1 // SPDX-FileCopyrightText: Copyright (c) 2017-2024, HONEE contributors. 2 // SPDX-License-Identifier: Apache-2.0 OR BSD-2-Clause 3 4 /// @file 5 /// Advection initial condition and operator for Navier-Stokes example using PETSc 6 #include <ceed.h> 7 #include <math.h> 8 9 #include "advection_types.h" 10 #include "newtonian_state.h" 11 #include "newtonian_types.h" 12 #include "stabilization_types.h" 13 #include "utils.h" 14 15 // ***************************************************************************** 16 // This QFunction sets the initial conditions and the boundary conditions 17 // for two test cases: ROTATION and TRANSLATION 18 // 19 // -- ROTATION (default) 20 // Initial Conditions: 21 // Mass Density: 22 // Constant mass density of 1.0 23 // Momentum Density: 24 // Rotational field in x,y 25 // Energy Density: 26 // Maximum of 1. x0 decreasing linearly to 0. as radial distance 27 // increases to (1.-r/rc), then 0. everywhere else 28 // 29 // Boundary Conditions: 30 // Mass Density: 31 // 0.0 flux 32 // Momentum Density: 33 // 0.0 34 // Energy Density: 35 // 0.0 flux 36 // 37 // -- TRANSLATION 38 // Initial Conditions: 39 // Mass Density: 40 // Constant mass density of 1.0 41 // Momentum Density: 42 // Constant rectilinear field in x,y 43 // Energy Density: 44 // Maximum of 1. x0 decreasing linearly to 0. as radial distance 45 // increases to (1.-r/rc), then 0. everywhere else 46 // 47 // Boundary Conditions: 48 // Mass Density: 49 // 0.0 flux 50 // Momentum Density: 51 // 0.0 52 // Energy Density: 53 // Inflow BCs: 54 // E = E_wind 55 // Outflow BCs: 56 // E = E(boundary) 57 // Both In/Outflow BCs for E are applied weakly in the 58 // QFunction "Advection2d_Sur" 59 // 60 // ***************************************************************************** 61 62 // ***************************************************************************** 63 // This helper function provides the exact, time-dependent solution and IC formulation for 2D advection 64 // ***************************************************************************** 65 CEED_QFUNCTION_HELPER int Exact_AdvectionGeneric(CeedInt dim, CeedScalar time, const CeedScalar X[], CeedInt Nf, CeedScalar q[], void *ctx) { 66 const SetupContextAdv context = (SetupContextAdv)ctx; 67 const CeedScalar rc = context->rc; 68 const CeedScalar lx = context->lx; 69 const CeedScalar ly = context->ly; 70 const CeedScalar lz = dim == 2 ? 0. : context->lz; 71 const CeedScalar *wind = context->wind; 72 73 const CeedScalar center[3] = {0.5 * lx, 0.5 * ly, 0.5 * lz}; 74 const CeedScalar theta = dim == 2 ? M_PI / 3 : M_PI; 75 const CeedScalar x0[3] = {center[0] + .25 * lx * cos(theta + time), center[1] + .25 * ly * sin(theta + time), 0.5 * lz}; 76 77 const CeedScalar x = X[0], y = X[1], z = dim == 2 ? 0. : X[2]; 78 79 switch (context->wind_type) { 80 case ADVDIF_WIND_ROTATION: 81 q[0] = 1.; 82 q[1] = -(y - center[1]); 83 q[2] = (x - center[0]); 84 q[3] = 0; 85 break; 86 case ADVDIF_WIND_TRANSLATION: 87 q[0] = 1.; 88 q[1] = wind[0]; 89 q[2] = wind[1]; 90 q[3] = dim == 2 ? 