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 StatePrimitive StatePrimitiveFromConservative( 50 NewtonianIdealGasContext gas, StateConservative U, const CeedScalar x[3]) { 51 StatePrimitive Y; 52 for (CeedInt i=0; i<3; i++) Y.velocity[i] = U.momentum[i] / U.density; 53 CeedScalar e_kinetic = .5 * Dot3(Y.velocity, Y.velocity); 54 CeedScalar e_potential = -Dot3(gas->g, x); 55 CeedScalar e_total = U.E_total / U.density; 56 CeedScalar e_internal = e_total - e_kinetic - e_potential; 57 Y.temperature = e_internal / gas->cv; 58 Y.pressure = (gas->cp / gas->cv - 1) * U.density * e_internal; 59 return Y; 60 } 61 62 CEED_QFUNCTION_HELPER StatePrimitive StatePrimitiveFromConservative_fwd( 63 NewtonianIdealGasContext gas, State s, StateConservative dU, 64 const CeedScalar x[3], const CeedScalar dx[3]) { 65 StatePrimitive dY; 66 for (CeedInt i=0; i<3; i++) { 67 dY.velocity[i] = (dU.momentum[i] - s.Y.velocity[i] * dU.density) / s.U.density; 68 } 69 CeedScalar e_kinetic = .5 * Dot3(s.Y.velocity, s.Y.velocity); 70 CeedScalar de_kinetic = Dot3(dY.velocity, s.Y.velocity); 71 CeedScalar e_potential = -Dot3(gas->g, x); 72 CeedScalar de_potential = -Dot3(gas->g, dx); 73 CeedScalar e_total = s.U.E_total / s.U.density; 74 CeedScalar de_total = (dU.E_total - e_total * dU.density) / s.U.density; 75 CeedScalar e_internal = e_total - e_kinetic - e_potential; 76 CeedScalar de_internal = de_total - de_kinetic - de_potential; 77 dY.temperature = de_internal / gas->cv; 78 dY.pressure = (gas->cp / gas->cv - 1) 79 * (dU.density * e_internal + s.U.density * de_internal); 80 return dY; 81 } 82 83 CEED_QFUNCTION_HELPER StateConservative StateConservativeFromPrimitive( 84 NewtonianIdealGasContext gas, StatePrimitive Y, const CeedScalar x[3]) { 85 StateConservative U; 86 CeedScalar R = gas->cp - gas->cv; 87 U.density = Y.pressure / (R * Y.temperature); 88 for (int i=0; i<3; i++) U.momentum[i] = U.density*Y.velocity[i]; 89 CeedScalar e_internal = gas->cv * Y.temperature; 90 CeedScalar e_kinetic = .5 * Dot3(Y.velocity, Y.velocity); 91 CeedScalar e_potential = -Dot3(gas->g, x); 92 CeedScalar e_total = e_internal + e_kinetic + e_potential; 93 U.E_total = U.density*e_total; 94 return U; 95 } 96 97 CEED_QFUNCTION_HELPER StateConservative StateConservativeFromPrimitive_fwd( 98 NewtonianIdealGasContext gas, State s, StatePrimitive dY, 99 const CeedScalar x[3], const CeedScalar dx[3]) { 100 StateConservative dU; 101 CeedScalar R = gas->cp - gas->cv; 102 dU.density = (dY.pressure * s.Y.temperature - s.Y.pressure * dY.temperature) / 103 (R * s.Y.temperature * s.Y.temperature); 104 for (int i=0; i<3; i++) { 105 dU.momentum[i] = dU.density * s.Y.velocity[i] + s.U.density * dY.velocity[i]; 106 } 107 CeedScalar e_kinetic = .5 * Dot3(s.Y.velocity, s.Y.velocity); 108 CeedScalar de_kinetic = Dot3(dY.velocity, s.Y.velocity); 109 CeedScalar e_potential = -Dot3(gas->g, x); 110 CeedScalar de_potential = -Dot3(gas->g, dx); 111 CeedScalar e_internal = gas->cv * s.Y.temperature; 112 CeedScalar de_internal = gas->cv * dY.temperature; 113 CeedScalar e_total = e_internal + e_kinetic + e_potential; 114 CeedScalar de_total = de_internal + de_kinetic + de_potential; 115 dU.E_total = dU.density*e_total + s.U.density*de_total; 116 return dU; 117 } 118 119 CEED_QFUNCTION_HELPER State StateFromU(NewtonianIdealGasContext gas, 120 const CeedScalar U[5], const CeedScalar x[3]) { 121 State s; 122 s.U.density = U[0]; 123 s.U.momentum[0] = U[1]; 124 s.U.momentum[1] = U[2]; 125 s.U.momentum[2] = U[3]; 126 s.U.E_total = U[4]; 127 s.Y = StatePrimitiveFromConservative(gas, s.U, x); 128 return s; 129 } 130 131 CEED_QFUNCTION_HELPER State StateFromU_fwd(NewtonianIdealGasContext gas, 132 State s, const CeedScalar dU[5], 133 const CeedScalar x[3], const CeedScalar dx[3]) { 134 State ds; 135 ds.U.density = dU[0]; 136 ds.U.momentum[0] = dU[1]; 137 ds.U.momentum[1] = dU[2]; 138 ds.U.momentum[2] = dU[3]; 139 ds.U.E_total = dU[4]; 140 ds.Y = StatePrimitiveFromConservative_fwd(gas, s, ds.U, x, dx); 141 return ds; 142 } 143 144 CEED_QFUNCTION_HELPER State StateFromY(NewtonianIdealGasContext gas, 145 const CeedScalar Y[5], const CeedScalar x[3]) { 146 State s; 147 s.Y.pressure = Y[0]; 148 s.Y.velocity[0] = Y[1]; 149 s.Y.velocity[1] = Y[2]; 150 s.Y.velocity[2] = Y[3]; 151 s.Y.temperature = Y[4]; 152 s.U = StateConservativeFromPrimitive(gas, s.Y, x); 153 return s; 154 } 155 156 CEED_QFUNCTION_HELPER State StateFromY_fwd(NewtonianIdealGasContext gas, 157 State s, const CeedScalar dY[5], 158 const CeedScalar x[3], const CeedScalar dx[3]) { 159 State ds; 160 ds.Y.pressure = dY[0]; 161 ds.Y.velocity[0] = dY[1]; 162 ds.Y.velocity[1] = dY[2]; 163 ds.Y.velocity[2] = dY[3]; 164 ds.Y.temperature = dY[4]; 165 ds.U = StateConservativeFromPrimitive_fwd(gas, s, ds.Y, x, dx); 166 return ds; 167 } 168 169 CEED_QFUNCTION_HELPER void FluxInviscid(NewtonianIdealGasContext gas, State s, 170 StateConservative Flux[3]) { 171 for (CeedInt i=0; i<3; i++) { 172 Flux[i].density = s.U.momentum[i]; 173 for (CeedInt j=0; j<3; j++) 174 Flux[i].momentum[j] = s.U.momentum[i] * s.Y.velocity[j] 175 + s.Y.pressure * (i == j); 176 Flux[i].E_total = (s.U.E_total + s.Y.pressure) * s.Y.velocity[i]; 177 } 178 } 179 180 CEED_QFUNCTION_HELPER void FluxInviscid_fwd(NewtonianIdealGasContext gas, 181 State s, State ds, StateConservative dFlux[3]) { 182 for (CeedInt i=0; i<3; i++) { 183 dFlux[i].density = ds.U.momentum[i]; 184 for (CeedInt j=0; j<3; j++) 185 dFlux[i].momentum[j] = ds.U.momentum[i] * s.Y.velocity[j] + 186 s.U.momentum[i] * ds.Y.velocity[j] + ds.Y.pressure * (i == j); 187 dFlux[i].E_total = (ds.U.E_total + ds.Y.pressure) * s.Y.velocity[i] + 188 (s.U.E_total + s.Y.pressure) * ds.Y.velocity[i]; 189 } 190 } 191 192 CEED_QFUNCTION_HELPER void FluxInviscidStrong(NewtonianIdealGasContext gas, 193 State s, State ds[3], CeedScalar strong_conv[5]) { 194 for (CeedInt i=0; i<5; i++) strong_conv[i] = 0; 195 for (CeedInt i=0; i<3; i++) { 196 StateConservative