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 /// Implementation of the Synthetic Turbulence Generation (STG) algorithm 10 /// presented in Shur et al. 2014 11 // 12 /// SetupSTG_Rand reads in the input files and fills in STGShur14Context. 13 /// Then STGShur14_CalcQF is run over quadrature points. 14 /// Before the program exits, TearDownSTG is run to free the memory of the allocated arrays. 15 16 #ifndef stg_shur14_h 17 #define stg_shur14_h 18 19 #include <ceed.h> 20 #include <math.h> 21 #include <stdlib.h> 22 23 #include "newtonian_state.h" 24 #include "setupgeo_helpers.h" 25 #include "stg_shur14_type.h" 26 #include "utils.h" 27 28 #define STG_NMODES_MAX 1024 29 30 /* 31 * @brief Interpolate quantities from input profile to given location 32 * 33 * Assumed that prof_wd[i+1] > prof_wd[i] and prof_wd[0] = 0 34 * If wall_dist > prof_wd[-1], then the interpolation takes the values at prof_wd[-1] 35 * 36 * @param[in] wall_dist Distance to the nearest wall 37 * @param[out] ubar Mean velocity at wall_dist 38 * @param[out] cij Cholesky decomposition at wall_dist 39 * @param[out] eps Turbulent dissipation at wall_dist 40 * @param[out] lt Turbulent length scale at wall_dist 41 * @param[in] stg_ctx STGShur14Context for the problem 42 */ 43 CEED_QFUNCTION_HELPER void InterpolateProfile(const CeedScalar wall_dist, CeedScalar ubar[3], CeedScalar cij[6], CeedScalar *eps, CeedScalar *lt, 44 const StgShur14Context stg_ctx) { 45 const CeedInt nprofs = stg_ctx->nprofs; 46 const CeedScalar *prof_wd = &stg_ctx->data[stg_ctx->offsets.wall_dist]; 47 const CeedScalar *prof_eps = &stg_ctx->data[stg_ctx->offsets.eps]; 48 const CeedScalar *prof_lt = &stg_ctx->data[stg_ctx->offsets.lt]; 49 const CeedScalar *prof_ubar = &stg_ctx->data[stg_ctx->offsets.ubar]; 50 const CeedScalar *prof_cij = &stg_ctx->data[stg_ctx->offsets.cij]; 51 CeedInt idx = -1; 52 53 for (CeedInt i = 0; i < nprofs; i++) { 54 if (wall_dist < prof_wd[i]) { 55 idx = i; 56 break; 57 } 58 } 59 60 if (idx > 0) { // y within the bounds of prof_wd 61 CeedScalar coeff = (wall_dist - prof_wd[idx - 1]) / (prof_wd[idx] - prof_wd[idx - 1]); 62 63 ubar[0] = prof_ubar[0 * nprofs + idx - 1] + coeff * (prof_ubar[0 * nprofs + idx] - prof_ubar[0 * nprofs + idx - 1]); 64 ubar[1] = prof_ubar[1 * nprofs + idx - 1] + coeff * (prof_ubar[1 * nprofs + idx] - prof_ubar[1 * nprofs + idx - 1]); 65 ubar[2] = prof_ubar[2 * nprofs + idx - 1] + coeff * (prof_ubar[2 * nprofs + idx] - prof_ubar[2 * nprofs + idx - 1]); 66 cij[0] = prof_cij[0 * nprofs + idx - 1] + coeff * (prof_cij[0 * nprofs + idx] - prof_cij[0 * nprofs + idx - 1]); 67 cij[1] = prof_cij[1 * nprofs + idx - 1] + coeff * (prof_cij[1 * nprofs + idx] - prof_cij[1 * nprofs + idx - 1]); 68 cij[2] = prof_cij[2 * nprofs + idx - 1] + coeff * (prof_cij[2 * nprofs + idx] - prof_cij[2 * nprofs + idx - 1]); 69 cij[3] = prof_cij[3 * nprofs + idx - 1] + coeff * (prof_cij[3 * nprofs + idx] - prof_cij[3 * nprofs + idx - 1]); 70 cij[4] = prof_cij[4 * nprofs + idx - 1] + coeff * (prof_cij[4 * nprofs + idx] - prof_cij[4 * nprofs + idx - 1]); 71 cij[5] = prof_cij[5 * nprofs + idx - 1] + coeff * (prof_cij[5 * nprofs + idx] - prof_cij[5 * nprofs + idx - 1]); 72 *eps = prof_eps[idx - 1] + coeff * (prof_eps[idx] - prof_eps[idx - 1]); 73 *lt = prof_lt[idx - 1] + coeff * (prof_lt[idx] - prof_lt[idx - 1]); 74 } else { // y outside bounds of prof_wd 75 ubar[0] = prof_ubar[1 * nprofs - 1]; 76 ubar[1] = prof_ubar[2 * nprofs - 1]; 77 ubar[2] = prof_ubar[3 * nprofs - 1]; 78 cij[0] = prof_cij[1 * nprofs - 1]; 79 cij[1] = prof_cij[2 * nprofs - 1]; 80 cij[2] = prof_cij[3 * nprofs - 1]; 81 cij[3] = prof_cij[4 * nprofs - 1]; 82 cij[4] = prof_cij[5 * nprofs - 1]; 83 cij[5] = prof_cij[6 * nprofs - 1]; 84 *eps = prof_eps[nprofs - 1]; 85 *lt = prof_lt[nprofs - 1]; 86 } 87 } 88 89 /* 90 * @brief Calculate spectrum coefficient, qn 91 * 92 * Calculates q_n at a given distance to the wall 93 * 94 * @param[in] kappa nth wavenumber 95 * @param[in] dkappa Difference between wavenumbers 96 * @param[in] keta Dissipation wavenumber 97 * @param[in] kcut Mesh-induced cutoff wavenumber 98 * @param[in] ke Energy-containing wavenumber 99 * @param[in] Ektot_inv Inverse of total turbulent kinetic energy of spectrum 100 * @returns qn Spectrum coefficient 101 */ 102 CEED_QFUNCTION_HELPER CeedScalar Calc_qn(const CeedScalar kappa, const CeedScalar dkappa, const CeedScalar keta, const CeedScalar kcut, 103 const CeedScalar ke, const CeedScalar Ektot_inv) { 104 const CeedScalar feta_x_fcut = exp(-Square(12 * kappa / keta) - Cube(4 * Max(kappa - 0.9 * kcut, 0) / kcut)); 105 return pow(kappa / ke, 4.) * pow(1 + 2.4 * Square(kappa / ke), -17. / 6) * feta_x_fcut * dkappa * Ektot_inv; 106 } 107 108 // Calculate hmax, ke, keta, and kcut 109 CEED_QFUNCTION_HELPER void SpectrumConstants(const CeedScalar wall_dist, const CeedScalar eps, const CeedScalar lt, const CeedScalar h[3], 110 const CeedScalar nu, CeedScalar *hmax, CeedScalar *ke, CeedScalar *keta, CeedScalar *kcut) { 111 *hmax = Max(Max(h[0], h[1]), h[2]); 112 *ke = wall_dist == 0 ? 1e16 : 2 * M_PI / Min(2 * wall_dist, 3 * lt); 113 *keta = 2 * M_PI * pow(Cube(nu) / eps, -0.25); 114 *kcut = M_PI / Min(Max(Max(h[1], h[2]), 0.3 * (*hmax)) + 0.1 * wall_dist, *hmax); 115 } 116 117 /* 118 * @brief Calculate spectrum coefficients for STG 119 * 120 * Calculates q_n at a given distance to the wall 121 * 122 * @param[in] wall_dist Distance to the nearest wall 123 * @param[in] eps Turbulent dissipation w/rt wall_dist 124 * @param[in] lt Turbulent length scale w/rt wall_dist 125 * @param[in] h Element lengths in coordinate directions 126 * @param[in] nu Dynamic Viscosity; 127 * @param[in] stg_ctx STGShur14Context for the problem 128 * @param[out] qn Spectrum coefficients, [nmodes] 129 */ 130 CEED_QFUNCTION_HELPER void CalcSpectrum(const CeedScalar wall_dist, const CeedScalar eps, const CeedScalar lt, const