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 /// Structs and helper functions regarding the state of a newtonian simulation 10 11 #ifndef newtonian_state_h 12 #define newtonian_state_h 13 14 #include <ceed.h> 15 #include <math.h> 16 17 #include "newtonian_types.h" 18 #include "utils.h" 19 20 typedef struct { 21 CeedScalar density; 22 CeedScalar momentum[3]; 23 CeedScalar E_total; 24 } StateConservative; 25 26 typedef struct { 27 StateConservative U; 28 StatePrimitive Y; 29 } State; 30 31 CEED_QFUNCTION_HELPER void UnpackState_U(StateConservative s, CeedScalar U[5]) { 32 U[0] = s.density; 33 for (int i = 0; i < 3; i++) U[i + 1] = s.momentum[i]; 34 U[4] = s.E_total; 35 } 36 37 CEED_QFUNCTION_HELPER void UnpackState_Y(StatePrimitive s, CeedScalar Y[5]) { 38 Y[0] = s.pressure; 39 for (int i = 0; i < 3; i++) Y[i + 1] = s.velocity[i]; 40 Y[4] = s.temperature; 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 // Ignoring potential energy 55 CeedScalar e_internal = gas->cv * s.Y.temperature; 56 CeedScalar e_kinetic = 0.5 * Dot3(s.Y.velocity, s.Y.velocity); 57 return e_internal + e_kinetic + s.Y.pressure / s.U.density; 58 } 59 60 CEED_QFUNCTION_HELPER CeedScalar TotalSpecificEnthalpy_fwd(NewtonianIdealGasContext gas, const State s, const State ds) { 61 // Ignoring potential energy 62 CeedScalar de_kinetic = Dot3(ds.Y.velocity, s.Y.velocity); 63 CeedScalar de_internal = gas->cv * ds.Y.temperature; 64 return de_internal + de_kinetic + ds.Y.pressure / s.U.density - s.Y.pressure / Square(s.U.density) * ds.U.density; 65 } 66 67 CEED_QFUNCTION_HELPER StatePrimitive StatePrimitiveFromConservative(NewtonianIdealGasContext gas, StateConservative U, const CeedScalar x[3]) { 68 StatePrimitive Y; 69 for (CeedInt i = 0; i < 3; i++) Y.velocity[i] = U.momentum[i] / U.density; 70 CeedScalar e_kinetic = .5 * Dot3(Y.velocity, Y.velocity); 71 CeedScalar e_potential = -Dot3(gas->g, x); 72 CeedScalar e_total = U.E_total / U.density; 73 CeedScalar e_internal = e_total - e_kinetic - e_potential; 74 Y.temperature = e_internal / gas->cv; 75 Y.pressure = (HeatCapacityRatio(gas) - 1) * U.density * e_internal; 76 return Y; 77 } 78 79 CEED_QFUNCTION_HELPER StatePrimitive StatePrimitiveFromConservative_fwd(NewtonianIdealGasContext gas, State s, StateConservative dU, 80 const CeedScalar x[3], const CeedScalar dx[3]) { 81 StatePrimitive dY; 82 for (CeedInt i = 0; i < 3; i++) { 83 dY.velocity[i] = (dU.momentum[i] - s.Y.velocity[i] * dU.density) / s.U.density; 84 } 85 CeedScalar e_kinetic = .5 * Dot3(s.Y.velocity, s.Y.velocity); 86 CeedScalar de_kinetic = Dot3(dY.velocity, s.Y.velocity); 87 CeedScalar e_potential = -Dot3(gas->g, x); 88 CeedScalar de_potential = -Dot3(gas->g, dx); 89 CeedScalar e_total = s.U.E_total / s.U.density; 90 CeedScalar de_total = (dU.E_total - e_total * dU.density) / s.U.density; 91 CeedScalar e_internal = e_total - e_kinetic - e_potential; 92 CeedScalar de_internal = de_total - de_kinetic - de_potential; 93 dY.temperature = de_internal / gas->cv; 94 dY.pressure = (HeatCapacityRatio(gas) - 1) * (dU.density * e_internal + s.U.density * de_internal); 95 return dY; 96 } 97 98 CEED_QFUNCTION_HELPER StateConservative StateConservativeFromPrimitive(NewtonianIdealGasContext gas, StatePrimitive Y, const CeedScalar x[3]) { 99 StateConservative U; 100 U.density = Y.pressure / (GasConstant(gas) * Y.temperature); 101 for (int i = 0; i < 3; i++) U.momentum[i] = U.density * Y.velocity[i]; 102 CeedScalar e_internal = gas->cv * Y.temperature; 103 CeedScalar e_kinetic = .5 * Dot3(Y.velocity, Y.velocity); 104 CeedScalar e_potential = -Dot3(gas->g, x); 105 CeedScalar e_total = e_internal + e_kinetic + e_potential; 106 U.E_total = U.density * e_total; 107 return U; 108 } 109 110 CEED_QFUNCTION_HELPER StateConservative StateConservativeFromPrimitive_fwd(NewtonianIdealGasContext gas, State s, StatePrimitive dY, 111 const CeedScalar x[3], const CeedScalar dx[3]) { 112 StateConservative dU; 113 dU.density = (dY.pressure * s.Y.temperature - s.Y.pressure * dY.temperature) / (GasConstant(gas) * s.Y.temperature * s.Y.temperature); 114 for (int i = 0; i < 3; i++) { 115 dU.momentum[i] = dU.density * s.Y.velocity[i] + s.U.density * dY.velocity[i]; 116 } 117 CeedScalar e_kinetic = .5 * Dot3(s.Y.velocity, s.Y.velocity); 118 CeedScalar de_kinetic = Dot3(dY.velocity, s.Y.velocity); 119 CeedScalar e_potential = -Dot3(gas->g, x); 120 CeedScalar de_potential = -Dot3(gas->g, dx); 121 CeedScalar e_internal = gas->cv * s.Y.temperature; 122 CeedScalar de_internal = gas->cv * dY.temperature; 123 CeedScalar e_total = e_internal + e_kinetic + e_potential; 124 CeedScalar de_total = de_internal + de_kinetic + de_potential; 125 dU.E_total = dU.density * e_total + s.U.density * de_total; 126 return dU; 127 } 128 129 CEED_QFUNCTION_HELPER State StateFromPrimitive(NewtonianIdealGasContext gas, StatePrimitive Y, const CeedScalar x[3]) { 130 StateConservative U = StateConservativeFromPrimitive(gas, Y, x); 131 State s; 132 s.U = U; 133 s.Y = Y; 134 return s; 135 } 136 137 CEED_QFUNCTION_HELPER State StateFromPrimitive_fwd(NewtonianIdealGasContext gas, State s, StatePrimitive dY, const CeedScalar x[3], 138 const CeedScalar dx[3]) { 139 StateConservative dU = StateConservativeFromPrimitive_fwd(gas, s, dY, x, dx); 140 State ds; 141 ds.U = dU; 142 ds.Y = dY; 143 return ds; 144 } 145 146 // linear combination of n states 147 CEED_QFUNCTION_HELPER StateConservative StateConservativeMult(CeedInt n, const CeedScalar a[], const StateConservative X[]) { 148 StateConservative R = {0}; 149 for (CeedInt i = 0; i < n; i++) { 150 R.density += a[i] * X[i].density; 151 for (int j = 0; j < 3; j++) R.momentum[j] += a[i] * X[i].momentum[j]; 152 R.E_total += a[i] * X[i].E_total; 153 } 154 return R; 155 } 156 157 CEED_QFUNCTION_HELPER StateConservative StateConservativeAXPBYPCZ(CeedScalar a, StateConservative X, CeedScalar b, StateConservative Y, CeedScalar c, 158 StateConservative Z) { 159 StateConservative R; 160 R.density = a * X.density + b * Y.density + c * Z.density; 161 for (int i = 0; i < 3; i++) R.momentum[i] = a * X.momentum[i] + b * Y.momentum[i] + c * Z.momentum[i]; 162 R.E_total = a * X.E_total + b * Y.E_total + c * Z.E_total; 163 return R; 164 } 165 166 // Function pointer types for generic state array -> State struct functions 167 typedef State (*StateFromQi_t)(NewtonianIdealGasContext gas, const CeedScalar qi[5], const CeedScalar x[3]); 168 // Function pointer types for State struct -> generic state array 169 typedef void (*StateToQi_t)(NewtonianIdealGasContext gas, const State input, CeedScalar qi[5]); 170 171 CEED_QFUNCTION_HELPER void StateToU(NewtonianIdealGasContext gas, const State input, CeedScalar U[5]) { UnpackState_U(input.U, U); } 172 173 CEED_QFUNCTION_HELPER void StateToY(NewtonianIdealGasContext gas, const State input, CeedScalar Y[5]) { UnpackState_Y(input.Y, Y); } 174 typedef State (*StateFromQi_fwd_t)(NewtonianIdealGasContext gas, State s, const CeedScalar dqi[5], const