1 // SPDX-FileCopyrightText: Copyright (c) 2017-2024, HONEE contributors. 2 // SPDX-License-Identifier: Apache-2.0 OR BSD-2-Clause 3 4 /// @file 5 /// Structs and helper functions regarding the state of a newtonian simulation 6 #pragma once 7 8 #include <ceed.h> 9 #include <math.h> 10 11 #include "newtonian_types.h" 12 #include "utils.h" 13 14 typedef struct { 15 CeedScalar density; 16 CeedScalar momentum[3]; 17 CeedScalar E_total; 18 } StateConservative; 19 20 typedef struct { 21 StateConservative U; 22 StatePrimitive Y; 23 } State; 24 25 CEED_QFUNCTION_HELPER void UnpackState_U(StateConservative s, CeedScalar U[5]) { 26 U[0] = s.density; 27 for (int i = 0; i < 3; i++) U[i + 1] = s.momentum[i]; 28 U[4] = s.E_total; 29 } 30 31 CEED_QFUNCTION_HELPER void UnpackState_Y(StatePrimitive s, CeedScalar Y[5]) { 32 Y[0] = s.pressure; 33 for (int i = 0; i < 3; i++) Y[i + 1] = s.velocity[i]; 34 Y[4] = s.temperature; 35 } 36 37 CEED_QFUNCTION_HELPER void UnpackState_V(StateEntropy s, CeedScalar V[5]) { 38 V[0] = s.S_density; 39 for (int i = 0; i < 3; i++) V[i + 1] = s.S_momentum[i]; 40 V[4] = s.S_energy; 41 } 42 43 CEED_QFUNCTION_HELPER CeedScalar HeatCapacityRatio(NewtonianIdealGasContext gas) { return gas->cp / gas->cv; } 44 45 CEED_QFUNCTION_HELPER CeedScalar GasConstant(NewtonianIdealGasContext gas) { return gas->cp - gas->cv; } 46 47 CEED_QFUNCTION_HELPER CeedScalar Prandtl(NewtonianIdealGasContext gas) { return gas->cp * gas->mu / gas->k; } 48 49 CEED_QFUNCTION_HELPER CeedScalar SoundSpeed(NewtonianIdealGasContext gas, CeedScalar T) { return sqrt(gas->cp * (HeatCapacityRatio(gas) - 1.) * T); } 50 51 CEED_QFUNCTION_HELPER CeedScalar Mach(NewtonianIdealGasContext gas, CeedScalar T, CeedScalar u) { return u / SoundSpeed(gas, T); } 52 53 CEED_QFUNCTION_HELPER CeedScalar TotalSpecificEnthalpy(NewtonianIdealGasContext gas, const State s) { 54 CeedScalar e_kinetic = 0.5 * Dot3(s.Y.velocity, s.Y.velocity); 55 CeedScalar e_internal = gas->cv * s.Y.temperature; 56 return e_internal + e_kinetic + s.Y.pressure / s.U.density; 57 } 58 59 CEED_QFUNCTION_HELPER CeedScalar TotalSpecificEnthalpy_fwd(NewtonianIdealGasContext gas, const State s, const State ds) { 60 CeedScalar de_kinetic = Dot3(ds.Y.velocity, s.Y.velocity); 61 CeedScalar de_internal = gas->cv * ds.Y.temperature; 62 return de_internal + de_kinetic + ds.Y.pressure / s.U.density - s.Y.pressure / Square(s.U.density) * ds.U.density; 63 } 64 65 CEED_QFUNCTION_HELPER StatePrimitive StatePrimitiveFromConservative(NewtonianIdealGasContext gas, StateConservative U) { 66 StatePrimitive Y; 67 for (CeedInt i = 0; i < 3; i++) Y.velocity[i] = U.momentum[i] / U.density; 68 CeedScalar e_kinetic = .5 * Dot3(Y.velocity, Y.velocity); 69 CeedScalar e_total = U.E_total / U.density; 70 CeedScalar e_internal = e_total - e_kinetic; 71 Y.temperature = e_internal / gas->cv; 72 Y.pressure = (HeatCapacityRatio(gas) - 1) * U.density * e_internal; 73 return Y; 74 } 75 76 CEED_QFUNCTION_HELPER StatePrimitive StatePrimitiveFromConservative_fwd(NewtonianIdealGasContext gas, State s, StateConservative dU) { 77 StatePrimitive dY; 78 for (CeedInt i = 0; i < 3; i++) { 79 dY.velocity[i] = (dU.momentum[i] - s.Y.velocity[i] * dU.density) / s.U.density; 80 } 81 CeedScalar e_kinetic = .5 * Dot3(s.Y.velocity, s.Y.velocity); 82 CeedScalar