0. : wind[2]; 91 break; 92 case ADVDIF_WIND_BOUNDARY_LAYER: 93 q[0] = 1.; 94 q[1] = y / ly; 95 q[2] = 0.; 96 q[3] = 0.; 97 break; 98 } 99 100 switch (context->initial_condition_type) { 101 case ADVDIF_IC_BUBBLE_SPHERE: 102 case ADVDIF_IC_BUBBLE_CYLINDER: { 103 CeedScalar r = sqrt(Square(x - x0[0]) + Square(y - x0[1]) + Square(z - x0[2])); 104 105 switch (context->bubble_continuity_type) { 106 // original continuous, smooth shape 107 case ADVDIF_BUBBLE_CONTINUITY_SMOOTH: 108 q[4] = r <= rc ? (1. - r / rc) : 0.; 109 break; 110 // discontinuous, sharp back half shape 111 case ADVDIF_BUBBLE_CONTINUITY_BACK_SHARP: 112 q[4] = ((r <= rc) && (y < center[1])) ? (1. - r / rc) : 0.; 113 break; 114 // attempt to define a finite thickness that will get resolved under grid refinement 115 case ADVDIF_BUBBLE_CONTINUITY_THICK: 116 q[4] = ((r <= rc) && (y < center[1])) ? (1. - r / rc) * fmin(1.0, (center[1] - y) / 1.25) : 0.; 117 break; 118 case ADVDIF_BUBBLE_CONTINUITY_COSINE: 119 q[4] = r <= rc ? .5 + .5 * cos(r * M_PI / rc) : 0; 120 break; 121 } 122 break; 123 } 124 125 case ADVDIF_IC_COSINE_HILL: { 126 CeedScalar r = sqrt(Square(x - center[0]) + Square(y - center[1])); 127 CeedScalar half_width = context->lx / 2; 128 q[4] = r > half_width ? 0. : cos(2 * M_PI * r / half_width + M_PI) + 1.; 129 } break; 130 131 case ADVDIF_IC_SKEW: { 132 CeedScalar skewed_barrier[3] = {wind[0], wind[1], 0}; 133 CeedScalar inflow_to_point[3] = {x - context->lx / 2, y, 0}; 134 CeedScalar cross_product[3] = {0}; 135 const CeedScalar boundary_threshold = 20 * CEED_EPSILON; 136 Cross3(skewed_barrier, inflow_to_point, cross_product); 137 138 q[4] = cross_product[2] > boundary_threshold ? 0 : 1; 139 if ((x < boundary_threshold && wind[0] < boundary_threshold) || // outflow at -x boundary 140 (y < boundary_threshold && wind[1] < boundary_threshold) || // outflow at -y boundary 141 (x > context->lx - boundary_threshold && wind[0] > boundary_threshold) || // outflow at +x boundary 142 (y > context->ly - boundary_threshold && wind[1] > boundary_threshold) // outflow at +y boundary 143 ) { 144 q[4] = 0; 145 } 146 } break; 147 148 case ADVDIF_IC_WAVE: { 149 CeedScalar theta = context->wave_frequency * DotN(X, wind, dim) + context->wave_phase; 150 switch (context->wave_type) { 151 case ADVDIF_WAVE_SINE: 152 q[4] = sin(theta); 153 break; 154 case ADVDIF_WAVE_SQUARE: 155 q[4] = sin(theta) > 100 * CEED_EPSILON ? 1 : -1; 156 break; 157 } 158 } break; 159 case ADVDIF_IC_BOUNDARY_LAYER: { 160 const CeedScalar boundary_threshold = 20 * CEED_EPSILON; 161 162 if ((x < boundary_threshold) || (y > ly - boundary_threshold)) { 163 q[4] = 1; // inflow and top boundary 164 } else if (y < boundary_threshold) { 165 q[4] = 0; // lower wall 166 } else { 167 q[4] = y / ly; // interior and outflow boundary 168 } 169 } break; 170 } 171 return 0; 172 } 173 174 // ***************************************************************************** 175 // This QFunction sets the initial conditions for 3D advection 176 // ***************************************************************************** 177 CEED_QFUNCTION(ICsAdvection)(void *ctx, CeedInt Q, const CeedScalar *const *in, CeedScalar *const *out) { 178 const CeedScalar(*X)[CEED_Q_VLA] = (const CeedScalar(*)[CEED_Q_VLA])in[0]; 179 CeedScalar(*q0)[CEED_Q_VLA] = (CeedScalar(*)[CEED_Q_VLA])out[0]; 180 181 CeedPragmaSIMD for (CeedInt i = 0; i < Q; i++) { 182 const CeedScalar x[] = {X[0][i], X[1][i], X[2][i]}; 183 CeedScalar q[5] = {0.