CeedScalar x[3], const CeedScalar dx[3]); 175 176 CEED_QFUNCTION_HELPER State StateFromU(NewtonianIdealGasContext gas, const CeedScalar U[5], const CeedScalar x[3]) { 177 State s; 178 s.U.density = U[0]; 179 s.U.momentum[0] = U[1]; 180 s.U.momentum[1] = U[2]; 181 s.U.momentum[2] = U[3]; 182 s.U.E_total = U[4]; 183 s.Y = StatePrimitiveFromConservative(gas, s.U, x); 184 return s; 185 } 186 187 CEED_QFUNCTION_HELPER State StateFromU_fwd(NewtonianIdealGasContext gas, State s, const CeedScalar dU[5], const CeedScalar x[3], 188 const CeedScalar dx[3]) { 189 State ds; 190 ds.U.density = dU[0]; 191 ds.U.momentum[0] = dU[1]; 192 ds.U.momentum[1] = dU[2]; 193 ds.U.momentum[2] = dU[3]; 194 ds.U.E_total = dU[4]; 195 ds.Y = StatePrimitiveFromConservative_fwd(gas, s, ds.U, x, dx); 196 return ds; 197 } 198 199 CEED_QFUNCTION_HELPER State StateFromY(NewtonianIdealGasContext gas, const CeedScalar Y[5], const CeedScalar x[3]) { 200 State s; 201 s.Y.pressure = Y[0]; 202 s.Y.velocity[0] = Y[1]; 203 s.Y.velocity[1] = Y[2]; 204 s.Y.velocity[2] = Y[3]; 205 s.Y.temperature = Y[4]; 206 s.U = StateConservativeFromPrimitive(gas, s.Y, x); 207 return s; 208 } 209 210 CEED_QFUNCTION_HELPER State StateFromY_fwd(NewtonianIdealGasContext gas, State s, const CeedScalar dY[5], const CeedScalar x[3], 211 const CeedScalar dx[3]) { 212 State ds; 213 ds.Y.pressure = dY[0]; 214 ds.Y.velocity[0] = dY[1]; 215 ds.Y.velocity[1] = dY[2]; 216 ds.Y.velocity[2] = dY[3]; 217 ds.Y.temperature = dY[4]; 218 ds.U = StateConservativeFromPrimitive_fwd(gas, s, ds.Y, x, dx); 219 return ds; 220 } 221 222 CEED_QFUNCTION_HELPER void FluxInviscid(NewtonianIdealGasContext gas, State s, StateConservative Flux[3]) { 223 for (CeedInt i = 0; i < 3; i++) { 224 Flux[i].density = s.U.momentum[i]; 225 for (CeedInt j = 0; j < 3; j++) Flux[i].momentum[j] = s.U.momentum[i] * s.Y.velocity[j] + s.Y.pressure * (i == j); 226 Flux[i].E_total = (s.U.E_total + s.Y.pressure) * s.Y.velocity[i]; 227 } 228 } 229 230 CEED_QFUNCTION_HELPER void FluxInviscid_fwd(NewtonianIdealGasContext gas, State s, State ds, StateConservative dFlux[3]) { 231 for (CeedInt i = 0; i < 3; i++) { 232 dFlux[i].density = ds.U.momentum[i]; 233 for (CeedInt j = 0; j < 3; j++) { 234 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); 235 } 236 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]; 237 } 238 } 239 240 CEED_QFUNCTION_HELPER StateConservative FluxInviscidDotNormal(NewtonianIdealGasContext gas, State s, const CeedScalar normal[3]) { 241 StateConservative Flux[3], Flux_dot_n = {0}; 242 FluxInviscid(gas, s, Flux); 243 for (CeedInt i = 0; i < 3; i++) { 244 Flux_dot_n.density += Flux[i].density * normal[i]; 245 for (CeedInt j = 0; j < 3; j++) Flux_dot_n.momentum[j] += Flux[i].momentum[j] * normal[i]; 246 Flux_dot_n.E_total += Flux[i].E_total * normal[i]; 247 } 248 return Flux_dot_n; 249 } 250 251 CEED_QFUNCTION_HELPER StateConservative FluxInviscidDotNormal_fwd(NewtonianIdealGasContext gas, State s, State ds, const CeedScalar normal[3]) { 252 StateConservative dFlux[3], Flux_dot_n = {0}; 253 FluxInviscid_fwd(gas, s, ds, dFlux); 254 for (CeedInt i = 0; i < 3; i++) { 255 Flux_dot_n.density += dFlux[i].density * normal[i]; 256 for (CeedInt j = 0; j < 3; j++) Flux_dot_n.momentum[j] += dFlux[i].momentum[j] * normal[i]; 257 Flux_dot_n.E_total += dFlux[i].E_total * normal[i]; 258 } 259 return Flux_dot_n; 260 } 261 262 CEED_QFUNCTION_HELPER void FluxInviscidStrong(NewtonianIdealGasContext gas, State s, State