1 // Copyright (c) 2017-2022, Lawrence Livermore National Security, LLC and other CEED contributors. 2 // All Rights Reserved. See the top-level LICENSE and NOTICE files for details. 3 // 4 // SPDX-License-Identifier: BSD-2-Clause 5 // 6 // This file is part of CEED: http://github.com/ceed 7 8 /// @file 9 /// Utility functions for setting up Blasius Boundary Layer 10 11 #include "../navierstokes.h" 12 #include "../qfunctions/blasius.h" 13 #include "stg_shur14.h" 14 15 PetscErrorCode CompressibleBlasiusResidual(SNES snes, Vec X, Vec R, void *ctx) { 16 const BlasiusContext blasius = (BlasiusContext)ctx; 17 const PetscScalar *Tf, *Th; // Chebyshev coefficients 18 PetscScalar *r, f[4], h[4]; 19 PetscInt N = blasius->n_cheb; 20 PetscScalar Ma = Mach(&blasius->newtonian_ctx, blasius->T_inf, blasius->U_inf), 21 Pr = Prandtl(&blasius->newtonian_ctx), 22 gamma = HeatCapacityRatio(&blasius->newtonian_ctx); 23 PetscFunctionBegin; 24 PetscCall(VecGetArrayRead(X, &Tf)); 25 Th = Tf + N; 26 PetscCall(VecGetArray(R, &r)); 27 28 // Left boundary conditions f = f' = 0 29 ChebyshevEval(N, Tf, -1., blasius->eta_max, f); 30 r[0] = f[0]; 31 r[1] = f[1]; 32 33 // f - right end boundary condition 34 ChebyshevEval(N, Tf, 1., blasius->eta_max, f); 35 r[2] = f[1] - 1.; 36 37 for (int i=0; i<N-3; i++) { 38 ChebyshevEval(N, Tf, blasius->X[i], blasius->eta_max, f); 39 ChebyshevEval(N-1, Th, blasius->X[i], blasius->eta_max, h); 40 // mu and rho generally depend on h. We naively assume constant mu. 41 // For an ideal gas at constant pressure, density is inversely proportional to enthalpy. 42 // The *_tilde values are *relative* to their freestream values, and we proved first derivatives here. 43 const PetscScalar mu_tilde[2] = {1, 0}; 44 const PetscScalar rho_tilde[2] = {1 / h[0], -h[1] / PetscSqr(h[0])}; 45 const PetscScalar mu_rho_tilde[2] = { 46 mu_tilde[0] *rho_tilde[0], 47 mu_tilde[1] *rho_tilde[0] + mu_tilde[0] *rho_tilde[1], 48 }; 49 r[3+i] = 2*(mu_rho_tilde[0] * f[3] + mu_rho_tilde[1] * f[2]) + f[2] * f[0]; 50 r[N+2+i] = (mu_rho_tilde[0] * h[2] + mu_rho_tilde[1] * h[1]) + Pr * f[0] * h[1] 51 + Pr * (gamma - 1) * mu_rho_tilde[0] * PetscSqr(Ma * f[2]); 52 } 53 54 // h - left end boundary condition 55 ChebyshevEval(N-1, Th, -1., blasius->eta_max, h); 56 r[N] = h[0] - blasius->T_wall / blasius->T_inf; 57 58 // h - right end boundary condition 59 ChebyshevEval(N-1, Th, 1., blasius->eta_max, h); 60 r[N+1] = h[0] - 1.; 61 62 // Restore vectors 63 PetscCall(VecRestoreArrayRead(X, &Tf)); 64 PetscCall(VecRestoreArray(R, &r)); 65 PetscFunctionReturn(0); 66 } 67 68 PetscErrorCode ComputeChebyshevCoefficients(BlasiusContext blasius) { 69 SNES snes; 70 Vec sol, res; 71 PetscReal *w; 72 PetscInt N = blasius->n_cheb; 73 SNESConvergedReason reason; 74 const PetscScalar *cheb_coefs; 75 PetscFunctionBegin; 76 77 // Allocate memory 78 PetscCall(PetscMalloc2(N-3, &blasius->X, N-3, &w)); 79 PetscCall(PetscDTGaussQuadrature(N-3, -1., 1., blasius->X, w)); 80 81 // Snes solve 82 PetscCall(SNESCreate(PETSC_COMM_SELF, &snes)); 83 PetscCall(VecCreate(PETSC_COMM_SELF, &sol)); 84 PetscCall(VecSetSizes(sol, PETSC_DECIDE, 