de_kinetic = Dot3(dY.velocity, s.Y.velocity); 83 CeedScalar e_total = s.U.E_total / s.U.density; 84 CeedScalar de_total = (dU.E_total - e_total * dU.density) / s.U.density; 85 CeedScalar e_internal = e_total - e_kinetic; 86 CeedScalar de_internal = de_total - de_kinetic; 87 dY.temperature = de_internal / gas->cv; 88 dY.pressure = (HeatCapacityRatio(gas) - 1) * (dU.density * e_internal + s.U.density * de_internal); 89 return dY; 90 } 91 92 CEED_QFUNCTION_HELPER StateEntropy StateEntropyFromPrimitive(NewtonianIdealGasContext gas, StatePrimitive Y) { 93 StateEntropy V; 94 const CeedScalar gamma = HeatCapacityRatio(gas); 95 const CeedScalar rho = Y.pressure / (GasConstant(gas) * Y.temperature); 96 const CeedScalar entropy = log(Y.pressure) - gamma * log(rho); 97 const CeedScalar rho_div_p = rho / Y.pressure; 98 const CeedScalar e_kinetic = 0.5 * Dot3(Y.velocity, Y.velocity); 99 100 V.S_density = (gamma - entropy) / (gamma - 1) - rho_div_p * e_kinetic; 101 for (int i = 0; i < 3; i++) V.S_momentum[i] = rho_div_p * Y.velocity[i]; 102 V.S_energy = -rho_div_p; 103 return V; 104 } 105 106 CEED_QFUNCTION_HELPER StateEntropy StateEntropyFromPrimitive_fwd(NewtonianIdealGasContext gas, State s, StatePrimitive dY) { 107 StateEntropy dV; 108 const CeedScalar gamma = HeatCapacityRatio(gas); 109 CeedScalar drho = (dY.pressure * s.Y.temperature - s.Y.pressure * dY.temperature) / (GasConstant(gas) * s.Y.temperature * s.Y.temperature); 110 111 const CeedScalar e_kinetic = .5 * Dot3(s.Y.velocity, s.Y.velocity); 112 const CeedScalar de_kinetic = Dot3(dY.velocity, s.Y.velocity); 113 const CeedScalar rho_div_p = s.U.density / s.Y.pressure; 114 const CeedScalar drho_div_p = (drho * s.Y.pressure - s.U.density * dY.pressure) / Square(s.Y.pressure); 115 116 CeedScalar dentropy = dY.pressure / s.Y.pressure - gamma * drho / s.U.density; 117 118 dV.S_density = -dentropy / (gamma - 1) - de_kinetic * rho_div_p - e_kinetic * drho_div_p; 119 for (CeedInt i = 0; i < 3; i++) dV.S_momentum[i] = rho_div_p * dY.velocity[i] + drho_div_p * s.Y.velocity[i]; 120 dV.S_energy = -drho_div_p; 121 return dV; 122 } 123 124 CEED_QFUNCTION_HELPER StatePrimitive StatePrimitiveFromEntropy(NewtonianIdealGasContext gas, StateEntropy V) { 125 StatePrimitive Y; 126 for (int i = 0; i < 3; i++) Y.velocity[i] = -V.S_momentum[i] / V.S_energy; 127 Y.temperature = -1 / (GasConstant(gas) * V.S_energy); 128 const CeedScalar gamma = HeatCapacityRatio(gas); 129 const CeedScalar e_kinetic = 0.5 * Dot3(Y.velocity, Y.velocity); 130 const CeedScalar entropy = gamma - (gamma - 1) * (V.S_density - e_kinetic * V.S_energy); 131 const CeedScalar log_P = -(entropy + gamma * log(-V.S_energy)) / (gamma - 1); 132 Y.pressure = exp(log_P); 133 return Y; 134 } 135 136 CEED_QFUNCTION_HELPER StatePrimitive StatePrimitiveFromEntropy_fwd(NewtonianIdealGasContext gas, State s, StateEntropy dV) { 137 StatePrimitive dY; 138 StateEntropy V = StateEntropyFromPrimitive(gas, s.Y); 139 for (int i = 0; i < 3; i++) dY.velocity[i] = -(dV.S_momentum[i] - V.S_momentum[i] * dV.S_energy / V.S_energy) / V.S_energy; 140 dY.temperature = dV.S_energy / (GasConstant(gas) * V.S_energy * V.S_energy); 141 const CeedScalar gamma = HeatCapacityRatio(gas); 142 const CeedScalar e_kinetic = 0.5 * Dot3(s.Y.velocity, s.Y.velocity); 143 const CeedScalar