoreArrayRead(X, &Tf)); PetscCall(VecRestoreArray(R, &r)); PetscFunctionReturn(PETSC_SUCCESS); } PetscErrorCode ComputeChebyshevCoefficients(BlasiusContext blasius) { SNES snes; Vec sol, res; PetscReal *w; PetscInt N = blasius->n_cheb; SNESConvergedReason reason; const PetscScalar *cheb_coefs; PetscFunctionBeginUser; // Allocate memory PetscCall(PetscMalloc2(N - 3, &blasius->X, N - 3, &w)); PetscCall(PetscDTGaussQuadrature(N - 3, -1., 1., blasius->X, w)); // Snes solve PetscCall(SNESCreate(PETSC_COMM_SELF, &snes)); PetscCall(VecCreate(PETSC_COMM_SELF, &sol)); PetscCall(VecSetSizes(sol, PETSC_DECIDE, 2 * N - 1)); PetscCall(VecSetFromOptions(sol)); // Constant relative enthalpy 1 as initial guess PetscCall(VecSetValue(sol, N, 1., INSERT_VALUES)); PetscCall(VecDuplicate(sol, &res)); PetscCall(SNESSetFunction(snes, res, CompressibleBlasiusResidual, blasius)); PetscCall(SNESSetOptionsPrefix(snes, "chebyshev_")); PetscCall(SNESSetFromOptions(snes)); PetscCall(SNESSolve(snes, NULL, sol)); PetscCall(SNESGetConvergedReason(snes, &reason)); PetscCheck(reason >= 0, PETSC_COMM_WORLD, PETSC_ERR_CONV_FAILED, "The Chebyshev solve failed.\n"); // Assign Chebyshev coefficients PetscCall(VecGetArrayRead(sol, &cheb_coefs)); for (int i = 0; i < N; i++) blasius->Tf_cheb[i] = cheb_coefs[i]; for (int i = 0; i < N - 1; i++) blasius->Th_cheb[i] = cheb_coefs[i + N]; // Destroy objects PetscCall(PetscFree2(blasius->X, w)); PetscCall(VecDestroy(&sol)); PetscCall(VecDestroy(&res)); PetscCall(SNESDestroy(&snes)); PetscFunctionReturn(PETSC_SUCCESS); } static PetscErrorCode GetYNodeLocs(const MPI_Comm comm, const char path[PETSC_MAX_PATH_LEN], PetscReal **pynodes, PetscInt *nynodes) { int ndims, dims[2]; FILE *fp; const PetscInt char_array_len = 512; char line[char_array_len]; PetscReal *node_locs; PetscFunctionBeginUser; PetscCall(PetscFOpen(comm, path, "r", &fp)); PetscCall(PetscSynchronizedFGets(comm, fp, char_array_len, line)); { char **array; PetscCall(PetscStrToArray(line, ' ', &ndims, &array)); for (PetscInt i = 0; i < ndims; i++) dims[i] = atoi(array[i]); PetscCall(PetscStrToArrayDestroy(ndims, array)); } if (ndims < 2) dims[1] = 1; // Assume 1 column of data is not otherwise specified *nynodes = dims[0]; PetscCall(PetscMalloc1(*nynodes, &node_locs)); for (PetscInt i = 0; i < dims[0]; i++) { char **array; PetscCall(PetscSynchronizedFGets(comm, fp, char_array_len, line)); PetscCall(PetscStrToArray(line, ' ', &ndims, &array)); PetscCheck(ndims == dims[1], comm, PETSC_ERR_FILE_UNEXPECTED, "Line %" PetscInt_FMT " of %s does not contain correct number of columns (%d instead of %d)", i, path, ndims, dims[1]); node_locs[i] = (PetscReal)atof(array[0]); PetscCall(PetscStrToArrayDestroy(ndims, array)); } PetscCall(PetscFClose(comm, fp)); *pynodes = node_locs; PetscFunctionReturn(PETSC_SUCCESS); } /* \brief Modify the domain and mesh for blasius * * Modifies mesh such that `N` elements are within `refine_height` with a geometric growth ratio of `growth`. Excess elements are then distributed * linearly in logspace to the top surface. * * The top surface is also angled downwards, so that it may be used as an outflow. * It's angle is controlled by `top_angle` (in units of degrees). * * If `node_locs` is not NULL, then the nodes will be placed at `node_locs` locations. * If it is NULL, then the modified coordinate values will be set in the array, along with `num_node_locs`. */ static PetscErrorCode ModifyMesh(MPI_Comm comm, DM dm, PetscInt dim, PetscReal growth, PetscInt N, PetscReal refine_height, PetscReal top_angle, PetscReal *node_locs[], PetscInt *num_node_locs) { PetscInt narr, ncoords; PetscReal domain_min[3], domain_max[3], domain_size[3]; PetscScalar *arr_coords; Vec vec_coords; PetscFunctionBeginUser; PetscReal angle_coeff = tan(top_angle * (M_PI / 180)); // Get domain boundary information PetscCall(DMGetBoundingBox(dm, domain_min, domain_max)); for (PetscInt i = 0; i < 3; i++) domain_size[i] = domain_max[i] - domain_min[i]; // Get coords array from DM PetscCall(DMGetCoordinatesLocal(dm, &vec_coords)); PetscCall(VecGetLocalSize(vec_coords, &narr)); PetscCall(VecGetArray(vec_coords, &arr_coords)); PetscScalar(*coords)[dim] = (PetscScalar(*)[dim])arr_coords; ncoords = narr / dim; // Get mesh information PetscInt nmax = 3, faces[3]; PetscCall(PetscOptionsGetIntArray(NULL, NULL, "-dm_plex_box_faces", faces, &nmax, NULL)); // Get element size of the box mesh, for indexing each node const PetscReal dybox = domain_size[1] / faces[1]; if (!*node_locs) { // Calculate the first element height PetscReal dy1 = refine_height * (growth - 1) / (pow(growth, N) - 1); // Calculate log of sizing outside BL PetscReal logdy = (log(domain_max[1]) - log(refine_height)) / (faces[1] - N); *num_node_locs = faces[1] + 1; PetscReal *temp_node_locs; PetscCall(PetscMalloc1(*num_node_locs, &temp_node_locs)); for (PetscInt i = 0; i < ncoords; i++) { PetscInt y_box_index = round(coords[i][1] / dybox); if (y_box_index <= N) { coords[i][1] = (1 - (coords[i][0] - domain_min[0]) * angle_coeff / domain_max[1]) * dy1 * (pow(growth, coords[i][1] / dybox) - 1) / (growth - 1); } else { PetscInt j = y_box_index - N; coords[i][1] = (1 - (coords[i][0] - domain_min[0]) * angle_coeff / domain_max[1]) * exp(log(refine_height) + logdy * j); } if (coords[i][0] == domain_min[0] && coords[i][2] == domain_min[2]) temp_node_locs[y_box_index] = coords[i][1]; } *node_locs = temp_node_locs; } else { PetscCheck(*num_node_locs >= faces[1] + 1, comm, PETSC_ERR_FILE_UNEXPECTED, "The y_node_locs_path has too few locations; There are %" PetscInt_FMT " + 1 nodes, but only %" PetscInt_FMT " locations given", faces[1] + 1, *num_node_locs); if (*num_node_locs > faces[1] + 1) { PetscCall(PetscPrintf(comm, "WARNING: y_node_locs_path has more locations (%" PetscInt_FMT ") " "than the mesh has nodes (%" PetscInt_FMT "). This maybe unintended.\n", *num_node_locs, faces[1] + 1)); } PetscScalar max_y = (*node_locs)[faces[1]]; for (PetscInt i = 0; i < ncoords; i++) { // Determine which y-node we're at PetscInt y_box_index = round(coords[i][1] / dybox); coords[i][1] = (1 - (coords[i][0] - domain_min[0]) * angle_coeff / max_y) * (*node_locs)[y_box_index]; } } PetscCall(VecRestoreArray(vec_coords, &arr_coords)); PetscCall(DMSetCoordinatesLocal(dm, vec_coords)); PetscFunctionReturn(PETSC_SUCCESS); } PetscErrorCode NS_BLASIUS(ProblemData problem, DM dm, void *ctx, SimpleBC bc) { User user = *(User *)ctx; MPI_Comm comm = user->comm; Ceed ceed = user->ceed; PetscBool use_stg = PETSC_FALSE; BlasiusContext