}; 184 185 Exact_AdvectionGeneric(3, 0., x, 5, q, ctx); 186 for (CeedInt j = 0; j < 5; j++) q0[j][i] = q[j]; 187 } 188 return 0; 189 } 190 191 // ***************************************************************************** 192 // This QFunction sets the initial conditions for 2D advection 193 // ***************************************************************************** 194 CEED_QFUNCTION(ICsAdvection2d)(void *ctx, CeedInt Q, const CeedScalar *const *in, CeedScalar *const *out) { 195 const CeedScalar(*X)[CEED_Q_VLA] = (const CeedScalar(*)[CEED_Q_VLA])in[0]; 196 CeedScalar(*q0)[CEED_Q_VLA] = (CeedScalar(*)[CEED_Q_VLA])out[0]; 197 const SetupContextAdv context = (SetupContextAdv)ctx; 198 199 CeedPragmaSIMD for (CeedInt i = 0; i < Q; i++) { 200 const CeedScalar x[] = {X[0][i], X[1][i]}; 201 CeedScalar q[5] = {0.}; 202 203 Exact_AdvectionGeneric(2, context->time, x, 5, q, ctx); 204 for (CeedInt j = 0; j < 5; j++) q0[j][i] = q[j]; 205 } 206 return 0; 207 } 208 209 CEED_QFUNCTION_HELPER void StatePhysicalGradientFromReference_ND(CeedInt N, CeedInt Q, CeedInt i, NewtonianIdealGasContext gas, State s, 210 StateVariable state_var, const CeedScalar *grad_q, const CeedScalar *dXdx, 211 State *grad_s) { 212 switch (N) { 213 case 2: { 214 for (CeedInt k = 0; k < 2; k++) { 215 CeedScalar dqi[5]; 216 for (CeedInt j = 0; j < 5; j++) { 217 dqi[j] = grad_q[(Q * 5) * 0 + Q * j + i] * dXdx[0 * N + k] + grad_q[(Q * 5) * 1 + Q * j + i] * dXdx[1 * N + k]; 218 } 219 grad_s[k] = StateFromQ_fwd(gas, s, dqi, state_var); 220 } 221 CeedScalar U[5] = {0.}; 222 grad_s[2] = StateFromU(gas, U); 223 } break; 224 case 3: 225 // Cannot directly use StatePhysicalGradientFromReference helper functions due to SYCL online compiler incompatabilities 226 for (CeedInt k = 0; k < 3; k++) { 227 CeedScalar dqi[5]; 228 for (CeedInt j = 0; j < 5; j++) { 229 dqi[j] = grad_q[(Q * 5) * 0 + Q * j + i] * dXdx[0 * N + k] + grad_q[(Q * 5) * 1 + Q * j + i] * dXdx[1 * N + k] + 230 grad_q[(Q * 5) * 2 + Q * j + i] * dXdx[2 * N + k]; 231 } 232 grad_s[k] = StateFromQ_fwd(gas, s, dqi, state_var); 233 } 234 break; 235 } 236 } 237 238 // @brief Calculate the stabilization constant \tau 239 CEED_QFUNCTION_HELPER CeedScalar Tau(AdvectionContext context, const State s, const CeedScalar *dXdx, CeedInt dim) { 240 switch (context->stabilization_tau) { 241 case STAB_TAU_CTAU: { 242 CeedScalar uX[3] = {0.}; 243 244 MatVecNM(dXdx, s.Y.velocity, dim, dim, CEED_NOTRANSPOSE, uX); 245 return context->CtauS / sqrt(DotN(uX, uX, dim)); 246 } break; 247 case STAB_TAU_ADVDIFF_SHAKIB: { 248 CeedScalar gijd_mat[9] = {0.}, gij_uj[3] = {0.