de_kinetic = Dot3(dY.velocity, s.Y.velocity); 144 const CeedScalar dentropy = (1 - gamma) * (dV.S_density - e_kinetic * dV.S_energy - de_kinetic * V.S_energy); 145 dY.pressure = s.Y.pressure * (-dentropy - gamma * dV.S_energy / V.S_energy) / (gamma - 1); 146 return dY; 147 } 148 149 CEED_QFUNCTION_HELPER StateConservative StateConservativeFromPrimitive(NewtonianIdealGasContext gas, StatePrimitive Y) { 150 StateConservative U; 151 U.density = Y.pressure / (GasConstant(gas) * Y.temperature); 152 for (int i = 0; i < 3; i++) U.momentum[i] = U.density * Y.velocity[i]; 153 CeedScalar e_internal = gas->cv * Y.temperature; 154 CeedScalar e_kinetic = .5 * Dot3(Y.velocity, Y.velocity); 155 CeedScalar e_total = e_internal + e_kinetic; 156 U.E_total = U.density * e_total; 157 return U; 158 } 159 160 CEED_QFUNCTION_HELPER StateConservative StateConservativeFromPrimitive_fwd(NewtonianIdealGasContext gas, State s, StatePrimitive dY) { 161 StateConservative dU; 162 dU.density = (dY.pressure * s.Y.temperature - s.Y.pressure * dY.temperature) / (GasConstant(gas) * s.Y.temperature * s.Y.temperature); 163 for (int i = 0; i < 3; i++) { 164 dU.momentum[i] = dU.density * s.Y.velocity[i] + s.U.density * dY.velocity[i]; 165 } 166 CeedScalar e_kinetic = .5 * Dot3(s.Y.velocity, s.Y.velocity); 167 CeedScalar de_kinetic = Dot3(dY.velocity, s.Y.velocity); 168 CeedScalar e_internal = gas->cv * s.Y.temperature; 169 CeedScalar de_internal = gas->cv * dY.temperature; 170 CeedScalar e_total = e_internal + e_kinetic; 171 CeedScalar de_total = de_internal + de_kinetic; 172 dU.E_total = dU.density * e_total + s.U.density * de_total; 173 return dU; 174 } 175 176 CEED_QFUNCTION_HELPER StateEntropy StateEntropyFromConservative(NewtonianIdealGasContext gas, StateConservative U) { 177 StateEntropy V; 178 const CeedScalar gamma = HeatCapacityRatio(gas); 179 const CeedScalar e_kinetic = .5 * Dot3(U.momentum, U.momentum) / U.density; 180 const CeedScalar e_internal = U.E_total - e_kinetic; 181 const CeedScalar p = (gamma - 1) * e_internal; 182 const CeedScalar entropy = log(p) - gamma * log(U.density); 183 184 V.S_density = (gamma - entropy) / (gamma - 1) - e_kinetic / p; 185 for (int i = 0; i < 3; i++) V.S_momentum[i] = U.momentum[i] / p; 186 V.S_energy = -U.density / p; 187 return V; 188 } 189 190 CEED_QFUNCTION_HELPER StateEntropy StateEntropyFromConservative_fwd(NewtonianIdealGasContext gas, State s, StateConservative dU) { 191 StateEntropy dV; 192 const CeedScalar gamma = HeatCapacityRatio(gas); 193 const CeedScalar e_kinetic = .5 * Dot3(s.U.momentum, s.U.momentum) / s.U.density; 194 const CeedScalar de_kinetic = (Dot3(s.U.momentum, dU.momentum) - e_kinetic * dU.density) / s.U.density; 195 const CeedScalar de_internal = dU.E_total - de_kinetic; 196 const CeedScalar p = s.Y.pressure; 197 const CeedScalar dp = (gamma - 1) * de_internal; 198 199 CeedScalar dentropy = dp / p - gamma * dU.density / s.U.density; 200 201 dV.S_density = -dentropy / (gamma - 1) - de_kinetic / p + dp * e_kinetic / Square(p); 202 for (CeedInt i = 0; i < 3; i++) { 203 dV.S_momentum[i] = (dU.momentum[i] - s.U.momentum[i] * dp / p) / p; 204 } 205 dV.S_energy = -(dU.density - s.U.density * dp / p) / p; 206 return dV; 207 } 208 209 CEED_QFUNCTION_HELPER StateConservative StateConservativeFromEntropy(NewtonianIdealGasContext