2*N-1)); 85 PetscCall(VecSetFromOptions(sol)); 86 // Constant relative enthalpy 1 as initial guess 87 PetscCall(VecSetValue(sol, N, 1., INSERT_VALUES)); 88 PetscCall(VecDuplicate(sol, &res)); 89 PetscCall(SNESSetFunction(snes, res, CompressibleBlasiusResidual, blasius)); 90 PetscCall(SNESSetOptionsPrefix(snes, "chebyshev_")); 91 PetscCall(SNESSetFromOptions(snes)); 92 PetscCall(SNESSolve(snes, NULL, sol)); 93 PetscCall(SNESGetConvergedReason(snes, &reason)); 94 if (reason < 0) 95 SETERRQ(PETSC_COMM_WORLD, PETSC_ERR_CONV_FAILED, 96 "The Chebyshev solve failed.\n"); 97 98 // Assign Chebyshev coefficients 99 PetscCall(VecGetArrayRead(sol, &cheb_coefs)); 100 for (int i=0; i<N; i++) blasius->Tf_cheb[i] = cheb_coefs[i]; 101 for (int i=0; i<N-1; i++) blasius->Th_cheb[i] = cheb_coefs[i+N]; 102 103 // Destroy objects 104 PetscCall(PetscFree2(blasius->X, w)); 105 PetscCall(VecDestroy(&sol)); 106 PetscCall(VecDestroy(&res)); 107 PetscCall(SNESDestroy(&snes)); 108 PetscFunctionReturn(0); 109 } 110 111 static PetscErrorCode GetYNodeLocs(const MPI_Comm comm, 112 const char path[PETSC_MAX_PATH_LEN], PetscReal **pynodes, 113 PetscInt *nynodes) { 114 PetscErrorCode ierr; 115 PetscInt ndims, dims[2]; 116 FILE *fp; 117 const PetscInt char_array_len = 512; 118 char line[char_array_len]; 119 char **array; 120 PetscReal *node_locs; 121 PetscFunctionBeginUser; 122 123 ierr = PetscFOpen(comm, path, "r", &fp); CHKERRQ(ierr); 124 ierr = PetscSynchronizedFGets(comm, fp, char_array_len, line); CHKERRQ(ierr); 125 ierr = PetscStrToArray(line, ' ', &ndims, &array); CHKERRQ(ierr); 126 127 for (PetscInt i=0; i<ndims; i++) dims[i] = atoi(array[i]); 128 if (ndims<2) dims[1] = 1; // Assume 1 column of data is not otherwise specified 129 *nynodes = dims[0]; 130 ierr = PetscMalloc1(*nynodes, &node_locs); CHKERRQ(ierr); 131 132 for (PetscInt i=0; i<dims[0]; i++) { 133 ierr = PetscSynchronizedFGets(comm, fp, char_array_len, line); CHKERRQ(ierr); 134 ierr = PetscStrToArray(line, ' ', &ndims, &array); CHKERRQ(ierr); 135 if (ndims < dims[1]) SETERRQ(comm, -1, 136 "Line %" PetscInt_FMT" of %s does not contain enough columns (%" 137 PetscInt_FMT" instead of %" PetscInt_FMT ")", i, 138 path, ndims, dims[1]); 139 140 node_locs[i] = (PetscReal) atof(array[0]); 141 } 142 ierr = PetscFClose(comm, fp); CHKERRQ(ierr); 143 *pynodes = node_locs; 144 PetscFunctionReturn(0); 145 } 146 147 /* \brief Modify the domain and mesh for blasius 148 * 149 * Modifies mesh such that `N` elements are within `refine_height` with a 150 * geometric growth ratio of `growth`. Excess elements are then distributed 151 * linearly in logspace to the top surface. 152 * 153 * The top surface is also angled downwards, so that it may be used as an 154 * outflow. It's angle is controlled by `top_angle` (in units of degrees). 155 * 156 * If `node_locs` is not NULL, then the nodes will be placed at `node_locs` 157 * locations. If it is NULL, then the modified coordinate values will be set in 158 * the array, along with `num_node_locs`. 