}; 249 250 MatMatN(dXdx, dXdx, dim, CEED_TRANSPOSE, CEED_NOTRANSPOSE, gijd_mat); 251 MatVecNM(gijd_mat, s.Y.velocity, dim, dim, CEED_NOTRANSPOSE, gij_uj); 252 return 1 / sqrt(Square(2 * context->Ctau_t / context->dt) + DotN(s.Y.velocity, gij_uj, dim) * context->Ctau_a + 253 Square(context->diffusion_coeff) * DotN(gijd_mat, gijd_mat, dim * dim) * context->Ctau_d); 254 } break; 255 default: 256 return 0.; 257 } 258 } 259 260 // ***************************************************************************** 261 // This QFunction implements Advection for implicit time stepping method 262 // ***************************************************************************** 263 CEED_QFUNCTION_HELPER int IFunction_AdvectionGeneric(void *ctx, CeedInt Q, const CeedScalar *const *in, CeedScalar *const *out, CeedInt dim) { 264 AdvectionContext context = (AdvectionContext)ctx; 265 266 const CeedScalar(*q)[CEED_Q_VLA] = (const CeedScalar(*)[CEED_Q_VLA])in[0]; 267 const CeedScalar(*grad_q) = in[1]; 268 const CeedScalar(*q_dot)[CEED_Q_VLA] = (const CeedScalar(*)[CEED_Q_VLA])in[2]; 269 const CeedScalar(*q_data) = in[3]; 270 const CeedScalar(*divFdiff) = context->divFdiff_method != DIV_DIFF_FLUX_PROJ_NONE ? in[5] : NULL; 271 272 CeedScalar(*v)[CEED_Q_VLA] = (CeedScalar(*)[CEED_Q_VLA])out[0]; 273 CeedScalar(*grad_v)[5][CEED_Q_VLA] = (CeedScalar(*)[5][CEED_Q_VLA])out[1]; 274 275 NewtonianIdealGasContext gas; 276 struct NewtonianIdealGasContext_ gas_struct = {0}; 277 gas = &gas_struct; 278 279 CeedPragmaSIMD for (CeedInt i = 0; i < Q; i++) { 280 const CeedScalar qi[5] = {q[0][i], q[1][i], q[2][i], q[3][i], q[4][i]}; 281 const State s = StateFromU(gas, qi); 282 283 CeedScalar wdetJ, dXdx[9]; 284 QdataUnpack_ND(dim, Q, i, q_data, &wdetJ, dXdx); 285 State grad_s[3]; 286 StatePhysicalGradientFromReference_ND(dim, Q, i, gas, s, STATEVAR_CONSERVATIVE, grad_q, dXdx, grad_s); 287 288 const CeedScalar Grad_E[3] = {grad_s[0].U.E_total, grad_s[1].U.E_total, grad_s[2].U.E_total}; 289 290 for (CeedInt f = 0; f < 4; f++) { 291 for (CeedInt j = 0; j < dim; j++) grad_v[j][f][i] = 0; // No Change in density or momentum 292 v[f][i] = wdetJ * q_dot[f][i]; // K Mass/transient term 293 } 294 295 CeedScalar div_u = 0; 296 for (CeedInt j = 0; j < dim; j++) { 297 for (CeedInt k = 0; k < dim; k++) { 298 div_u += grad_s[k].Y.velocity[j]; 299 } 300 } 301 CeedScalar uX[3] = {0.}; 302 MatVecNM(dXdx, s.Y.velocity, dim, dim, CEED_NOTRANSPOSE, uX); 303 CeedScalar strong_conv = s.U.E_total * div_u + DotN(s.Y.velocity, Grad_E, dim); 304 305 v[4][i] = wdetJ * q_dot[4][i]; // transient part (ALWAYS) 306 if (context->strong_form) { // Strong Galerkin convection term: v div(E u) 307 v[4][i] += wdetJ * strong_conv; 308 } else { // Weak Galerkin convection term: -dv \cdot (E u) 309 for (CeedInt j = 0; j < dim; j++) grad_v[j][4][i] = -wdetJ * s.U.E_total * uX[j]; 310 } 311 312 { // Diffusion 313 CeedScalar Fe[3], Fe_dXdx[3] = {0.}; 314 315 for (CeedInt i = 0; i < dim; i++) Fe[i] = -context->diffusion_coeff * grad_s[i].U.E_total; 316 MatVecNM(dXdx, Fe, dim, dim, CEED_NOTRANSPOSE, Fe_dXdx); 317 for (CeedInt k = 0; k < dim; k++) grad_v[k][4][i] -= wdetJ * Fe_dXdx[k]; 318 } 319 320 const CeedScalar TauS = Tau(context, s, dXdx, dim); 321 for (CeedInt j = 0; j < dim; j++) { 322 switch (context->stabilization) { 323 case STAB_NONE: 324 break; 325 case STAB_SU: 326 grad_v[j][4][i] += wdetJ * TauS * uX[j] * strong_conv; 327 break; 328 case STAB_SUPG: { 329 CeedScalar divFdiff_i = context->divFdiff_method != DIV_DIFF_FLUX_PROJ_NONE ? divFdiff[i] : 0.; 330 grad_v[j][4][i] += wdetJ * TauS * uX[j] * (q_dot[4][i] + strong_conv + divFdiff_i); 331 } break; 332 } 333 } 334 } 335 return 0; 336 } 337 338 CEED_QFUNCTION(IFunction_Advection)(void *ctx, CeedInt Q, const CeedScalar *const *in, CeedScalar *const *out) { 339 return IFunction_AdvectionGeneric(ctx, Q, in, out, 3); 340 } 341 342 CEED_QFUNCTION(IFunction_Advection2d)(void *ctx, CeedInt Q, const CeedScalar *const *in, CeedScalar *const *out) { 343 return IFunction_AdvectionGeneric(ctx, Q, in, out, 2); 344 } 345 346 CEED_QFUNCTION_HELPER int MassFunction_AdvectionGeneric(void *ctx, CeedInt Q, const CeedScalar *const *in, CeedScalar *const *out, CeedInt dim) { 347 const CeedScalar(*q_dot)[CEED_Q_VLA] = (const CeedScalar(*)[CEED_Q_VLA])in[0]; 348 const CeedScalar(*q)[CEED_Q_VLA] = (const CeedScalar(*)[CEED_Q_VLA])in[1]; 349 const CeedScalar(*q_data) = in[2]; 350 351 CeedScalar(*v)[CEED_Q_VLA] = (CeedScalar(*)[CEED_Q_VLA])out[0]; 352 CeedScalar(*grad_v)[5][CEED_Q_VLA] = (CeedScalar(*)[5][CEED_Q_VLA])out[1]; 353 354 AdvectionContext context = (AdvectionContext)ctx; 355 struct NewtonianIdealGasContext_ gas_struct = {0}; 356 NewtonianIdealGasContext gas = &gas_struct; 357 358 CeedPragmaSIMD for (CeedInt i = 0; i < Q; i++) { 359 const CeedScalar qi[5] = {q[0][i], q[1][i], q[2][i], q[3][i], q[4][i]}; 360 const State s = StateFromU(gas, qi); 361 CeedScalar wdetJ, dXdx[9]; 362 QdataUnpack_ND(dim, Q, i, q_data, &wdetJ, dXdx); 363 364 for (CeedInt f = 0; f < 4; f++) { 365 for (CeedInt j = 0; j < dim; j++) grad_v[j][f][i] = 0; // No Change in density or momentum 366 v[f][i] = wdetJ * q_dot[f][i]; // K Mass/transient term 367 } 368 369 // Unstabilized mass term 370 v[4][i] = wdetJ * q_dot[4][i]; 371 372 // Stabilized mass term 373 CeedScalar uX[3] = {0.}; 374 MatVecNM(dXdx, s.Y.velocity, dim, dim, CEED_NOTRANSPOSE, uX); 375 const CeedScalar TauS = Tau(context, s, dXdx, dim); 376 for (CeedInt j = 0; j < dim; j++) { 377 switch (context->stabilization) { 378 case STAB_NONE: 379 case STAB_SU: 380 grad_v[j][4][i] = 0; 381 break; // These should be run with the unstabilized mass matrix anyways 382 case STAB_SUPG: 383 grad_v[j][4][i] = wdetJ * TauS * q_dot[4][i] * uX[j]; 384 break; 385 } 386 } 387 } 388 return 0; 389 } 390 391 CEED_QFUNCTION(MassFunction_Advection)(void *ctx, CeedInt Q, const CeedScalar *const *in, CeedScalar *const *out) { 392 return MassFunction_AdvectionGeneric(ctx, Q, in, out, 3); 393 } 394 395 CEED_QFUNCTION(MassFunction_Advection2D)(void *ctx, CeedInt Q, const CeedScalar *const *in, CeedScalar *const *out) { 396 return MassFunction_AdvectionGeneric(ctx, Q, in, out, 2); 397 } 398 399 // ***************************************************************************** 400 // This QFunction implements Advection for explicit time stepping method 401 // ***************************************************************************** 402 CEED_QFUNCTION_HELPER int RHSFunction_AdvectionGeneric(void *ctx, CeedInt Q, const CeedScalar *const *in, CeedScalar *const *out, CeedInt dim) { 403 AdvectionContext context = (AdvectionContext)ctx; 404 405 const CeedScalar(*q)[CEED_Q_VLA] = (const CeedScalar(*)[CEED_Q_VLA])in[0]; 406 const CeedScalar(*grad_q) = in[1]; 407 const CeedScalar(*q_data) = in[2]; 408 const CeedScalar(*divFdiff) = context->divFdiff_method != DIV_DIFF_FLUX_PROJ_NONE ? in[4] : NULL; 409 410 CeedScalar(*v)[CEED_Q_VLA] = (CeedScalar(*)[CEED_Q_VLA])out[0]; 411 CeedScalar(*grad_v)[5][CEED_Q_VLA] = (CeedScalar(*)[5][CEED_Q_VLA])out[1]; 412 413 struct NewtonianIdealGasContext_ gas_struct = {0}; 414 NewtonianIdealGasContext gas = &gas_struct; 415 416 CeedPragmaSIMD for (CeedInt i = 0; i < Q; i++) { 417 const CeedScalar qi[5] = {q[0][i], q[1][i], q[2][i], q[3][i], q[4][i]}; 418 const State s = StateFromU(gas, qi); 419 420 CeedScalar wdetJ, dXdx[9]; 421 QdataUnpack_ND(dim, Q, i, q_data, &wdetJ, dXdx); 422 State grad_s[3]; 423 StatePhysicalGradientFromReference_ND(dim, Q, i, gas, s, STATEVAR_CONSERVATIVE, grad_q, dXdx, grad_s); 424 425 const CeedScalar Grad_E[3] = {grad_s[0].U.E_total, grad_s[1].U.E_total, grad_s[2].U.E_total}; 426 427 for (CeedInt f = 0; f < 4; f++) { 428 for (CeedInt j = 0; j < dim; j++) grad_v[j][f][i] = 0; // No Change in density or momentum 429 v[f][i] = 0.; 430 } 431 432 CeedScalar div_u = 0; 433 for (CeedInt j = 0; j < dim; j++) { 434 for (CeedInt k = 0; k < dim; k++) { 435 div_u += grad_s[k].Y.velocity[j]; 436 } 437 } 438 CeedScalar strong_conv = s.U.E_total * div_u + DotN(s.Y.velocity, Grad_E, dim); 439 440 CeedScalar uX[3] = {0.}; 441 MatVecNM(dXdx, s.Y.velocity, dim, dim, CEED_NOTRANSPOSE, uX); 442 443 if (context->strong_form) { // Strong Galerkin convection term: v div(E u) 444 v[4][i] = -wdetJ * strong_conv; 445 for (CeedInt j = 0; j < dim; j++) grad_v[j][4][i] = 0; 446 } else { // Weak Galerkin convection term: -dv \cdot (E u) 447 for (CeedInt j = 0; j < dim; j++) grad_v[j][4][i] = wdetJ * s.U.E_total * uX[j]; 448 v[4][i] = 0.; 449 } 450 451 { // Diffusion 452 CeedScalar Fe[3], Fe_dXdx[3] = {0.}; 453 454 for (CeedInt i = 0; i < dim; i++) Fe[i] = -context->diffusion_coeff * grad_s[i].U.E_total; 455 MatVecNM(dXdx, Fe, dim, dim, CEED_NOTRANSPOSE, Fe_dXdx); 456 for (CeedInt k = 0; k < dim; k++) grad_v[k][4][i] += wdetJ * Fe_dXdx[k]; 457 } 458 459 const CeedScalar TauS = Tau(context, s, dXdx, dim); 460 for (CeedInt j = 0; j < dim; j++) { 461 switch (context->stabilization) { 462 case STAB_NONE: 463 break; 464 case STAB_SU: 465 case STAB_SUPG: { 466 CeedScalar divFdiff_i = context->divFdiff_method != DIV_DIFF_FLUX_PROJ_NONE ? divFdiff[i] : 0.; 467 grad_v[j][4][i] -= wdetJ * TauS * (strong_conv + divFdiff_i) * uX[j]; 468 } break; 469 } 470 } 471 } 472 return 0; 473 } 474 475 CEED_QFUNCTION(RHS_Advection)(void *ctx, CeedInt Q, const CeedScalar *const *in, CeedScalar *const *out) { 476 return RHSFunction_AdvectionGeneric(ctx, Q, in, out, 3); 477 } 478 479 CEED_QFUNCTION(RHS_Advection2d)(void *ctx, CeedInt Q, const CeedScalar *const *in, CeedScalar *const *out) { 480 return RHSFunction_AdvectionGeneric(ctx, Q, in, out, 2); 481 } 482 483 // ***************************************************************************** 484 // This QFunction implements consistent outflow and inflow BCs 485 // for advection 486 // 487 // Inflow and outflow faces are determined based on sign(dot(wind, normal)): 488 // sign(dot(wind, normal)) > 0 : outflow BCs 489 // sign(dot(wind, normal)) < 0 : inflow BCs 490 // 491 // Outflow BCs: 492 // The validity of the weak form of the governing equations is extended to the outflow and the current values of E are applied. 