CeedScalar h[3], 131 const CeedScalar nu, CeedScalar qn[], const StgShur14Context stg_ctx) { 132 const CeedInt nmodes = stg_ctx->nmodes; 133 const CeedScalar *kappa = &stg_ctx->data[stg_ctx->offsets.kappa]; 134 CeedScalar hmax, ke, keta, kcut, Ektot = 0.0; 135 136 SpectrumConstants(wall_dist, eps, lt, h, nu, &hmax, &ke, &keta, &kcut); 137 138 for (CeedInt n = 0; n < nmodes; n++) { 139 const CeedScalar dkappa = n == 0 ? kappa[0] : kappa[n] - kappa[n - 1]; 140 qn[n] = Calc_qn(kappa[n], dkappa, keta, kcut, ke, 1.0); 141 Ektot += qn[n]; 142 } 143 144 if (Ektot == 0) return; 145 for (CeedInt n = 0; n < nmodes; n++) qn[n] /= Ektot; 146 } 147 148 /****************************************************** 149 * @brief Calculate u(x,t) for STG inflow condition 150 * 151 * @param[in] X Location to evaluate u(X,t) 152 * @param[in] t Time to evaluate u(X,t) 153 * @param[in] ubar Mean velocity at X 154 * @param[in] cij Cholesky decomposition at X 155 * @param[in] qn Wavemode amplitudes at X, [nmodes] 156 * @param[out] u Velocity at X and t 157 * @param[in] stg_ctx STGShur14Context for the problem 158 */ 159 CEED_QFUNCTION_HELPER void StgShur14Calc(const CeedScalar X[3], const CeedScalar t, const CeedScalar ubar[3], const CeedScalar cij[6], 160 const CeedScalar qn[], CeedScalar u[3], const StgShur14Context stg_ctx) { 161 const CeedInt nmodes = stg_ctx->nmodes; 162 const CeedScalar *kappa = &stg_ctx->data[stg_ctx->offsets.kappa]; 163 const CeedScalar *phi = &stg_ctx->data[stg_ctx->offsets.phi]; 164 const CeedScalar *sigma = &stg_ctx->data[stg_ctx->offsets.sigma]; 165 const CeedScalar *d = &stg_ctx->data[stg_ctx->offsets.d]; 166 CeedScalar xdotd, vp[3] = {0.}; 167 CeedScalar xhat[] = {0., X[1], X[2]}; 168 169 CeedPragmaSIMD for (CeedInt n = 0; n < nmodes; n++) { 170 xhat[0] = (X[0] - stg_ctx->u0 * t) * Max(2 * kappa[0] / kappa[n], 0.1); 171 xdotd = 0.; 172 for (CeedInt i = 0; i < 3; i++) xdotd += d[i * nmodes + n] * xhat[i]; 173 const CeedScalar cos_kxdp = cos(kappa[n] * xdotd + phi[n]); 174 vp[0] += sqrt(qn[n]) * sigma[0 * nmodes + n] * cos_kxdp; 175 vp[1] += sqrt(qn[n]) * sigma[1 * nmodes + n] * cos_kxdp; 176 vp[2] += sqrt(qn[n]) * sigma[2 * nmodes + n] * cos_kxdp; 177 } 178 for (CeedInt i = 0; i < 3; i++) vp[i] *= 2 * sqrt(1.5); 179 180 u[0] = ubar[0] + cij[0] * vp[0]; 181 u[1] = ubar[1] + cij[3] * vp[0] + cij[1] * vp[1]; 182 u[2] = ubar[2] + cij[4] * vp[0] + cij[5] * vp[1] + cij[2] * vp[2]; 183 } 184 185 /****************************************************** 186 * @brief Calculate u(x,t) for STG inflow condition 187 * 188 * @param[in] X Location to evaluate u(X,t) 189 * @param[in] t Time to evaluate u(X,t) 190 * @param[in] ubar Mean velocity at X 191 * @param[in] cij Cholesky decomposition at X 192 * @param[in] Ektot Total spectrum energy at this location 193 * @param[in] h Element size in 3 directions 194 * @param[in] wall_dist Distance to closest wall 195 * @param[in] eps Turbulent dissipation 196 * @param[in] lt Turbulent length scale 197 * @param[out] u Velocity at X and t 198 * @param[in] stg_ctx STGShur14Context for the problem 199 */ 200 CEED_QFUNCTION_HELPER void StgShur14Calc_PrecompEktot(const CeedScalar X[3], const CeedScalar t, const CeedScalar ubar[3], const CeedScalar cij[6], 201 const CeedScalar Ektot, const CeedScalar h[3], const CeedScalar wall_dist, const CeedScalar eps, 202 const CeedScalar lt, const CeedScalar nu, CeedScalar u[3], const StgShur14Context stg_ctx) { 203 const CeedInt nmodes = stg_ctx->nmodes; 204 const CeedScalar *kappa = &stg_ctx->data[stg_ctx->offsets.kappa]; 205 const CeedScalar *phi = &stg_ctx->data[stg_ctx->offsets.phi]; 206 const CeedScalar *sigma = &stg_ctx->data[stg_ctx->offsets.sigma]; 207 const CeedScalar *d = &stg_ctx->data[stg_ctx->offsets.d]; 208 CeedScalar hmax, ke, keta, kcut; 209 SpectrumConstants(wall_dist, eps, lt, h, nu, &hmax, &ke, &keta, &kcut); 210 CeedScalar xdotd, vp[3] = {0.}; 211 CeedScalar xhat[] = {0., X[1], X[2]}; 212 213 CeedPragmaSIMD for (CeedInt n = 0; n < nmodes; n++) { 214 xhat[0] = (X[0] - stg_ctx->u0 * t) * Max(2 * kappa[0] / kappa[n], 0.1); 215 xdotd = 0.; 216 for (CeedInt i = 0; i < 3; i++) xdotd += d[i * nmodes + n] * xhat[i]; 217 const CeedScalar cos_kxdp = cos(kappa[n] * xdotd + phi[n]); 218 const CeedScalar dkappa = n == 0 ? kappa[0] : kappa[n] - kappa[n - 1]; 219 const CeedScalar qn = Calc_qn(kappa[n], dkappa, keta, kcut, ke, Ektot); 220 vp[0] += sqrt(qn) * sigma[0 * nmodes + n] * cos_kxdp; 221 vp[1] += sqrt(qn) * sigma[1 * nmodes + n] * cos_kxdp; 222 vp[2] += sqrt(qn) * sigma[2 * nmodes + n] * cos_kxdp; 223 } 224 for (CeedInt i = 0; i < 3; i++) vp[i] *= 2 * sqrt(1.5); 225 226 u[0] = ubar[0] + cij[0] * vp[0]; 227 u[1] = ubar[1] + cij[3] * vp[0] + cij[1] * vp[1]; 228 u[2] = ubar[2] + cij[4] * vp[0] + cij[5] * vp[1] + cij[2] * vp[2]; 229 } 230 231 // Create preprocessed input for the stg calculation 232 // 233 // stg_data[0] = 1 / Ektot (inverse of total spectrum energy) 234 CEED_QFUNCTION(StgShur14Preprocess)(void *ctx, CeedInt Q, const CeedScalar *const *in, CeedScalar *const *out) { 235 const CeedScalar(*dXdx_q)[3][CEED_Q_VLA] = (const CeedScalar(*)[3][CEED_Q_VLA])in[0]; 236 const CeedScalar(*x)[CEED_Q_VLA] = (const CeedScalar(*)[CEED_Q_VLA])in[1]; 237 238 CeedScalar(*stg_data) = (CeedScalar(*))out[0]; 239 240 CeedScalar ubar[3], cij[6], eps, lt; 241 const StgShur14Context stg_ctx = (StgShur14Context)ctx; 242 const CeedScalar dx = stg_ctx->dx; 243 const CeedScalar mu = stg_ctx->newtonian_ctx.mu; 244 const CeedScalar theta0 = stg_ctx->theta0; 245 const CeedScalar P0 = stg_ctx->P0; 246 const CeedScalar Rd = GasConstant(&stg_ctx->newtonian_ctx); 247 const CeedScalar rho = P0 / (Rd * theta0); 248 const CeedScalar nu = mu / rho; 249 250 const CeedInt nmodes = stg_ctx->nmodes; 251 const CeedScalar *kappa = &stg_ctx->data[stg_ctx->offsets.kappa]; 252 CeedScalar hmax, ke, keta, kcut; 253 254 CeedPragmaSIMD for (CeedInt i = 0; i < Q; i++) { 255 const CeedScalar wall_dist = x[1][i]; 256 const CeedScalar dXdx[2][3] = { 257 {dXdx_q[0][0][i], dXdx_q[0][1][i], dXdx_q[0][2][i]}, 258 {dXdx_q[1][0][i], dXdx_q[1][1][i], dXdx_q[1][2][i]}, 259 }; 260 261 CeedScalar h[3]; 262 h[0] = dx; 263 for (CeedInt j = 1; j < 3; j++) h[j] = 2 / sqrt(dXdx[0][j] * dXdx[0][j] + dXdx[1][j] * dXdx[1][j]); 264 265 InterpolateProfile(wall_dist, ubar, cij, &eps, <, stg_ctx); 266 SpectrumConstants(wall_dist, eps, lt, h, nu, &hmax, &ke, &keta, &kcut); 267 268 // Calculate total TKE per spectrum 269 CeedScalar Ek_tot = 0; 270 CeedPragmaSIMD for (CeedInt n = 0; n < nmodes; n++) { 271 const CeedScalar dkappa = n == 0 ? kappa[0] : kappa[n] - kappa[n - 1]; 272 Ek_tot += Calc_qn(kappa[n], dkappa, keta, kcut, ke, 1.0); 273 } 274 // avoid underflowed and poorly defined spectrum coefficients 275 stg_data[i] = Ek_tot != 0 ? 1 / Ek_tot : 0; 276 } 277 return 0; 278 } 279 280 // Extrude the STGInflow profile through out the domain for an initial condition 281 CEED_QFUNCTION(ICsStg)(void *ctx, CeedInt Q, const CeedScalar *const *in, CeedScalar *const *out) { 282 // Inputs 283 const CeedScalar(*x)[CEED_Q_VLA] = (const CeedScalar(*)[CEED_Q_VLA])in[0]; 284 const CeedScalar(*J)[3][CEED_Q_VLA] = (const CeedScalar(*)[3][CEED_Q_VLA])in[1]; 285 286 // Outputs 287 CeedScalar(*q0)[CEED_Q_VLA] = (CeedScalar(*)[CEED_Q_VLA])out[0]; 288 289 const StgShur14Context stg_ctx = (StgShur14Context)ctx; 290 CeedScalar qn[STG_NMODES_MAX], u[3], ubar[3], cij[6], eps, lt; 291 const CeedScalar dx = stg_ctx->dx; 292 const CeedScalar time = stg_ctx->time; 293 const CeedScalar theta0 = stg_ctx->theta0; 294 const CeedScalar P0 = stg_ctx->P0; 295 const CeedScalar cv = stg_ctx->newtonian_ctx.cv; 296 const CeedScalar rho = P0 / (GasConstant(&stg_ctx->newtonian_ctx) * theta0); 297 const CeedScalar nu = stg_ctx->newtonian_ctx.mu / rho; 298 299 CeedPragmaSIMD for (CeedInt i = 0; i < Q; i++) { 300 const CeedScalar x_i[3] = {x[0][i], x[1][i], x[2][i]}; 301 CeedScalar dXdx[3][3]; 302 InvertMappingJacobian_3D(Q, i, J, dXdx, NULL); 303 CeedScalar h[3]; 304 h[0] = dx; 305 for (CeedInt j = 1; j < 3; j++) h[j] = 2 / sqrt(Square(dXdx[0][j]) + Square(dXdx[1][j]) + Square(dXdx[2][j])); 306 307 InterpolateProfile(x_i[1], ubar, cij, &eps, <, stg_ctx); 308 if (stg_ctx->use_fluctuating_IC) { 309 CalcSpectrum(x_i[1], eps, lt, h, nu, qn, stg_ctx); 310 StgShur14Calc(x_i, time, ubar, cij, qn, u, stg_ctx); 311 } else { 312 for (CeedInt j = 0; j < 3; j++) u[j] = ubar[j]; 313 } 314 315 switch (stg_ctx->newtonian_ctx.state_var) { 316 case STATEVAR_CONSERVATIVE: 317 q0[0][i] = rho; 318 q0[1][i] = u[0] * rho; 319 q0[2][i] = u[1] * rho; 320 q0[3][i] = u[2] * rho; 321 q0[4][i] = rho * (0.5 * Dot3(u, u) + cv * theta0); 322 break; 323 324 case STATEVAR_PRIMITIVE: 325 q0[0][i] = P0; 326 q0[1][i] = u[0]; 327 q0[2][i] = u[1]; 328 q0[3][i] = u[2]; 329 q0[4][i] = theta0; 330 break; 331 } 332 } // End of Quadrature Point Loop 333 return 0; 334 } 335 336 /******************************************************************** 337 * @brief QFunction to calculate the inflow boundary condition 338 * 339 * This will loop through quadrature points, calculate the wavemode amplitudes 340 * at each location, then calculate the actual velocity. 