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 <math.h> 16 #include <ceed.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 StatePrimitive StatePrimitiveFromConservative( 38 NewtonianIdealGasContext gas, StateConservative U, const CeedScalar x[3]) { 39 StatePrimitive Y; 40 for (CeedInt i=0; i<3; i++) Y.velocity[i] = U.momentum[i] / U.density; 41 CeedScalar e_kinetic = .5 * Dot3(Y.velocity, Y.velocity); 42 CeedScalar e_potential = -Dot3(gas->g, x); 43 CeedScalar e_total = U.E_total / U.density; 44 CeedScalar e_internal = e_total - e_kinetic - e_potential; 45 Y.temperature = e_internal / gas->cv; 46 Y.pressure = (gas->cp / gas->cv - 1) * U.density * e_internal; 47 return Y; 48 } 49 50 CEED_QFUNCTION_HELPER StatePrimitive StatePrimitiveFromConservative_fwd( 51 NewtonianIdealGasContext gas, State s, StateConservative dU, 52 const CeedScalar x[3], const CeedScalar dx[3]) { 53 StatePrimitive dY; 54 for (CeedInt i=0; i<3; i++) { 55 dY.velocity[i] = (dU.momentum[i] - s.Y.velocity[i] * dU.density) / s.U.density; 56 } 57 CeedScalar e_kinetic = .5 * Dot3(s.Y.velocity, s.Y.velocity); 58 CeedScalar de_kinetic = Dot3(dY.velocity, s.Y.velocity); 59 CeedScalar e_potential = -Dot3(gas->g, x); 60 CeedScalar de_potential = -Dot3(gas->g, dx); 61 CeedScalar e_total = s.U.E_total / s.U.density; 62 CeedScalar de_total = (dU.E_total - e_total * dU.density) / s.U.density; 63 CeedScalar e_internal = e_total - e_kinetic - e_potential; 64 CeedScalar de_internal = de_total - de_kinetic - de_potential; 65 dY.temperature = de_internal / gas->cv; 66 dY.pressure = (gas->cp / gas->cv - 1) 67 * (dU.density * e_internal + s.U.density * de_internal); 68 return dY; 69 } 70 71 CEED_QFUNCTION_HELPER State StateFromU(NewtonianIdealGasContext gas, 72 const CeedScalar U[5], const CeedScalar x[3]) { 73 State s; 74 s.U.density = U[0]; 75 s.U.momentum[0] = U[1]; 76 s.U.momentum[1] = U[2]; 77 s.U.momentum[2] = U[3]; 78 s.U.E_total = U[4]; 79 s.Y = StatePrimitiveFromConservative(gas, s.U, x); 80 return s; 81 } 82 83 CEED_QFUNCTION_HELPER State StateFromU_fwd(NewtonianIdealGasContext gas, 84 State s, const CeedScalar dU[5], 85 const CeedScalar x[3], const CeedScalar dx[3]) { 86 State ds; 87 ds.U.density = dU[0]; 88 ds.U.momentum[0] = dU[1]; 89 ds.U.momentum[1] = dU[2]; 90 ds.U.momentum[2] = dU[3]; 91 ds.U.E_total = dU[4]; 92 ds.Y = StatePrimitiveFromConservative_fwd(gas, s, ds.U, x, dx); 93 return ds; 94 } 95 96 CEED_QFUNCTION_HELPER void FluxInviscid(NewtonianIdealGasContext gas, State s, 97 StateConservative Flux[3]) { 98 for (CeedInt i=0; i<3; i++) { 99 Flux[i].density = s.U.momentum[i]; 100 for (CeedInt j=0; j<3; j++) 101 Flux[i].momentum[j] = s.U.momentum[i] * s.Y.velocity[j] 102 + s.Y.pressure * (i == j); 103 Flux[i].E_total = (s.U.E_total + s.Y.pressure) * s.Y.velocity[i]; 104 } 105 } 106 107 CEED_QFUNCTION_HELPER void FluxInviscid_fwd(NewtonianIdealGasContext gas, 108 State s, State ds, StateConservative dFlux[3]) { 109 for (CeedInt i=0; i<3; i++) { 110 dFlux[i].density = ds.U.momentum[i]; 111 for (CeedInt j=0; j<3; j++) 112 dFlux[i].momentum[j] = ds.U.momentum[i] * s.Y.velocity[j] + 113 s.U.momentum[i] * ds.Y.velocity[j] + ds.Y.pressure * (i == j); 114 dFlux[i].E_total = (ds.U.E_total + ds.Y.pressure) * s.Y.velocity[i] + 115 (s.U.E_total + s.Y.pressure) * ds.Y.velocity[i]; 116 } 117 } 118 119 // Kelvin-Mandel notation 120 CEED_QFUNCTION_HELPER void KMStrainRate(const State grad_s[3], 121 CeedScalar strain_rate[6]) { 122 const CeedScalar weight = 1 / sqrt(2.); 123 strain_rate[0] = grad_s[0].Y.velocity[0]; 124 strain_rate[1] = grad_s[1].Y.velocity[1]; 125 strain_rate[2] = grad_s[2].Y.velocity[2]; 126 strain_rate[3] = weight * (grad_s[2].Y.velocity[1] + grad_s[1].Y.velocity[2]); 127 strain_rate[4] = weight * (grad_s[2].Y.velocity[0] + grad_s[0].Y.velocity[2]); 128 strain_rate[5] = weight * (grad_s[1].Y.velocity[0] + grad_s[0].Y.velocity[1]); 129 } 130 131 CEED_QFUNCTION_HELPER void NewtonianStress(NewtonianIdealGasContext gas, 132 const CeedScalar strain_rate[6], CeedScalar stress[6]) { 133 CeedScalar div_u = strain_rate[0] + strain_rate[1] + strain_rate[2]; 134 for (CeedInt i=0; i<6; i++) { 135 stress[i] = gas->mu * (2 * strain_rate[i] + gas->lambda * div_u * (i < 3)); 136 } 137 } 138 139 CEED_QFUNCTION_HELPER void ViscousEnergyFlux(NewtonianIdealGasContext gas, 140 StatePrimitive Y, const State grad_s[3], const CeedScalar stress[3][3], 141 CeedScalar Fe[3]) { 142 for (CeedInt i=0; i<3; i++) { 143 Fe[i] = - Y.velocity[0] * stress[0][i] 144 - Y.velocity[1] * stress[1][i] 145 - Y.velocity[2] * stress[2][i] 146 - gas->k * grad_s[i].Y.temperature; 147 } 148 } 149 150 CEED_QFUNCTION_HELPER void ViscousEnergyFlux_fwd(NewtonianIdealGasContext gas, 151 StatePrimitive Y, StatePrimitive dY, const State grad_ds[3], 152 const CeedScalar stress[3][3], 153 const CeedScalar dstress[3][3], 154 CeedScalar dFe[3]) { 155 for (CeedInt i=0; i<3; i++) { 156 dFe[i] = - Y.velocity[0] * dstress[0][i] - dY.velocity[0] * stress[0][i] 157 - Y.velocity[1] * dstress[1][i] - dY.velocity[1] * stress[1][i] 158 - Y.velocity[2] * dstress[2][i] - dY.velocity[2] * stress[2][i] 159 - gas->k * grad_ds[i].Y.temperature; 160 } 161 } 162 163 #endif // newtonian_state_h 164