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 12 #ifndef newtonian_state_h 13 #define newtonian_state_h 14 15 #include <ceed.h> 16 #include <math.h> 17 #include "newtonian_types.h" 18 #include "utils.h" 19 20 typedef struct { 21 CeedScalar pressure; 22 CeedScalar velocity[3]; 23 CeedScalar temperature; 24 } StatePrimitive; 25 26 typedef struct { 27 CeedScalar density; 28 CeedScalar momentum[3]; 29 CeedScalar E_total; 30 } StateConservative; 31 32 typedef struct { 33 StateConservative U; 34 StatePrimitive Y; 35 } State; 36 37 CEED_QFUNCTION_HELPER void UnpackState_U(StateConservative s, CeedScalar U[5]) { 38 U[0] = s.density; 39 for (int i=0; i<3; i++) U[i+1] = s.momentum[i]; 40 U[4] = s.E_total; 41 } 42 43 CEED_QFUNCTION_HELPER void UnpackState_Y(StatePrimitive s, CeedScalar Y[5]) { 44 Y[0] = s.pressure; 45 for (int i=0; i<3; i++) Y[i+1] = s.velocity[i]; 46 Y[4] = s.temperature; 47 } 48 49 CEED_QFUNCTION_HELPER CeedScalar HeatCapacityRatio( 50 NewtonianIdealGasContext gas) { 51 return gas->cp / gas->cv; 52 } 53 54 CEED_QFUNCTION_HELPER CeedScalar GasConstant( 55 NewtonianIdealGasContext gas) { 56 return gas->cp - gas->cv; 57 } 58 59 CEED_QFUNCTION_HELPER CeedScalar Prandtl(NewtonianIdealGasContext gas) { 60 return gas->cp * gas->mu / gas->k; 61 } 62 63 CEED_QFUNCTION_HELPER CeedScalar SoundSpeed(NewtonianIdealGasContext gas, 64 CeedScalar T) { 65 return sqrt(gas->cp * (HeatCapacityRatio(gas) - 1.) * T); 66 } 67 68 CEED_QFUNCTION_HELPER CeedScalar Mach(NewtonianIdealGasContext gas, 69 CeedScalar T, CeedScalar u) { 70 return u / SoundSpeed(gas, T); 71 } 72 73 CEED_QFUNCTION_HELPER StatePrimitive StatePrimitiveFromConservative( 74 NewtonianIdealGasContext gas, StateConservative U, const CeedScalar x[3]) { 75 StatePrimitive Y; 76 for (CeedInt i=0; i<3; i++) Y.velocity[i] = U.momentum[i] / U.density; 77 CeedScalar e_kinetic = .5 * Dot3(Y.velocity, Y.velocity); 78 CeedScalar e_potential = -Dot3(gas->g, x); 79 CeedScalar e_total = U.E_total / U.density; 80 CeedScalar e_internal = e_total - e_kinetic - e_potential; 81 Y.temperature = e_internal / gas->cv; 82 Y.pressure = (HeatCapacityRatio(gas) - 1) * U.density * e_internal; 83 return Y; 84 } 85 86 CEED_QFUNCTION_HELPER StatePrimitive StatePrimitiveFromConservative_fwd( 87 NewtonianIdealGasContext gas, State s, StateConservative dU, 88 const CeedScalar x[3], const CeedScalar dx[3]) { 89 StatePrimitive dY; 90 for (CeedInt i=0; i<3; i++) { 91 dY.velocity[i] = (dU.momentum[i] - s.Y.velocity[i] * dU.density) / s.U.density; 92 } 93 CeedScalar e_kinetic = .5 * Dot3(s.Y.velocity, s.Y.velocity); 94 CeedScalar de_kinetic = Dot3(dY.velocity, s.Y.velocity); 95 CeedScalar e_potential = -Dot3(gas->g, x); 96 CeedScalar