159 */ 160 static PetscErrorCode ModifyMesh(MPI_Comm comm, DM dm, PetscInt dim, 161 PetscReal growth, PetscInt N, 162 PetscReal refine_height, PetscReal top_angle, 163 PetscReal *node_locs[], PetscInt *num_node_locs) { 164 PetscInt ierr, narr, ncoords; 165 PetscReal domain_min[3], domain_max[3], domain_size[3]; 166 PetscScalar *arr_coords; 167 Vec vec_coords; 168 PetscFunctionBeginUser; 169 170 PetscReal angle_coeff = tan(top_angle*(M_PI/180)); 171 172 // Get domain boundary information 173 ierr = DMGetBoundingBox(dm, domain_min, domain_max); CHKERRQ(ierr); 174 for (PetscInt i=0; i<3; i++) domain_size[i] = domain_max[i] - domain_min[i]; 175 176 // Get coords array from DM 177 ierr = DMGetCoordinatesLocal(dm, &vec_coords); CHKERRQ(ierr); 178 ierr = VecGetLocalSize(vec_coords, &narr); CHKERRQ(ierr); 179 ierr = VecGetArray(vec_coords, &arr_coords); CHKERRQ(ierr); 180 181 PetscScalar (*coords)[dim] = (PetscScalar(*)[dim]) arr_coords; 182 ncoords = narr/dim; 183 184 // Get mesh information 185 PetscInt nmax = 3, faces[3]; 186 ierr = PetscOptionsGetIntArray(NULL, NULL, "-dm_plex_box_faces", faces, &nmax, 187 NULL); CHKERRQ(ierr); 188 // Get element size of the box mesh, for indexing each node 189 const PetscReal dybox = domain_size[1]/faces[1]; 190 191 if (!*node_locs) { 192 // Calculate the first element height 193 PetscReal dy1 = refine_height*(growth-1)/(pow(growth, N)-1); 194 195 // Calculate log of sizing outside BL 196 PetscReal logdy = (log(domain_max[1]) - log(refine_height)) / (faces[1] - N); 197 198 *num_node_locs = faces[1] + 1; 199 PetscReal *temp_node_locs; 200 ierr = PetscMalloc1(*num_node_locs, &temp_node_locs); CHKERRQ(ierr); 201 202 for (PetscInt i=0; i<ncoords; i++) { 203 PetscInt y_box_index = round(coords[i][1]/dybox); 204 if (y_box_index <= N) { 205 coords[i][1] = (1 - (coords[i][0] - domain_min[0])*angle_coeff/domain_max[1]) 206 * dy1 * (pow(growth, coords[i][1]/dybox)-1)/(growth-1); 207 } else { 208 PetscInt j = y_box_index - N; 209 coords[i][1] = (1 - (coords[i][0] - domain_min[0])*angle_coeff/domain_max[1]) 210 * exp(log(refine_height) + logdy*j); 211 } 212 if (coords[i][0] == domain_min[0] && coords[i][2] == domain_min[2]) 213 temp_node_locs[y_box_index] = coords[i][1]; 214 } 215 216 *node_locs = temp_node_locs; 217 } else { 218 // Error checking 219 if (*num_node_locs < faces[1] +1) 220 SETERRQ(comm, -1, "The y_node_locs_path has too few locations; " 221 "There are %d + 1 nodes, but only %d locations given", 222 faces[1]+1, *num_node_locs); 223 if (*num_node_locs > faces[1] +1) { 224 ierr = PetscPrintf(comm, "WARNING: y_node_locs_path has more locations (%d) " 225 "than the mesh has nodes (%d). This maybe unintended.\n", 226 *num_node_locs, faces[1]+1); CHKERRQ(ierr); 227 } 228 PetscScalar max_y = (*node_locs)[faces[1]]; 229 230 for (PetscInt i=0; i<ncoords; i++) { 231 // Determine which y-node we're at 232 PetscInt y_box_index = round(coords[i][1]/dybox); 233 coords[i][1] = (1 - (coords[i][0] - domain_min[0])*angle_coeff/max_y) 234 * (*node_locs)[y_box_index]; 235 } 236 } 237 238 ierr = VecRestoreArray(vec_coords, &arr_coords); CHKERRQ(ierr); 239 ierr = DMSetCoordinatesLocal(dm, vec_coords); CHKERRQ(ierr); 240 241 