blasius_ctx; NewtonianIdealGasContext newtonian_ig_ctx; CeedQFunctionContext blasius_context; PetscFunctionBeginUser; PetscCall(NS_NEWTONIAN_IG(problem, dm, ctx, bc)); PetscCall(PetscCalloc1(1, &blasius_ctx)); // ------------------------------------------------------ // SET UP Blasius // ------------------------------------------------------ problem->ics.qfunction = ICsBlasius; problem->ics.qfunction_loc = ICsBlasius_loc; CeedScalar U_inf = 40; // m/s CeedScalar T_inf = 288.; // K CeedScalar T_wall = 288.; // K CeedScalar delta0 = 4.2e-3; // m CeedScalar P_inf = 1.01e5; // Pa PetscInt N = 20; // Number of Chebyshev terms PetscBool weakT = PETSC_FALSE; // weak density or temperature PetscReal mesh_refine_height = 5.9e-4; // m PetscReal mesh_growth = 1.08; // [-] PetscInt mesh_Ndelta = 45; // [-] PetscReal mesh_top_angle = 5; // degrees char mesh_ynodes_path[PETSC_MAX_PATH_LEN] = ""; PetscBool P0_set; PetscOptionsBegin(comm, NULL, "Options for BLASIUS problem", NULL); PetscCall(PetscOptionsBool("-weakT", "Change from rho weak to T weak at inflow", NULL, weakT, &weakT, NULL)); PetscCall(PetscOptionsScalar("-velocity_infinity", "Velocity at boundary layer edge", NULL, U_inf, &U_inf, NULL)); PetscCall(PetscOptionsScalar("-temperature_infinity", "Temperature at boundary layer edge", NULL, T_inf, &T_inf, NULL)); PetscCall(PetscOptionsHasName(NULL, NULL, "-P0", &P0_set)); // For maintaining behavior of -P0 flag (which is deprecated) PetscCall( PetscOptionsDeprecated("-P0", "-pressure_infinity", "libCEED 0.12.0", "Use -pressure_infinity to set pressure at boundary layer edge and -idl_pressure to set the IDL reference pressure")); PetscCall(PetscOptionsScalar("-pressure_infinity", "Pressure at boundary layer edge", NULL, P_inf, &P_inf, NULL)); PetscCall(PetscOptionsScalar("-temperature_wall", "Temperature at wall", NULL, T_wall, &T_wall, NULL)); PetscCall(PetscOptionsScalar("-delta0", "Boundary layer height at inflow", NULL, delta0, &delta0, NULL)); PetscCall(PetscOptionsInt("-n_chebyshev", "Number of Chebyshev terms", NULL, N, &N, NULL)); PetscCheck(3 <= N && N <= BLASIUS_MAX_N_CHEBYSHEV, comm, PETSC_ERR_ARG_OUTOFRANGE, "-n_chebyshev %" PetscInt_FMT " must be in range [3, %d]", N, BLASIUS_MAX_N_CHEBYSHEV); if (user->app_ctx->mesh_transform_type == MESH_TRANSFORM_PLATEMESH) { PetscCall(PetscOptionsBoundedInt("-platemesh_Ndelta", "Velocity at boundary layer edge", NULL, mesh_Ndelta, &mesh_Ndelta, NULL, 1)); PetscCall(PetscOptionsScalar("-platemesh_refine_height", "Height of boundary layer mesh refinement", NULL, mesh_refine_height, &mesh_refine_height, NULL)); PetscCall(PetscOptionsScalar("-platemesh_growth", "Geometric growth rate of boundary layer mesh", NULL, mesh_growth, &mesh_growth, NULL)); PetscCall(PetscOptionsScalar("-platemesh_top_angle", "Geometric top_angle rate of boundary layer mesh", NULL, mesh_top_angle, &mesh_top_angle, NULL)); PetscCall(PetscOptionsString("-platemesh_y_node_locs_path", "Path to file with y node locations. " "If empty, will use the algorithmic mesh warping.", NULL, mesh_ynodes_path, mesh_ynodes_path, sizeof(mesh_ynodes_path), NULL)); } PetscCall(PetscOptionsBool("-stg_use", "Use STG inflow boundary condition", NULL, use_stg, &use_stg, NULL)); PetscOptionsEnd(); PetscScalar meter = user->units->meter; PetscScalar