de_potential = -Dot3(gas->g, dx); 97 CeedScalar e_total = s.U.E_total / s.U.density; 98 CeedScalar de_total = (dU.E_total - e_total * dU.density) / s.U.density; 99 CeedScalar e_internal = e_total - e_kinetic - e_potential; 100 CeedScalar de_internal = de_total - de_kinetic - de_potential; 101 dY.temperature = de_internal / gas->cv; 102 dY.pressure = (HeatCapacityRatio(gas) - 1) 103 * (dU.density * e_internal + s.U.density * de_internal); 104 return dY; 105 } 106 107 CEED_QFUNCTION_HELPER StateConservative StateConservativeFromPrimitive( 108 NewtonianIdealGasContext gas, StatePrimitive Y, const CeedScalar x[3]) { 109 StateConservative U; 110 U.density = Y.pressure / (GasConstant(gas) * Y.temperature); 111 for (int i=0; i<3; i++) U.momentum[i] = U.density*Y.velocity[i]; 112 CeedScalar e_internal = gas->cv * Y.temperature; 113 CeedScalar e_kinetic = .5 * Dot3(Y.velocity, Y.velocity); 114 CeedScalar e_potential = -Dot3(gas->g, x); 115 CeedScalar e_total = e_internal + e_kinetic + e_potential; 116 U.E_total = U.density*e_total; 117 return U; 118 } 119 120 CEED_QFUNCTION_HELPER StateConservative StateConservativeFromPrimitive_fwd( 121 NewtonianIdealGasContext gas, State s, StatePrimitive dY, 122 const CeedScalar x[3], const CeedScalar dx[3]) { 123 StateConservative dU; 124 dU.density = (dY.pressure * s.Y.temperature - s.Y.pressure * dY.temperature) / 125 (GasConstant(gas) * s.Y.temperature * s.Y.temperature); 126 for (int i=0; i<3; i++) { 127 dU.momentum[i] = dU.density * s.Y.velocity[i] + s.U.density * dY.velocity[i]; 128 } 129 CeedScalar e_kinetic = .5 * Dot3(s.Y.velocity, s.Y.velocity); 130 CeedScalar de_kinetic = Dot3(dY.velocity, s.Y.velocity); 131 CeedScalar e_potential = -Dot3(gas->g, x); 132 CeedScalar de_potential = -Dot3(gas->g, dx); 133 CeedScalar e_internal = gas->cv * s.Y.temperature; 134 CeedScalar de_internal = gas->cv * dY.temperature; 135 CeedScalar e_total = e_internal + e_kinetic + e_potential; 136 CeedScalar de_total = de_internal + de_kinetic + de_potential; 137 dU.E_total = dU.density*e_total + s.U.density*de_total; 138 return dU; 139 } 140 141 // Function pointer types for generic state array -> State struct functions 142 typedef State (*StateFromQi_t)(NewtonianIdealGasContext gas, 143 const CeedScalar qi[5], const CeedScalar x[3]); 144 typedef State (*StateFromQi_fwd_t)(NewtonianIdealGasContext gas, 145 State s, const CeedScalar dqi[5], 146 const CeedScalar x[3], const CeedScalar dx[3]); 147 148 CEED_QFUNCTION_HELPER State StateFromU(NewtonianIdealGasContext gas, 149 const CeedScalar U[5], const CeedScalar x[3]) { 150 State s; 151 s.U.density = U[0]; 152 s.U.momentum[0] = U[1]; 153 s.U.momentum[1] = U[2]; 154 s.U.momentum[2] = U[3]; 155 