PetscFunctionReturn(0); 242 } 243 244 PetscErrorCode NS_BLASIUS(ProblemData *problem, DM dm, void *ctx) { 245 246 PetscInt ierr; 247 User user = *(User *)ctx; 248 MPI_Comm comm = PETSC_COMM_WORLD; 249 PetscBool use_stg = PETSC_FALSE; 250 BlasiusContext blasius_ctx; 251 NewtonianIdealGasContext newtonian_ig_ctx; 252 CeedQFunctionContext blasius_context; 253 254 PetscFunctionBeginUser; 255 ierr = NS_NEWTONIAN_IG(problem, dm, ctx); CHKERRQ(ierr); 256 ierr = PetscCalloc1(1, &blasius_ctx); CHKERRQ(ierr); 257 258 // ------------------------------------------------------ 259 // SET UP Blasius 260 // ------------------------------------------------------ 261 problem->ics.qfunction = ICsBlasius; 262 problem->ics.qfunction_loc = ICsBlasius_loc; 263 264 CeedScalar U_inf = 40; // m/s 265 CeedScalar T_inf = 288.; // K 266 CeedScalar T_wall = 288.; // K 267 CeedScalar delta0 = 4.2e-3; // m 268 CeedScalar P0 = 1.01e5; // Pa 269 CeedInt N = 20; // Number of Chebyshev terms 270 PetscBool weakT = PETSC_FALSE; // weak density or temperature 271 PetscReal mesh_refine_height = 5.9e-4; // m 272 PetscReal mesh_growth = 1.08; // [-] 273 PetscInt mesh_Ndelta = 45; // [-] 274 PetscReal mesh_top_angle = 5; // degrees 275 char mesh_ynodes_path[PETSC_MAX_PATH_LEN] = ""; 276 277 PetscOptionsBegin(comm, NULL, "Options for BLASIUS problem", NULL); 278 ierr = PetscOptionsBool("-weakT", "Change from rho weak to T weak at inflow", 279 NULL, weakT, &weakT, NULL); CHKERRQ(ierr); 280 ierr = PetscOptionsScalar("-velocity_infinity", 281 "Velocity at boundary layer edge", 282 NULL, U_inf, &U_inf, NULL); CHKERRQ(ierr); 283 ierr = PetscOptionsScalar("-temperature_infinity", 284 "Temperature at boundary layer edge", 285 NULL, T_inf, &T_inf, NULL); CHKERRQ(ierr); 286 ierr = PetscOptionsScalar("-temperature_wall", "Temperature at wall", 287 NULL, T_wall, &T_wall, NULL); CHKERRQ(ierr); 288 ierr = PetscOptionsScalar("-delta0", "Boundary layer height at inflow", 289 NULL, delta0, &delta0, NULL); CHKERRQ(ierr); 290 ierr = PetscOptionsScalar("-P0", "Pressure at outflow", 291 NULL, P0, &P0, NULL); CHKERRQ(ierr); 292 ierr = PetscOptionsInt("-n_chebyshev", "Number of Chebyshev terms", 293 NULL, N, &N, NULL); CHKERRQ(ierr); 294 PetscCheck(3 <= N && N <= BLASIUS_MAX_N_CHEBYSHEV, 295 comm, PETSC_ERR_ARG_OUTOFRANGE, 296 "-n_chebyshev %" PetscInt_FMT " must be in range [3, %d]", N, 297 BLASIUS_MAX_N_CHEBYSHEV); 298 ierr = PetscOptionsBoundedInt("-platemesh_Ndelta", 299 "Velocity at boundary layer edge", 300 NULL, mesh_Ndelta, &mesh_Ndelta, NULL, 1); CHKERRQ(ierr); 301 ierr = PetscOptionsScalar("-platemesh_refine_height", 302 "Height of boundary layer mesh refinement", 303 NULL, mesh_refine_height, &mesh_refine_height, NULL); CHKERRQ(ierr); 304 ierr = PetscOptionsScalar("-platemesh_growth", 305 "Geometric growth rate of boundary layer mesh", 306 NULL, mesh_growth, &mesh_growth, NULL); CHKERRQ(ierr); 307 ierr = PetscOptionsScalar("-platemesh_top_angle", 308 "Geometric top_angle rate of boundary layer mesh", 309 NULL, mesh_top_angle, &mesh_top_angle, NULL); CHKERRQ(ierr); 310 ierr = PetscOptionsString("-platemesh_y_node_locs_path", 