ds[3], CeedScalar strong_conv[5]) { 263 for (CeedInt i = 0; i < 5; i++) strong_conv[i] = 0; 264 for (CeedInt i = 0; i < 3; i++) { 265 StateConservative dF[3]; 266 FluxInviscid_fwd(gas, s, ds[i], dF); 267 CeedScalar dF_i[5]; 268 UnpackState_U(dF[i], dF_i); 269 for (CeedInt j = 0; j < 5; j++) strong_conv[j] += dF_i[j]; 270 } 271 } 272 273 CEED_QFUNCTION_HELPER void FluxTotal(const StateConservative F_inviscid[3], CeedScalar stress[3][3], CeedScalar Fe[3], CeedScalar Flux[5][3]) { 274 for (CeedInt j = 0; j < 3; j++) { 275 Flux[0][j] = F_inviscid[j].density; 276 for (CeedInt k = 0; k < 3; k++) Flux[k + 1][j] = F_inviscid[j].momentum[k] - stress[k][j]; 277 Flux[4][j] = F_inviscid[j].E_total + Fe[j]; 278 } 279 } 280 281 CEED_QFUNCTION_HELPER void FluxTotal_Boundary(const StateConservative F_inviscid[3], const CeedScalar stress[3][3], const CeedScalar Fe[3], 282 const CeedScalar normal[3], CeedScalar Flux[5]) { 283 for (CeedInt j = 0; j < 5; j++) Flux[j] = 0.; 284 for (CeedInt j = 0; j < 3; j++) { 285 Flux[0] += F_inviscid[j].density * normal[j]; 286 for (CeedInt k = 0; k < 3; k++) { 287 Flux[k + 1] += (F_inviscid[j].momentum[k] - stress[k][j]) * normal[j]; 288 } 289 Flux[4] += (F_inviscid[j].E_total + Fe[j]) * normal[j]; 290 } 291 } 292 293 CEED_QFUNCTION_HELPER void FluxTotal_RiemannBoundary(const StateConservative F_inviscid_normal, const CeedScalar stress[3][3], const CeedScalar Fe[3], 294 const CeedScalar normal[3], CeedScalar Flux[5]) { 295 Flux[0] = F_inviscid_normal.density; 296 for (CeedInt k = 0; k < 3; k++) Flux[k + 1] = F_inviscid_normal.momentum[k]; 297 Flux[4] = F_inviscid_normal.E_total; 298 for (CeedInt j = 0; j < 3; j++) { 299 for (CeedInt k = 0; k < 3; k++) { 300 Flux[k + 1] -= stress[k][j] * normal[j]; 301 } 302 Flux[4] += Fe[j] * normal[j]; 303 } 304 } 305 306 // Kelvin-Mandel notation 307 CEED_QFUNCTION_HELPER void KMStrainRate(const State grad_s[3], CeedScalar strain_rate[6]) { 308 const CeedScalar weight = 1 / sqrt(2.); 309 strain_rate[0] = grad_s[0].Y.velocity[0]; 310 strain_rate[1] = grad_s[1].Y.velocity[1]; 311 strain_rate[2] = grad_s[2].Y.velocity[2]; 312 strain_rate[3] = weight * (grad_s[2].Y.velocity[1] + grad_s[1].Y.velocity[2]); 313 strain_rate[4] = weight * (grad_s[2].Y.velocity[0] + grad_s[0].Y.velocity[2]); 314 strain_rate[5] = weight * (grad_s[1].Y.velocity[0] + grad_s[0].Y.velocity[1]); 315 } 316 317 CEED_QFUNCTION_HELPER void NewtonianStress(NewtonianIdealGasContext gas, const CeedScalar strain_rate[6], CeedScalar stress[6]) { 318 CeedScalar div_u = strain_rate[0] + strain_rate[1] + strain_rate[2]; 319 for (CeedInt i = 0; i < 6; i++) { 320 stress[i] = gas->mu * (2 * strain_rate[i] + gas->lambda * div_u * (i < 3)); 321 } 322 } 323 324 CEED_QFUNCTION_HELPER void ViscousEnergyFlux(NewtonianIdealGasContext gas, StatePrimitive Y, const State grad_s[3], const CeedScalar stress[3][3], 325 CeedScalar Fe[3]) { 326 for (CeedInt i = 0; i < 3; i++) { 327 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; 328 } 329 } 330 331 CEED_QFUNCTION_HELPER void ViscousEnergyFlux_fwd(NewtonianIdealGasContext gas, StatePrimitive Y, StatePrimitive dY, const State grad_ds[3], 332 const CeedScalar stress[3][3], const CeedScalar dstress[3][3], CeedScalar dFe[3]) { 333 for (CeedInt i = 0; i < 3; i++) { 334 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] - 335 Y.velocity[2] * dstress[2][i] - dY.velocity[2] * stress[2][i] - gas->k * grad_ds[i].Y.temperature; 336 } 337 } 338 339 #endif // newtonian_state_h 340