dF[3]; 197 FluxInviscid_fwd(gas, s, ds[i], dF); 198 CeedScalar dF_i[5]; 199 UnpackState_U(dF[i], dF_i); 200 for (CeedInt j=0; j<5; j++) 201 strong_conv[j] += dF_i[j]; 202 } 203 } 204 205 CEED_QFUNCTION_HELPER void FluxTotal(StateConservative F_inviscid[3], 206 CeedScalar stress[3][3], CeedScalar Fe[3], CeedScalar Flux[5][3]) { 207 for (CeedInt j=0; j<3; j++) { 208 Flux[0][j] = F_inviscid[j].density; 209 for (CeedInt k=0; k<3; k++) 210 Flux[k+1][j] = F_inviscid[j].momentum[k] - stress[k][j]; 211 Flux[4][j] = F_inviscid[j].E_total + Fe[j]; 212 } 213 } 214 215 CEED_QFUNCTION_HELPER void FluxTotal_Boundary( 216 const StateConservative F_inviscid[3], const CeedScalar stress[3][3], 217 const CeedScalar Fe[3], const CeedScalar normal[3], CeedScalar Flux[5]) { 218 219 for(CeedInt j=0; j<5; j++) Flux[j] = 0.; 220 for (CeedInt j=0; j<3; j++) { 221 Flux[0] += F_inviscid[j].density * normal[j]; 222 for (CeedInt k=0; k<3; k++) { 223 Flux[k+1] += (F_inviscid[j].momentum[k] - stress[k][j]) * normal[j]; 224 } 225 Flux[4] += (F_inviscid[j].E_total + Fe[j]) * normal[j]; 226 } 227 } 228 229 // Kelvin-Mandel notation 230 CEED_QFUNCTION_HELPER void KMStrainRate(const State grad_s[3], 231 CeedScalar strain_rate[6]) { 232 const CeedScalar weight = 1 / sqrt(2.); 233 strain_rate[0] = grad_s[0].Y.velocity[0]; 234 strain_rate[1] = grad_s[1].Y.velocity[1]; 235 strain_rate[2] = grad_s[2].Y.velocity[2]; 236 strain_rate[3] = weight * (grad_s[2].Y.velocity[1] + grad_s[1].Y.velocity[2]); 237 strain_rate[4] = weight * (grad_s[2].Y.velocity[0] + grad_s[0].Y.velocity[2]); 238 strain_rate[5] = weight * (grad_s[1].Y.velocity[0] + grad_s[0].Y.velocity[1]); 239 } 240 241 CEED_QFUNCTION_HELPER void NewtonianStress(NewtonianIdealGasContext gas, 242 const CeedScalar strain_rate[6], CeedScalar stress[6]) { 243 CeedScalar div_u = strain_rate[0] + strain_rate[1] + strain_rate[2]; 244 for (CeedInt i=0; i<6; i++) { 245 stress[i] = gas->mu * (2 * strain_rate[i] + gas->lambda * div_u * (i < 3)); 246 } 247 } 248 249 CEED_QFUNCTION_HELPER void ViscousEnergyFlux(NewtonianIdealGasContext gas, 250 StatePrimitive Y, const State grad_s[3], const CeedScalar stress[3][3], 251 CeedScalar Fe[3]) { 252 for (CeedInt i=0; i<3; i++) { 253 Fe[i] = - Y.velocity[0] * stress[0][i] 254 - Y.velocity[1] * stress[1][i] 255 - Y.velocity[2] * stress[2][i] 256 - gas->k * grad_s[i].Y.temperature; 257 } 258 } 259 260 CEED_QFUNCTION_HELPER void ViscousEnergyFlux_fwd(NewtonianIdealGasContext gas, 261 StatePrimitive Y, StatePrimitive dY, const State grad_ds[3], 262 const CeedScalar stress[3][3], 263 const CeedScalar dstress[3][3], 264 CeedScalar dFe[3]) { 265 for (CeedInt i=0; i<3; i++) { 266 dFe[i] = - Y.velocity[0] * dstress[0][i] - dY.velocity[0] * stress[0][i] 267 - Y.velocity[1] * dstress[1][i] - dY.velocity[1] * stress[1][i] 268 - Y.velocity[2] * dstress[2][i] - dY.velocity[2] * stress[2][i] 269 - gas->k * grad_ds[i].Y.temperature; 270 } 271 } 272 273 #endif // newtonian_state_h 274