gas, StateEntropy V) { 210 StateConservative U; 211 CeedScalar velocity[3]; 212 for (int i = 0; i < 3; i++) velocity[i] = -V.S_momentum[i] / V.S_energy; 213 const CeedScalar gamma = HeatCapacityRatio(gas); 214 const CeedScalar e_kinetic = 0.5 * Dot3(velocity, velocity); 215 const CeedScalar entropy = gamma - (gamma - 1) * (V.S_density - e_kinetic * V.S_energy); 216 const CeedScalar log_rho = -(entropy + log(-V.S_energy)) / (gamma - 1); 217 U.density = exp(log_rho); 218 for (int i = 0; i < 3; i++) U.momentum[i] = U.density * velocity[i]; 219 220 const CeedScalar e_internal = -gas->cv / (GasConstant(gas) * V.S_energy); 221 U.E_total = U.density * (e_internal + e_kinetic); 222 return U; 223 } 224 225 CEED_QFUNCTION_HELPER StateConservative StateConservativeFromEntropy_fwd(NewtonianIdealGasContext gas, State s, StateEntropy dV) { 226 StateConservative dU; 227 CeedScalar dvelocity[3]; 228 StateEntropy V = StateEntropyFromPrimitive(gas, s.Y); 229 for (int i = 0; i < 3; i++) dvelocity[i] = (-dV.S_momentum[i] - s.Y.velocity[i] * dV.S_energy) / V.S_energy; 230 const CeedScalar gamma = HeatCapacityRatio(gas); 231 const CeedScalar e_kinetic = 0.5 * Dot3(s.Y.velocity, s.Y.velocity); 232 const CeedScalar de_kinetic = Dot3(dvelocity, s.Y.velocity); 233 const CeedScalar entropy = gamma - (gamma - 1) * (V.S_density - e_kinetic * V.S_energy); 234 const CeedScalar dentropy = -(gamma - 1) * (dV.S_density - (de_kinetic * V.S_energy + e_kinetic * dV.S_energy)); 235 const CeedScalar log_rho = -(entropy + log(-V.S_energy)) / (gamma - 1); 236 const CeedScalar rho = exp(log_rho); 237 dU.density = -rho / (gamma - 1) * (dentropy + dV.S_energy / V.S_energy); 238 for (int i = 0; i < 3; i++) dU.momentum[i] = dU.density * s.Y.velocity[i] + s.U.density * dvelocity[i]; 239 240 const CeedScalar e_internal = -gas->cv / (GasConstant(gas) * V.S_energy); 241 const CeedScalar de_internal = gas->cv * dV.S_energy / (GasConstant(gas) * V.S_energy * V.S_energy); 242 const CeedScalar e_total = e_internal + e_kinetic; 243 dU.E_total = dU.density * e_total + s.U.density * (de_internal + de_kinetic); 244 return dU; 245 } 246 247 CEED_QFUNCTION_HELPER State StateFromPrimitive(NewtonianIdealGasContext gas, StatePrimitive Y) { 248 StateConservative U = StateConservativeFromPrimitive(gas, Y); 249 State s; 250 s.U = U; 251 s.Y = Y; 252 return s; 253 } 254 255 CEED_QFUNCTION_HELPER State StateFromPrimitive_fwd(NewtonianIdealGasContext gas, State s, StatePrimitive dY) { 256 StateConservative dU = StateConservativeFromPrimitive_fwd(gas, s, dY); 257 State ds; 258 ds.U = dU; 259 ds.Y = dY; 260 return ds; 261 } 262 263 // linear combination of n states 264 CEED_QFUNCTION_HELPER StateConservative StateConservativeMult(CeedInt n, const CeedScalar a[], const StateConservative X[]) { 265 StateConservative R = {0}; 266 for (CeedInt i = 0; i < n; i++) { 267 R.density += a[i] * X[i].density; 268 for (int j = 0; j < 3; j++) R.momentum[j] += a[i] * X[i].momentum[j]; 269 R.E_total += a[i] * X[i].E_total; 270 } 271 return R; 272 } 273 274 CEED_QFUNCTION_HELPER StateConservative StateConservativeAXPBYPCZ(CeedScalar a, StateConservative X, CeedScalar b, StateConservative Y, CeedScalar c, 275 StateConservative Z) { 276 StateConservative R; 277 R.density = a * X.density + b * Y.density + c * Z.density; 278 for (int i = 0; i < 3; i++) R.momentum[i] = a * X.momentum[i] + b * Y.momentum[i] + c * Z.momentum[i]; 279 R.E_total = a * X.E_total + b * Y.E_total + c * Z.E_total; 280 return R; 281 } 282 283 CEED_QFUNCTION_HELPER void StateToU(NewtonianIdealGasContext gas, const State input, CeedScalar U[5]) { UnpackState_U(input.U, U); } 284 285 CEED_QFUNCTION_HELPER void StateToY(NewtonianIdealGasContext gas, const State input, CeedScalar Y[5]) { UnpackState_Y(input.Y, Y); } 286 287 CEED_QFUNCTION_HELPER void StateToV(NewtonianIdealGasContext gas, const State input, CeedScalar V[5]) { 288 StateEntropy state_V = StateEntropyFromPrimitive(gas, input.Y); 289 UnpackState_V(state_V, V); 290 } 291 292 CEED_QFUNCTION_HELPER void StateToQ(NewtonianIdealGasContext gas, const State input, CeedScalar Q[5], StateVariable state_var) { 293 switch (state_var) { 294 case STATEVAR_CONSERVATIVE: 295 StateToU(gas, input, Q); 296 break; 297 case STATEVAR_PRIMITIVE: 298 StateToY(gas, input, Q); 299 break; 300 case STATEVAR_ENTROPY: 301 StateToV(gas, input, Q); 302 break; 303 default: 304 SetValueN(Q, -1, 5); 305 break; 306 } 307 } 308 309 CEED_QFUNCTION_HELPER void StateToQ_fwd(NewtonianIdealGasContext gas, const State input, const State dinput, CeedScalar dQ[5], 310 StateVariable state_var) { 311 switch (state_var) { 312 case STATEVAR_CONSERVATIVE: 313 case STATEVAR_PRIMITIVE: 314 StateToQ(gas, dinput, dQ, state_var); 315 break; 316 case STATEVAR_ENTROPY: { 317 StateEntropy dstate_v; 318 319 dstate_v = StateEntropyFromPrimitive_fwd(gas, input, dinput.Y); 320 UnpackState_V(dstate_v, dQ); 321 } break; 322 } 323 } 324 325 CEED_QFUNCTION_HELPER State StateFromU(NewtonianIdealGasContext gas, const CeedScalar U[5]) { 326 State s; 327 s.U.density = U[0]; 328 s.U.momentum[0] = U[1]; 329 s.U.momentum[1] = U[2]; 330 s.U.momentum[2] = U[3]; 331 s.U.E_total = U[4]; 332 s.Y = StatePrimitiveFromConservative(gas, s.U); 333 return s; 334 } 335 336 CEED_QFUNCTION_HELPER State StateFromU_fwd(NewtonianIdealGasContext gas, State s, const CeedScalar dU[5]) { 337 State ds; 338 ds.U.density = dU[0]; 339 ds.U.momentum[0] = dU[1]; 340 ds.U.momentum[1] = dU[2]; 341 ds.U.momentum[2] = dU[3]; 342 ds.U.E_total = dU[4]; 343 ds.Y = StatePrimitiveFromConservative_fwd(gas, s, ds.U); 344 return ds; 345 } 346 347 CEED_QFUNCTION_HELPER State StateFromY(NewtonianIdealGasContext gas, const CeedScalar Y[5]) { 348 State s; 349 s.Y.pressure = Y[0]; 350 s.Y.velocity[0] = Y[1]; 351 s.Y.velocity[1] = Y[2]; 352 s.Y.velocity[2] = Y[3]; 353 s.Y.temperature = Y[4]; 354 s.U = StateConservativeFromPrimitive(gas, s.Y); 355 return s; 356 } 357 358 CEED_QFUNCTION_HELPER State StateFromY_fwd(NewtonianIdealGasContext gas, State s, const CeedScalar dY[5]) { 359 State ds; 360 ds.Y.pressure = dY[0]; 361 ds.Y.velocity[0] = dY[1]; 362 ds.Y.velocity[1] = dY[2]; 363 ds.Y.velocity[2] = dY[3]; 364 ds.Y.temperature = dY[4]; 365 ds.U = StateConservativeFromPrimitive_fwd(gas, s, ds.Y); 366 return ds; 367 } 368 369 CEED_QFUNCTION_HELPER State StateFromV(NewtonianIdealGasContext gas, const CeedScalar V[5]) { 370 State s; 371 StateEntropy state_V; 372 state_V.S_density = V[0]; 373 state_V.S_momentum[0] = V[1]; 374 state_V.S_momentum[1] = V[2]; 375 state_V.S_momentum[2] = V[3]; 376 state_V.S_energy = V[4]; 377 s.U = StateConservativeFromEntropy(gas, state_V); 378 s.Y = StatePrimitiveFromEntropy(gas, state_V); 379 return s; 380 } 381 382 CEED_QFUNCTION_HELPER State StateFromV_fwd(NewtonianIdealGasContext gas, State s, const CeedScalar dV[5]) { 383 State ds; 384 StateEntropy state_dV; 385 state_dV.S_density = dV[0]; 386 state_dV.S_momentum[0] = dV[1]; 387 state_dV.S_momentum[1] = dV[2]; 388 state_dV.S_momentum[2] = dV[3]; 389 state_dV.S_energy = dV[4]; 390 ds.U = StateConservativeFromEntropy_fwd(gas, s, state_dV); 391 ds.Y = StatePrimitiveFromEntropy_fwd(gas, s, state_dV); 392 return ds; 393 } 394 395 CEED_QFUNCTION_HELPER State StateFromQ(NewtonianIdealGasContext gas, const CeedScalar Q[5], StateVariable state_var) { 396 State s; 397 switch (state_var) { 398 case STATEVAR_CONSERVATIVE: 399 s = StateFromU(gas, Q); 400 break; 401 case STATEVAR_PRIMITIVE: 402 s = StateFromY(gas, Q); 403 break; 404 case STATEVAR_ENTROPY: 405 s = StateFromV(gas, Q); 406 break; 407 } 408 return s; 409 } 410 411 CEED_QFUNCTION_HELPER State StateFromQ_fwd(NewtonianIdealGasContext gas, State s, const CeedScalar dQ[5], StateVariable state_var) { 412 State ds; 413 switch (state_var) { 414 case STATEVAR_CONSERVATIVE: 415 ds = StateFromU_fwd(gas, s, dQ); 416 break; 417 case STATEVAR_PRIMITIVE: 418 ds = StateFromY_fwd(gas, s, dQ); 419 break; 420 case STATEVAR_ENTROPY: 421 ds = StateFromV_fwd(gas, s, dQ); 422 break; 423 } 424 return ds; 425 } 426 427 CEED_QFUNCTION_HELPER void FluxInviscid(NewtonianIdealGasContext gas, State s, StateConservative Flux[3]) { 428 for (CeedInt i = 0; i < 3; i++) { 429 Flux[i].density = s.U.momentum[i]; 430 for (CeedInt j = 0; j < 3; j++) Flux[i].momentum[j] = s.U.momentum[i] * s.Y.velocity[j] + s.Y.pressure * (i == j); 431 Flux[i].E_total = (s.U.E_total + s.Y.pressure) * s.Y.velocity[i]; 432 } 433 } 434 435 CEED_QFUNCTION_HELPER void FluxInviscid_fwd(NewtonianIdealGasContext gas, State s, State ds, StateConservative dFlux[3]) { 436 for (CeedInt i = 0; i < 3; i++) { 437 dFlux[i].density = ds.U.momentum[i]; 438 for (CeedInt j = 0; j < 3; j++) { 439 dFlux[i].momentum[j] = ds.U.momentum[i] * s.Y.velocity[j] + s.U.momentum[i] * ds.Y.velocity[j] + ds.Y.pressure * (i == j); 440 } 441 dFlux[i].E_total = (ds.U.E_total + ds.Y.pressure) * s.Y.velocity[i] + (s.U.E_total + s.Y.pressure) * ds.Y.velocity[i]; 442 } 443 } 444 445 CEED_QFUNCTION_HELPER StateConservative FluxInviscidDotNormal(NewtonianIdealGasContext gas, State s, const CeedScalar normal[3]) { 446 StateConservative Flux[3], Flux_dot_n = {0}; 447 FluxInviscid(gas, s, Flux); 448 for (CeedInt i = 0; i < 3; i++) { 449 Flux_dot_n.density += Flux[i].density * normal[i]; 450 for (CeedInt j = 0; j < 3; j++) Flux_dot_n.momentum[j] += Flux[i].momentum[j] * normal[i]; 451 Flux_dot_n.E_total += Flux[i].E_total * normal[i]; 452 } 453 return Flux_dot_n; 454 } 455 456 CEED_QFUNCTION_HELPER StateConservative FluxInviscidDotNormal_fwd(NewtonianIdealGasContext gas, State s, State ds, const CeedScalar normal[3]) { 457 StateConservative dFlux[3], Flux_dot_n = {0}; 458 FluxInviscid_fwd(gas, s, ds, dFlux); 459 for (CeedInt i = 0; i < 3; i++) { 460 Flux_dot_n.density += dFlux[i].density * normal[i]; 461 for (CeedInt j = 0; j < 3; j++) Flux_dot_n.momentum[j] += dFlux[i].momentum[j] * normal[i]; 462 Flux_dot_n.E_total += dFlux[i].E_total * normal[i]; 463 } 464 return Flux_dot_n; 465 } 466 467 CEED_QFUNCTION_HELPER void FluxInviscidStrong(NewtonianIdealGasContext gas, State s, State ds[3], CeedScalar strong_conv[5]) { 468 for (CeedInt i = 0; i < 5; i++) strong_conv[i] = 0; 469 for (CeedInt i = 0; i < 3; i++) { 470 StateConservative dF[3]; 471 FluxInviscid_fwd(gas, s, ds[i], dF); 472 CeedScalar dF_i[5]; 473 UnpackState_U(dF[i], dF_i); 474 for (CeedInt j = 0; j < 5; j++) strong_conv[j] += dF_i[j]; 475 } 476 } 477 478 CEED_QFUNCTION_HELPER void FluxTotal(const StateConservative F_inviscid[3], CeedScalar stress[3][3], CeedScalar Fe[3], CeedScalar Flux[5][3]) { 479 for (CeedInt j = 0; j < 3; j++) { 480 Flux[0][j] = F_inviscid[j].density; 481 for (CeedInt k = 0; k < 3; k++) Flux[k + 1][j] = F_inviscid[j].momentum[k] - stress[k][j]; 482 Flux[4][j] = F_inviscid[j].E_total + Fe[j]; 483 } 484 } 485 486 CEED_QFUNCTION_HELPER void FluxTotal_Boundary(const StateConservative F_inviscid[3], const CeedScalar stress[3][3], const CeedScalar Fe[3], 487 const CeedScalar normal[3], CeedScalar Flux[5]) { 488 for (CeedInt j = 0; j < 5; j++) Flux[j] = 0.; 489 for (CeedInt j = 0; j < 3; j++) { 490 Flux[0] += F_inviscid[j].density * normal[j]; 491 for (CeedInt k = 0; k < 3; k++) { 492 Flux[k + 1] += (F_inviscid[j].momentum[k] - stress[k][j]) * normal[j]; 493 } 494 Flux[4] += (F_inviscid[j].E_total + Fe[j]) * normal[j]; 495 } 496 } 497 498 CEED_QFUNCTION_HELPER void FluxTotal_RiemannBoundary(const StateConservative F_inviscid_normal, const CeedScalar stress[3][3], const CeedScalar Fe[3], 499 const CeedScalar normal[3], CeedScalar Flux[5]) { 500 Flux[0] = F_inviscid_normal.density; 501 for (CeedInt k = 0; k < 3; k++) Flux[k + 1] = F_inviscid_normal.momentum[k]; 502 Flux[4] = F_inviscid_normal.E_total; 503 for (CeedInt j = 0; j < 3; j++) { 504 for (CeedInt k = 0; k < 3; k++) { 505 Flux[k + 1] -= stress[k][j] * normal[j]; 506 } 507 Flux[4] += Fe[j] * normal[j]; 508 } 509 } 510 511 CEED_QFUNCTION_HELPER void VelocityGradient(const State grad_s[3], CeedScalar grad_velocity[3][3]) { 512 grad_velocity[0][0] = grad_s[0].Y.velocity[0]; 513 grad_velocity[0][1] = grad_s[1].Y.velocity[0]; 514 grad_velocity[0][2] = grad_s[2].Y.velocity[0]; 515 grad_velocity[1][0] = grad_s[0].Y.velocity[1]; 516 grad_velocity[1][1] = grad_s[1].Y.velocity[1]; 517 grad_velocity[1][2] = grad_s[2].Y.velocity[1]; 518 grad_velocity[2][0] = grad_s[0].Y.velocity[2]; 519 grad_velocity[2][1] = grad_s[1].Y.velocity[2]; 520 grad_velocity[2][2] = grad_s[2].Y.velocity[2]; 521 } 522 523 CEED_QFUNCTION_HELPER void KMStrainRate(const CeedScalar grad_velocity[3][3], CeedScalar strain_rate[6]) { 524 const CeedScalar weight = 1 / sqrt(2.); // Really sqrt(2.) / 2 525 strain_rate[0] = grad_velocity[0][0]; 526 strain_rate[1] = grad_velocity[1][1]; 527 strain_rate[2] = grad_velocity[2][2]; 528 strain_rate[3] = weight * (grad_velocity[1][2] + grad_velocity[2][1]); 529 strain_rate[4] = weight * (grad_velocity[0][2] + grad_velocity[2][0]); 530 strain_rate[5] = weight * (grad_velocity[0][1] + grad_velocity[1][0]); 531 } 532 533 // Kelvin-Mandel notation 534 CEED_QFUNCTION_HELPER void KMStrainRate_State(const State grad_s[3], CeedScalar strain_rate[6]) { 535 CeedScalar grad_velocity[3][3]; 536 VelocityGradient(grad_s, grad_velocity); 537 