311 "Path to file with y node locations. " 312 "If empty, will use the algorithmic mesh warping.", NULL, 313 mesh_ynodes_path, mesh_ynodes_path, 314 sizeof(mesh_ynodes_path), NULL); CHKERRQ(ierr); 315 ierr = PetscOptionsBool("-stg_use", "Use STG inflow boundary condition", 316 NULL, use_stg, &use_stg, NULL); CHKERRQ(ierr); 317 PetscOptionsEnd(); 318 319 PetscScalar meter = user->units->meter; 320 PetscScalar second = user->units->second; 321 PetscScalar Kelvin = user->units->Kelvin; 322 PetscScalar Pascal = user->units->Pascal; 323 324 T_inf *= Kelvin; 325 T_wall *= Kelvin; 326 P0 *= Pascal; 327 U_inf *= meter / second; 328 delta0 *= meter; 329 330 PetscReal *mesh_ynodes = NULL; 331 PetscInt mesh_nynodes = 0; 332 if (strcmp(mesh_ynodes_path, "")) { 333 ierr = GetYNodeLocs(comm, mesh_ynodes_path, &mesh_ynodes, &mesh_nynodes); 334 CHKERRQ(ierr); 335 } 336 ierr = ModifyMesh(comm, dm, problem->dim, mesh_growth, mesh_Ndelta, 337 mesh_refine_height, mesh_top_angle, &mesh_ynodes, 338 &mesh_nynodes); CHKERRQ(ierr); 339 340 // Some properties depend on parameters from NewtonianIdealGas 341 CeedQFunctionContextGetData(problem->apply_vol_rhs.qfunction_context, 342 CEED_MEM_HOST, &newtonian_ig_ctx); 343 344 blasius_ctx->weakT = weakT; 345 blasius_ctx->U_inf = U_inf; 346 blasius_ctx->T_inf = T_inf; 347 blasius_ctx->T_wall = T_wall; 348 blasius_ctx->delta0 = delta0; 349 blasius_ctx->P0 = P0; 350 blasius_ctx->n_cheb = N; 351 newtonian_ig_ctx->P0 = P0; 352 blasius_ctx->implicit = user->phys->implicit; 353 blasius_ctx->newtonian_ctx = *newtonian_ig_ctx; 354 355 { 356 PetscReal domain_min[3], domain_max[3]; 357 ierr = DMGetBoundingBox(dm, domain_min, domain_max); CHKERRQ(ierr); 358 blasius_ctx->x_inflow = domain_min[0]; 359 blasius_ctx->eta_max = 5 * domain_max[1] / blasius_ctx->delta0; 360 } 361 PetscCall(ComputeChebyshevCoefficients(blasius_ctx)); 362 363 CeedQFunctionContextRestoreData(problem->apply_vol_rhs.qfunction_context, 364 &newtonian_ig_ctx); 365 366 CeedQFunctionContextCreate(user->ceed, &blasius_context); 367 CeedQFunctionContextSetData(blasius_context, CEED_MEM_HOST, CEED_USE_POINTER, 368 sizeof(*blasius_ctx), blasius_ctx); 369 CeedQFunctionContextSetDataDestroy(blasius_context, CEED_MEM_HOST, 370 FreeContextPetsc); 371 372 CeedQFunctionContextDestroy(&problem->ics.qfunction_context); 373 problem->ics.qfunction_context = blasius_context; 374 if (use_stg) { 375 ierr = SetupSTG(comm, dm, problem, user, weakT, T_inf, P0, mesh_ynodes, 376 mesh_nynodes); CHKERRQ(ierr); 377 } else { 378 problem->apply_inflow.qfunction = Blasius_Inflow; 379 problem->apply_inflow.qfunction_loc = Blasius_Inflow_loc; 380 problem->apply_inflow_jacobian.qfunction = Blasius_Inflow_Jacobian; 381 problem->apply_inflow_jacobian.qfunction_loc = Blasius_Inflow_Jacobian_loc; 382 CeedQFunctionContextReferenceCopy(blasius_context, 383 &problem->apply_inflow.qfunction_context); 384 CeedQFunctionContextReferenceCopy(blasius_context, 385 &problem->apply_inflow_jacobian.qfunction_context); 386 } 387 ierr = PetscFree(mesh_ynodes); CHKERRQ(ierr); 388 PetscFunctionReturn(0); 389 } 390