s.U.E_total = U[4]; 156 s.Y = StatePrimitiveFromConservative(gas, s.U, x); 157 return s; 158 } 159 160 CEED_QFUNCTION_HELPER State StateFromU_fwd(NewtonianIdealGasContext gas, 161 State s, const CeedScalar dU[5], 162 const CeedScalar x[3], const CeedScalar dx[3]) { 163 State ds; 164 ds.U.density = dU[0]; 165 ds.U.momentum[0] = dU[1]; 166 ds.U.momentum[1] = dU[2]; 167 ds.U.momentum[2] = dU[3]; 168 ds.U.E_total = dU[4]; 169 ds.Y = StatePrimitiveFromConservative_fwd(gas, s, ds.U, x, dx); 170 return ds; 171 } 172 173 CEED_QFUNCTION_HELPER State StateFromY(NewtonianIdealGasContext gas, 174 const CeedScalar Y[5], const CeedScalar x[3]) { 175 State s; 176 s.Y.pressure = Y[0]; 177 s.Y.velocity[0] = Y[1]; 178 s.Y.velocity[1] = Y[2]; 179 s.Y.velocity[2] = Y[3]; 180 s.Y.temperature = Y[4]; 181 s.U = StateConservativeFromPrimitive(gas, s.Y, x); 182 return s; 183 } 184 185 CEED_QFUNCTION_HELPER State StateFromY_fwd(NewtonianIdealGasContext gas, 186 State s, const CeedScalar dY[5], 187 const CeedScalar x[3], const CeedScalar dx[3]) { 188 State ds; 189 ds.Y.pressure = dY[0]; 190 ds.Y.velocity[0] = dY[1]; 191 ds.Y.velocity[1] = dY[2]; 192 ds.Y.velocity[2] = dY[3]; 193 ds.Y.temperature = dY[4]; 194 ds.U = StateConservativeFromPrimitive_fwd(gas, s, ds.Y, x, dx); 195 return ds; 196 } 197 198 CEED_QFUNCTION_HELPER void FluxInviscid(NewtonianIdealGasContext gas, State s, 199 StateConservative Flux[3]) { 200 for (CeedInt i=0; i<3; i++) { 201 Flux[i].density = s.U.momentum[i]; 202 for (CeedInt j=0; j<3; j++) 203 Flux[i].momentum[j] = s.U.momentum[i] * s.Y.velocity[j] 204 + s.Y.pressure * (i == j); 205 Flux[i].E_total = (s.U.E_total + s.Y.pressure) * s.Y.velocity[i]; 206 } 207 } 208 209 CEED_QFUNCTION_HELPER void FluxInviscid_fwd(NewtonianIdealGasContext gas, 210 State s, State ds, StateConservative dFlux[3]) { 211 for (CeedInt i=0; i<3; i++) { 212 dFlux[i].density = ds.U.momentum[i]; 213 for (CeedInt j=0; j<3; j++) 214 dFlux[i].momentum[j] = ds.U.momentum[i] * s.Y.velocity[j] + 215 s.U.momentum[i] * ds.Y.velocity[j] + ds.Y.pressure * (i == j); 216 dFlux[i].E_total = (ds.U.E_total + ds.Y.pressure) * s.Y.velocity[i] + 217 (s.U.E_total + s.Y.pressure) * ds.Y.velocity[i]; 218 } 219 } 220 221 CEED_QFUNCTION_HELPER void FluxInviscidStrong(NewtonianIdealGasContext gas, 222 State s, State ds[3], CeedScalar strong_conv[5]) { 223 for (CeedInt i=0; i<5; i++) strong_conv[i] = 0; 224 for (CeedInt i=0; i<3; i++) { 225 StateConservative dF[3]; 226 FluxInviscid_fwd(gas, s, ds[i], dF); 227 CeedScalar dF_i[5]; 228 UnpackState_U(dF[i], dF_i); 229 for (CeedInt j=0; j<5; j++) 230 strong_conv[j] += dF_i[j]; 231 } 232 } 233 234 CEED_QFUNCTION_HELPER void FluxTotal(const StateConservative F_inviscid[3], 