341 */ 342 CEED_QFUNCTION(StgShur14Inflow)(void *ctx, CeedInt Q, const CeedScalar *const *in, CeedScalar *const *out) { 343 const CeedScalar(*q)[CEED_Q_VLA] = (const CeedScalar(*)[CEED_Q_VLA])in[0]; 344 const CeedScalar(*q_data_sur)[CEED_Q_VLA] = (const CeedScalar(*)[CEED_Q_VLA])in[2]; 345 const CeedScalar(*X)[CEED_Q_VLA] = (const CeedScalar(*)[CEED_Q_VLA])in[3]; 346 347 CeedScalar(*v)[CEED_Q_VLA] = (CeedScalar(*)[CEED_Q_VLA])out[0]; 348 CeedScalar(*jac_data_sur)[CEED_Q_VLA] = (CeedScalar(*)[CEED_Q_VLA])out[1]; 349 350 const StgShur14Context stg_ctx = (StgShur14Context)ctx; 351 CeedScalar qn[STG_NMODES_MAX], u[3], ubar[3], cij[6], eps, lt; 352 const bool is_implicit = stg_ctx->is_implicit; 353 const bool mean_only = stg_ctx->mean_only; 354 const bool prescribe_T = stg_ctx->prescribe_T; 355 const CeedScalar dx = stg_ctx->dx; 356 const CeedScalar mu = stg_ctx->newtonian_ctx.mu; 357 const CeedScalar time = stg_ctx->time; 358 const CeedScalar theta0 = stg_ctx->theta0; 359 const CeedScalar P0 = stg_ctx->P0; 360 const CeedScalar cv = stg_ctx->newtonian_ctx.cv; 361 const CeedScalar Rd = GasConstant(&stg_ctx->newtonian_ctx); 362 const CeedScalar gamma = HeatCapacityRatio(&stg_ctx->newtonian_ctx); 363 364 CeedPragmaSIMD for (CeedInt i = 0; i < Q; i++) { 365 const CeedScalar rho = prescribe_T ? q[0][i] : P0 / (Rd * theta0); 366 const CeedScalar x[] = {X[0][i], X[1][i], X[2][i]}; 367 const CeedScalar dXdx[2][3] = { 368 {q_data_sur[4][i], q_data_sur[5][i], q_data_sur[6][i]}, 369 {q_data_sur[7][i], q_data_sur[8][i], q_data_sur[9][i]} 370 }; 371 372 CeedScalar h[3]; 373 h[0] = dx; 374 for (CeedInt j = 1; j < 3; j++) h[j] = 2 / sqrt(Square(dXdx[0][j]) + Square(dXdx[1][j])); 375 376 InterpolateProfile(X[1][i], ubar, cij, &eps, <, stg_ctx); 377 if (!mean_only) { 378 CalcSpectrum(X[1][i], eps, lt, h, mu / rho, qn, stg_ctx); 379 StgShur14Calc(x, time, ubar, cij, qn, u, stg_ctx); 380 } else { 381 for (CeedInt j = 0; j < 3; j++) u[j] = ubar[j]; 382 } 383 384 const CeedScalar E_kinetic = .5 * rho * Dot3(u, u); 385 CeedScalar E_internal, P; 386 if (prescribe_T) { 387 // Temperature is being set weakly (theta0) and for constant cv this sets E_internal 388 E_internal = rho * cv * theta0; 389 // Find pressure using 390 P = rho * Rd * theta0; // interior rho with exterior T 391 } else { 392 E_internal = q[4][i] - E_kinetic; // uses prescribed rho and u, E from solution 393 P = E_internal * (gamma - 1.); 394 } 395 396 const CeedScalar wdetJb = (is_implicit ? -1. : 1.) * q_data_sur[0][i]; 397 // ---- Normal vect 398 const CeedScalar norm[3] = {q_data_sur[1][i], q_data_sur[2][i], q_data_sur[3][i]}; 