493 // 494 // Inflow BCs: 495 // A prescribed Total Energy (E_wind) is applied weakly. 496 // ***************************************************************************** 497 CEED_QFUNCTION_HELPER int Advection_InOutFlowGeneric(void *ctx, CeedInt Q, const CeedScalar *const *in, CeedScalar *const *out, CeedInt dim) { 498 const CeedScalar(*q)[CEED_Q_VLA] = (const CeedScalar(*)[CEED_Q_VLA])in[0]; 499 const CeedScalar(*q_data_sur) = in[2]; 500 501 CeedScalar(*v)[CEED_Q_VLA] = (CeedScalar(*)[CEED_Q_VLA])out[0]; 502 AdvectionContext context = (AdvectionContext)ctx; 503 const CeedScalar E_wind = context->E_wind; 504 const CeedScalar strong_form = context->strong_form; 505 const bool is_implicit = context->implicit; 506 507 CeedPragmaSIMD for (CeedInt i = 0; i < Q; i++) { 508 const CeedScalar rho = q[0][i]; 509 const CeedScalar u[3] = {q[1][i] / rho, q[2][i] / rho, q[3][i] / rho}; 510 const CeedScalar E = q[4][i]; 511 512 CeedScalar wdetJb, normal[3]; 513 QdataBoundaryUnpack_ND(dim, Q, i, q_data_sur, &wdetJb, NULL, normal); 514 wdetJb *= is_implicit ? -1. : 1.; 515 516 const CeedScalar u_normal = DotN(normal, u, dim); 517 518 // No Change in density or momentum 519 for (CeedInt j = 0; j < 4; j++) { 520 v[j][i] = 0; 521 } 522 // Implementing in/outflow BCs 523 if (u_normal > 0) { // outflow 524 v[4][i] = -(1 - strong_form) * wdetJb * E * u_normal; 525 } else { // inflow 526 v[4][i] = -(1 - strong_form) * wdetJb * E_wind * u_normal; 527 } 528 } 529 return 0; 530 } 531 532 CEED_QFUNCTION(Advection_InOutFlow)(void *ctx, CeedInt Q, const CeedScalar *const *in, CeedScalar *const *out) { 533 return Advection_InOutFlowGeneric(ctx, Q, in, out, 3); 534 } 535 536 CEED_QFUNCTION(Advection2d_InOutFlow)(void *ctx, CeedInt Q, const CeedScalar *const *in, CeedScalar *const *out) { 537 return Advection_InOutFlowGeneric(ctx, Q, in, out, 2); 538 } 539 540 // @brief Volume integral for RHS of divergence of diffusive flux direct projection 541 CEED_QFUNCTION_HELPER int DivDiffusiveFluxVolumeRHS_AdvDif_Generic(void *ctx, CeedInt Q, const CeedScalar *const *in, CeedScalar *const *out, 542 const CeedInt dim) { 543 const CeedScalar(*Grad_q) = in[0]; 544 const CeedScalar(*q_data) = in[1]; 545 CeedScalar(*Grad_v)[CEED_Q_VLA] = (CeedScalar(*)[CEED_Q_VLA])out[0]; 546 547 AdvectionContext context = (AdvectionContext)ctx; 548 549 CeedPragmaSIMD for (CeedInt i = 0; i < Q; i++) { 550 CeedScalar wdetJ, dXdx[9], F_diff[3] = {0.}; 551 552 QdataUnpack_ND(dim, Q, i, q_data, &wdetJ, dXdx); 553 { // Get physical diffusive flux 554 CeedScalar Grad_qn[15], grad_E_ref[3]; 555 556 GradUnpackN(Q, i, 5, dim, Grad_q, Grad_qn); 557 CopyN(&Grad_qn[4 * dim], grad_E_ref, dim); 558 MatVecNM(dXdx, grad_E_ref, dim, dim, CEED_NOTRANSPOSE, F_diff); 559 ScaleN(F_diff, -context->diffusion_coeff, dim); 560 } 561 562 CeedScalar F_diff_dXdx[3] = {0.