235 CeedScalar stress[3][3], CeedScalar Fe[3], CeedScalar Flux[5][3]) { 236 for (CeedInt j=0; j<3; j++) { 237 Flux[0][j] = F_inviscid[j].density; 238 for (CeedInt k=0; k<3; k++) 239 Flux[k+1][j] = F_inviscid[j].momentum[k] - stress[k][j]; 240 Flux[4][j] = F_inviscid[j].E_total + Fe[j]; 241 } 242 } 243 244 CEED_QFUNCTION_HELPER void FluxTotal_Boundary( 245 const StateConservative F_inviscid[3], const CeedScalar stress[3][3], 246 const CeedScalar Fe[3], const CeedScalar normal[3], CeedScalar Flux[5]) { 247 248 for(CeedInt j=0; j<5; j++) Flux[j] = 0.; 249 for (CeedInt j=0; j<3; j++) { 250 Flux[0] += F_inviscid[j].density * normal[j]; 251 for (CeedInt k=0; k<3; k++) { 252 Flux[k+1] += (F_inviscid[j].momentum[k] - stress[k][j]) * normal[j]; 253 } 254 Flux[4] += (F_inviscid[j].E_total + Fe[j]) * normal[j]; 255 } 256 } 257 258 // Kelvin-Mandel notation 259 CEED_QFUNCTION_HELPER void KMStrainRate(const State grad_s[3], 260 CeedScalar strain_rate[6]) { 261 const CeedScalar weight = 1 / sqrt(2.); 262 strain_rate[0] = grad_s[0].Y.velocity[0]; 263 strain_rate[1] = grad_s[1].Y.velocity[1]; 264 strain_rate[2] = grad_s[2].Y.velocity[2]; 265 strain_rate[3] = weight * (grad_s[2].Y.velocity[1] + grad_s[1].Y.velocity[2]); 266 strain_rate[4] = weight * (grad_s[2].Y.velocity[0] + grad_s[0].Y.velocity[2]); 267 strain_rate[5] = weight * (grad_s[1].Y.velocity[0] + grad_s[0].Y.velocity[1]); 268 } 269 270 CEED_QFUNCTION_HELPER void NewtonianStress(NewtonianIdealGasContext gas, 271 const CeedScalar strain_rate[6], CeedScalar stress[6]) { 272 CeedScalar div_u = strain_rate[0] + strain_rate[1] + strain_rate[2]; 273 for (CeedInt i=0; i<6; i++) { 274 stress[i] = gas->mu * (2 * strain_rate[i] + gas->lambda * div_u * (i < 3)); 275 } 276 } 277 278 CEED_QFUNCTION_HELPER void ViscousEnergyFlux(NewtonianIdealGasContext gas, 279 StatePrimitive Y, const State grad_s[3], const CeedScalar stress[3][3], 280 CeedScalar Fe[3]) { 281 for (CeedInt i=0; i<3; i++) { 282 Fe[i] = - Y.velocity[0] * stress[0][i] 283 - Y.velocity[1] * stress[1][i] 284 - Y.velocity[2] * stress[2][i] 285 - gas->k * grad_s[i].Y.temperature; 286 } 287 } 288 289 CEED_QFUNCTION_HELPER void ViscousEnergyFlux_fwd(NewtonianIdealGasContext gas, 290 StatePrimitive Y, StatePrimitive dY, const State grad_ds[3], 291 const CeedScalar stress[3][3], 292 const CeedScalar dstress[3][3], 293 CeedScalar dFe[3]) { 294 for (CeedInt i=0; i<3; i++) { 295 dFe[i] = - Y.velocity[0] * dstress[0][i] - dY.velocity[0] * stress[0][i] 296 - Y.velocity[1] * dstress[1][i] - dY.velocity[1] * stress[1][i] 297 - Y.velocity[2] * dstress[2][i] - dY.velocity[2] * stress[2][i] 298 - gas->k * grad_ds[i].Y.temperature; 299 } 300 } 301 302 #endif // newtonian_state_h 303