399 400 const CeedScalar E = E_internal + E_kinetic; 401 402 // Velocity normal to the boundary 403 const CeedScalar u_normal = Dot3(norm, u); 404 405 // The Physics 406 // Zero v so all future terms can safely sum into it 407 for (CeedInt j = 0; j < 5; j++) v[j][i] = 0.; 408 409 // The Physics 410 // -- Density 411 v[0][i] -= wdetJb * rho * u_normal; 412 413 // -- Momentum 414 for (CeedInt j = 0; j < 3; j++) v[j + 1][i] -= wdetJb * (rho * u_normal * u[j] + norm[j] * P); 415 416 // -- Total Energy Density 417 v[4][i] -= wdetJb * u_normal * (E + P); 418 419 jac_data_sur[0][i] = rho; 420 jac_data_sur[1][i] = u[0]; 421 jac_data_sur[2][i] = u[1]; 422 jac_data_sur[3][i] = u[2]; 423 jac_data_sur[4][i] = E; 424 for (int j = 0; j < 6; j++) jac_data_sur[5 + j][i] = 0.; 425 } 426 return 0; 427 } 428 429 CEED_QFUNCTION(StgShur14Inflow_Jacobian)(void *ctx, CeedInt Q, const CeedScalar *const *in, CeedScalar *const *out) { 430 // Inputs 431 const CeedScalar(*dq)[CEED_Q_VLA] = (const CeedScalar(*)[CEED_Q_VLA])in[0]; 432 const CeedScalar(*q_data_sur)[CEED_Q_VLA] = (const CeedScalar(*)[CEED_Q_VLA])in[2]; 433 const CeedScalar(*jac_data_sur)[CEED_Q_VLA] = (const CeedScalar(*)[CEED_Q_VLA])in[4]; 434 // Outputs 435 CeedScalar(*v)[CEED_Q_VLA] = (CeedScalar(*)[CEED_Q_VLA])out[0]; 436 437 const StgShur14Context stg_ctx = (StgShur14Context)ctx; 438 const bool implicit = stg_ctx->is_implicit; 439 const CeedScalar cv = stg_ctx->newtonian_ctx.cv; 440 const CeedScalar Rd = GasConstant(&stg_ctx->newtonian_ctx); 441 const CeedScalar gamma = HeatCapacityRatio(&stg_ctx->newtonian_ctx); 442 443 const CeedScalar theta0 = stg_ctx->theta0; 444 const bool prescribe_T = stg_ctx->prescribe_T; 445 446 CeedPragmaSIMD 447 // Quadrature Point Loop 448 for (CeedInt i = 0; i < Q; i++) { 449 // Setup 450 // -- Interp-to-Interp q_data 451 // For explicit mode, the surface integral is on the RHS of ODE q_dot = f(q). 452 // For implicit mode, it gets pulled to the LHS of implicit ODE/DAE g(q_dot, q). 453 // We can effect this by swapping the sign on this weight 454 const CeedScalar wdetJb = (implicit ? -1. : 1.) * q_data_sur[0][i]; 455 456 // Calculate inflow values 457 CeedScalar velocity[3]; 458 for (CeedInt j = 0; j < 3; j++) velocity[j] = jac_data_sur[5 + j][i]; 459 460 // enabling user to choose between weak T and weak rho inflow 461 CeedScalar drho, dE, dP; 462 if (prescribe_T) { 463 // rho should be from the current solution 464 drho = dq[0][i]; 465 CeedScalar dE_internal = drho * cv * theta0; 466 CeedScalar dE_kinetic = .5 * drho * Dot3(velocity, velocity); 467 dE = dE_internal + dE_kinetic; 468 dP = drho * Rd * theta0; // interior rho with exterior T 469 } else { // rho specified, E_internal from solution 470 drho = 0; 471 dE = dq[4][i]; 472 dP = dE * (gamma - 1.); 473 } 474 const CeedScalar norm[3] = {q_data_sur[1][i], q_data_sur[2][i], q_data_sur[3][i]}; 475 476 const CeedScalar u_normal = Dot3(norm, velocity); 477 