}; 563 MatVecNM(dXdx, F_diff, dim, dim, CEED_NOTRANSPOSE, F_diff_dXdx); 564 for (CeedInt k = 0; k < dim; k++) Grad_v[k][i] = -wdetJ * F_diff_dXdx[k]; 565 } 566 return 0; 567 } 568 569 CEED_QFUNCTION(DivDiffusiveFluxVolumeRHS_AdvDif_2D)(void *ctx, CeedInt Q, const CeedScalar *const *in, CeedScalar *const *out) { 570 return DivDiffusiveFluxVolumeRHS_AdvDif_Generic(ctx, Q, in, out, 2); 571 } 572 573 CEED_QFUNCTION(DivDiffusiveFluxVolumeRHS_AdvDif_3D)(void *ctx, CeedInt Q, const CeedScalar *const *in, CeedScalar *const *out) { 574 return DivDiffusiveFluxVolumeRHS_AdvDif_Generic(ctx, Q, in, out, 3); 575 } 576 577 // @brief Boundary integral for RHS of divergence of diffusive flux direct projection 578 CEED_QFUNCTION_HELPER int DivDiffusiveFluxBoundaryRHS_AdvDif_Generic(void *ctx, CeedInt Q, const CeedScalar *const *in, CeedScalar *const *out, 579 const CeedInt dim) { 580 const CeedScalar(*Grad_q) = in[0]; 581 const CeedScalar(*q_data) = in[1]; 582 CeedScalar(*v) = out[0]; 583 584 AdvectionContext context = (AdvectionContext)ctx; 585 586 CeedPragmaSIMD for (CeedInt i = 0; i < Q; i++) { 587 CeedScalar wdetJ, normal[3], dXdx[9], F_diff[3] = {0.}; 588 589 QdataBoundaryGradientUnpack_ND(dim, Q, i, q_data, &wdetJ, dXdx, normal); 590 { // Get physical diffusive flux 591 CeedScalar Grad_qn[15], grad_E_ref[3]; 592 593 GradUnpackN(Q, i, 5, dim, Grad_q, Grad_qn); 594 CopyN(&Grad_qn[4 * dim], grad_E_ref, dim); 595 MatVecNM(dXdx, grad_E_ref, dim, dim, CEED_NOTRANSPOSE, F_diff); 596 ScaleN(F_diff, -context->diffusion_coeff, dim); 597 } 598 599 v[i] = wdetJ * DotN(F_diff, normal, dim); 600 } 601 return 0; 602 } 603 604 CEED_QFUNCTION(DivDiffusiveFluxBoundaryRHS_AdvDif_2D)(void *ctx, CeedInt Q, const CeedScalar *const *in, CeedScalar *const *out) { 605 return DivDiffusiveFluxBoundaryRHS_AdvDif_Generic(ctx, Q, in, out, 2); 606 } 607 608 CEED_QFUNCTION(DivDiffusiveFluxBoundaryRHS_AdvDif_3D)(void *ctx, CeedInt Q, const CeedScalar *const *in, CeedScalar *const *out) { 609 return DivDiffusiveFluxBoundaryRHS_AdvDif_Generic(ctx, Q, in, out, 3); 610 } 611 612 // @brief Volume integral for RHS of diffusive flux indirect projection 613 CEED_QFUNCTION_HELPER int DiffusiveFluxRHS_AdvDif_Generic(void *ctx, CeedInt Q, const CeedScalar *const *in, CeedScalar *const *out, 614 const CeedInt dim) { 615 const CeedScalar(*Grad_q) = in[0]; 616 const CeedScalar(*q_data) = in[1]; 617 CeedScalar(*v)[CEED_Q_VLA] = (CeedScalar(*)[CEED_Q_VLA])out[0]; 618 619 AdvectionContext context = (AdvectionContext)ctx; 620 621 CeedPragmaSIMD for (CeedInt i = 0; i < Q; i++) { 622 CeedScalar wdetJ, dXdx[9], F_diff[3] = {0.}; 623 624 QdataUnpack_ND(dim, Q, i, q_data, &wdetJ, dXdx); 625 { // Get physical diffusive flux 626 CeedScalar Grad_qn[15], grad_E_ref[3]; 627 628 GradUnpackN(Q, i, 5, dim, Grad_q, Grad_qn); 629 CopyN(&Grad_qn[4 * dim], grad_E_ref, dim); 630 MatVecNM(dXdx, grad_E_ref, dim, dim, CEED_NOTRANSPOSE, F_diff); 631 ScaleN(F_diff, -context->diffusion_coeff, dim); 632 } 633 for (CeedInt k = 0; k < dim; k++) v[k][i] = wdetJ * F_diff[k]; 634 } 635 return 0; 636 } 637 638 CEED_QFUNCTION(DiffusiveFluxRHS_AdvDif_2D)(void *ctx, CeedInt Q, const CeedScalar *const *in, CeedScalar *const *out) { 639 return DiffusiveFluxRHS_AdvDif_Generic(ctx, Q, in, out, 2); 640 } 641 642 CEED_QFUNCTION(DiffusiveFluxRHS_AdvDif_3D)(void *ctx, CeedInt Q, const CeedScalar *const *in, CeedScalar *const *out) { 643 return DiffusiveFluxRHS_AdvDif_Generic(ctx, Q, in, out, 3); 644 } 645