KMStrainRate(grad_velocity, strain_rate); 538 } 539 540 //@brief Given velocity gradient du_i/dx_j, return 0.5*(du_i/dx_j - du_j/dx_i) 541 CEED_QFUNCTION_HELPER void RotationRate(const CeedScalar grad_velocity[3][3], CeedScalar rotation_rate[3][3]) { 542 rotation_rate[0][0] = 0; 543 rotation_rate[1][1] = 0; 544 rotation_rate[2][2] = 0; 545 rotation_rate[1][2] = 0.5 * (grad_velocity[1][2] - grad_velocity[2][1]); 546 rotation_rate[0][2] = 0.5 * (grad_velocity[0][2] - grad_velocity[2][0]); 547 rotation_rate[0][1] = 0.5 * (grad_velocity[0][1] - grad_velocity[1][0]); 548 rotation_rate[2][1] = -rotation_rate[1][2]; 549 rotation_rate[2][0] = -rotation_rate[0][2]; 550 rotation_rate[1][0] = -rotation_rate[0][1]; 551 } 552 553 CEED_QFUNCTION_HELPER void NewtonianStress(NewtonianIdealGasContext gas, const CeedScalar strain_rate[6], CeedScalar stress[6]) { 554 CeedScalar div_u = strain_rate[0] + strain_rate[1] + strain_rate[2]; 555 for (CeedInt i = 0; i < 6; i++) { 556 stress[i] = gas->mu * (2 * strain_rate[i] + gas->lambda * div_u * (i < 3)); 557 } 558 } 559 560 CEED_QFUNCTION_HELPER void ViscousEnergyFlux(NewtonianIdealGasContext gas, StatePrimitive Y, const State grad_s[3], const CeedScalar stress[3][3], 561 CeedScalar Fe[3]) { 562 for (CeedInt i = 0; i < 3; i++) { 563 Fe[i] = -Y.velocity[0] * stress[0][i] - Y.velocity[1] * stress[1][i] - Y.velocity[2] * stress[2][i] - gas->k * grad_s[i].Y.temperature; 564 } 565 } 566 567 CEED_QFUNCTION_HELPER void ViscousEnergyFlux_fwd(NewtonianIdealGasContext gas, StatePrimitive Y, StatePrimitive dY, const State grad_ds[3], 568 const CeedScalar stress[3][3], const CeedScalar dstress[3][3], CeedScalar dFe[3]) { 569 for (CeedInt i = 0; i < 3; i++) { 570 dFe[i] = -Y.velocity[0] * dstress[0][i] - dY.velocity[0] * stress[0][i] - Y.velocity[1] * dstress[1][i] - dY.velocity[1] * stress[1][i] - 571 Y.velocity[2] * dstress[2][i] - dY.velocity[2] * stress[2][i] - gas->k * grad_ds[i].Y.temperature; 572 } 573 } 574 575 CEED_QFUNCTION_HELPER void Vorticity(const State grad_s[3], CeedScalar vorticity[3]) { 576 CeedScalar grad_velocity[3][3]; 577 VelocityGradient(grad_s, grad_velocity); 578 Curl3(grad_velocity, vorticity); 579 } 580 581 CEED_QFUNCTION_HELPER void StatePhysicalGradientFromReference(CeedInt Q, CeedInt i, NewtonianIdealGasContext gas, State s, StateVariable state_var, 582 const CeedScalar *grad_q, const CeedScalar dXdx[3][3], State grad_s[3]) { 583 CeedScalar grad_qi[5][3], dq[5][3] = {{0.}}; 584 585 GradUnpack3(Q, i, 5, grad_q, grad_qi); 586 MatMatNM((CeedScalar *)grad_qi, (CeedScalar *)dXdx, (CeedScalar *)dq, 5, 3, 3); 587 for (CeedInt j = 0; j < 3; j++) { 588 CeedScalar dqi[5]; 589 590 for (CeedInt k = 0; k < 5; k++) dqi[k] = dq[k][j]; 591 grad_s[j] = StateFromQ_fwd(gas, s, dqi, state_var); 592 } 593 } 594 595 CEED_QFUNCTION_HELPER void StatePhysicalGradientFromReference_Boundary(CeedInt Q, CeedInt i, NewtonianIdealGasContext gas, State s, 596 StateVariable state_var, const CeedScalar *grad_q, const CeedScalar dXdx[2][3], 597 State grad_s[3]) { 598 for (CeedInt k = 0; k < 3; k++) { 599 CeedScalar dqi[5]; 600 for (CeedInt j = 0; j < 5; j++) { 601 dqi[j] = grad_q[(Q * 5) * 0 + Q * j + i] * dXdx[0][k] + grad_q[(Q * 5) * 1 + Q * j + i] * dXdx[1][k]; 602 } 603 grad_s[k] = StateFromQ_fwd(gas, s, dqi, state_var); 604 } 605 } 606