second = user->units->second; PetscScalar Kelvin = user->units->Kelvin; PetscScalar Pascal = user->units->Pascal; T_inf *= Kelvin; T_wall *= Kelvin; P_inf *= Pascal; U_inf *= meter / second; delta0 *= meter; if (user->app_ctx->mesh_transform_type == MESH_TRANSFORM_PLATEMESH) { PetscReal *mesh_ynodes = NULL; PetscInt mesh_nynodes = 0; if (strcmp(mesh_ynodes_path, "")) PetscCall(GetYNodeLocs(comm, mesh_ynodes_path, &mesh_ynodes, &mesh_nynodes)); PetscCall(ModifyMesh(comm, dm, problem->dim, mesh_growth, mesh_Ndelta, mesh_refine_height, mesh_top_angle, &mesh_ynodes, &mesh_nynodes)); PetscCall(PetscFree(mesh_ynodes)); } // Some properties depend on parameters from NewtonianIdealGas PetscCallCeed(ceed, CeedQFunctionContextGetData(problem->apply_vol_rhs.qfunction_context, CEED_MEM_HOST, &newtonian_ig_ctx)); StatePrimitive Y_inf = { .pressure = P_inf, .velocity = {U_inf, 0, 0}, .temperature = T_inf }; State S_infty = StateFromPrimitive(newtonian_ig_ctx, Y_inf); blasius_ctx->weakT = weakT; blasius_ctx->T_wall = T_wall; blasius_ctx->delta0 = delta0; blasius_ctx->S_infty = S_infty; blasius_ctx->n_cheb = N; blasius_ctx->implicit = user->phys->implicit; if (P0_set) newtonian_ig_ctx->idl_pressure = P_inf; // For maintaining behavior of -P0 flag (which is deprecated) blasius_ctx->newtonian_ctx = *newtonian_ig_ctx; { PetscReal domain_min[3], domain_max[3]; PetscCall(DMGetBoundingBox(dm, domain_min, domain_max)); blasius_ctx->x_inflow = domain_min[0]; blasius_ctx->eta_max = 5 * domain_max[1] / blasius_ctx->delta0; } PetscBool diff_filter_mms = PETSC_FALSE; PetscCall(PetscOptionsGetBool(NULL, NULL, "-diff_filter_mms", &diff_filter_mms, NULL)); if (!use_stg && !diff_filter_mms) PetscCall(ComputeChebyshevCoefficients(blasius_ctx)); PetscCallCeed(ceed, CeedQFunctionContextRestoreData(problem->apply_vol_rhs.qfunction_context, &newtonian_ig_ctx)); PetscCallCeed(ceed, CeedQFunctionContextCreate(user->ceed, &blasius_context)); PetscCallCeed(ceed, CeedQFunctionContextSetData(blasius_context, CEED_MEM_HOST, CEED_USE_POINTER, sizeof(*blasius_ctx), blasius_ctx)); PetscCallCeed(ceed, CeedQFunctionContextSetDataDestroy(blasius_context, CEED_MEM_HOST, FreeContextPetsc)); PetscCallCeed(ceed, CeedQFunctionContextDestroy(&problem->ics.qfunction_context)); problem->ics.qfunction_context = blasius_context; if (use_stg) { PetscCall(SetupStg(comm, dm, problem, user, weakT, S_infty.Y.temperature, S_infty.Y.pressure)); } else if (diff_filter_mms) { PetscCall(DifferentialFilterMmsICSetup(problem)); } else { PetscCheck((user->phys->state_var == STATEVAR_CONSERVATIVE) || (user->app_ctx->test_type == TESTTYPE_DIFF_FILTER), user->comm, PETSC_ERR_ARG_INCOMP, "Can only use conservative variables with Blasius and weak inflow"); problem->apply_inflow.qfunction = Blasius_Inflow; problem->apply_inflow.qfunction_loc = Blasius_Inflow_loc; problem->apply_inflow_jacobian.qfunction = Blasius_Inflow_Jacobian; problem->apply_inflow_jacobian.qfunction_loc = Blasius_Inflow_Jacobian_loc; PetscCallCeed(ceed, CeedQFunctionContextReferenceCopy(blasius_context, &problem->apply_inflow.qfunction_context)); PetscCallCeed(ceed, CeedQFunctionContextReferenceCopy(blasius_context, &problem->apply_inflow_jacobian.qfunction_context)); } PetscFunctionReturn(PETSC_SUCCESS); }