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