478 v[0][i] = -wdetJb * drho * u_normal; 479 for (int j = 0; j < 3; j++) v[j + 1][i] = -wdetJb * (drho * u_normal * velocity[j] + norm[j] * dP); 480 v[4][i] = -wdetJb * u_normal * (dE + dP); 481 } // End Quadrature Point Loop 482 return 0; 483 } 484 485 /******************************************************************** 486 * @brief QFunction to calculate the strongly enforce inflow BC 487 * 488 * This QF is for the strong application of STG via libCEED (rather than 489 * through the native PETSc `DMAddBoundary` -> `bcFunc` method. 490 */ 491 CEED_QFUNCTION(StgShur14InflowStrongQF)(void *ctx, CeedInt Q, const CeedScalar *const *in, CeedScalar *const *out) { 492 const CeedScalar(*dXdx_q)[3][CEED_Q_VLA] = (const CeedScalar(*)[3][CEED_Q_VLA])in[0]; 493 const CeedScalar(*coords)[CEED_Q_VLA] = (const CeedScalar(*)[CEED_Q_VLA])in[1]; 494 const CeedScalar(*scale) = (const CeedScalar(*))in[2]; 495 const CeedScalar(*inv_Ektotal) = (const CeedScalar(*))in[3]; 496 497 CeedScalar(*bcval)[CEED_Q_VLA] = (CeedScalar(*)[CEED_Q_VLA])out[0]; 498 499 const StgShur14Context stg_ctx = (StgShur14Context)ctx; 500 CeedScalar u[3], ubar[3], cij[6], eps, lt; 501 const bool mean_only = stg_ctx->mean_only; 502 const CeedScalar dx = stg_ctx->dx; 503 const CeedScalar time = stg_ctx->time; 504 const CeedScalar theta0 = stg_ctx->theta0; 505 const CeedScalar P0 = stg_ctx->P0; 506 const CeedScalar rho = P0 / (GasConstant(&stg_ctx->newtonian_ctx) * theta0); 507 const CeedScalar nu = stg_ctx->newtonian_ctx.mu / rho; 508 509 CeedPragmaSIMD for (CeedInt i = 0; i < Q; i++) { 510 const CeedScalar x[] = {coords[0][i], coords[1][i], coords[2][i]}; 511 const CeedScalar dXdx[2][3] = { 512 {dXdx_q[0][0][i], dXdx_q[0][1][i], dXdx_q[0][2][i]}, 513 {dXdx_q[1][0][i], dXdx_q[1][1][i], dXdx_q[1][2][i]}, 514 }; 515 516 CeedScalar h[3]; 517 h[0] = dx; 518 for (CeedInt j = 1; j < 3; j++) h[j] = 2 / sqrt(Square(dXdx[0][j]) + Square(dXdx[1][j])); 519 520 InterpolateProfile(coords[1][i], ubar, cij, &eps, <, stg_ctx); 521 if (!mean_only) { 522 if (1) { 523 StgShur14Calc_PrecompEktot(x, time, ubar, cij, inv_Ektotal[i], h, x[1], eps, lt, nu, u, stg_ctx); 524 } else { // Original way 525 CeedScalar qn[STG_NMODES_MAX]; 526 CalcSpectrum(coords[1][i], eps, lt, h, nu, qn, stg_ctx); 527 StgShur14Calc(x, time, ubar, cij, qn, u, stg_ctx); 528 } 529 } else { 530 for (CeedInt j = 0; j < 3; j++) u[j] = ubar[j]; 531 } 532 533 switch (stg_ctx->newtonian_ctx.state_var) { 534 case STATEVAR_CONSERVATIVE: 535 bcval[0][i] = scale[i] * rho; 536 bcval[1][i] = scale[i] * rho * u[0]; 537 bcval[2][i] = scale[i] * rho * u[1]; 538 bcval[3][i] = scale[i] * rho * u[2]; 539 bcval[4][i] = 0.; 540 break; 541 542 case STATEVAR_PRIMITIVE: 543 bcval[0][i] = 0; 544 bcval[1][i] = scale[i] * u[0]; 545 bcval[2][i] = scale[i] * u[1]; 546 bcval[3][i] = scale[i] * u[2]; 547 bcval[4][i] = scale[i] * theta0; 548 break; 549 } 550 } 551 return 0; 552 } 553 554 #endif // stg_shur14_h 555