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 /// Helper functions for computing stabilization terms of a newtonian simulation 10 11 #ifndef stabilization_h 12 #define stabilization_h 13 14 #include <ceed.h> 15 #include "newtonian_state.h" 16 17 // ***************************************************************************** 18 // Helper function for computing the variation in primitive variables, 19 // given Tau_d 20 // ***************************************************************************** 21 CEED_QFUNCTION_HELPER void dYFromTau(CeedScalar Y[5], CeedScalar Tau_d[3], 22 CeedScalar dY[5]) { 23 dY[0] = Tau_d[0] * Y[0]; 24 dY[1] = Tau_d[1] * Y[1]; 25 dY[2] = Tau_d[1] * Y[2]; 26 dY[3] = Tau_d[1] * Y[3]; 27 dY[4] = Tau_d[2] * Y[4]; 28 } 29 30 // ***************************************************************************** 31 // Helper functions for computing the stabilization terms 32 // ***************************************************************************** 33 CEED_QFUNCTION_HELPER void StabilizationMatrix(NewtonianIdealGasContext gas, 34 State s, CeedScalar Tau_d[3], CeedScalar R[5], const CeedScalar x[3], 35 CeedScalar stab[5][3]) { 36 CeedScalar dY[5]; 37 const CeedScalar dx_i[3] = {0}; 38 StateConservative dF[3]; 39 // Zero stab so all future terms can safely sum into it 40 for (CeedInt i=0; i<5; i++) 41 for (CeedInt j=0; j<3; j++) 42 stab[i][j] = 0; 43 dYFromTau(R, Tau_d, dY); 44 State ds = StateFromY_fwd(gas, s, dY, x, dx_i); 45 FluxInviscid_fwd(gas, s, ds, dF); 46 for (CeedInt i=0; i<3; i++) { 47 CeedScalar dF_i[5]; 48 UnpackState_U(dF[i], dF_i); 49 for (CeedInt j=0; j<5; j++) 50 stab[j][i] += dF_i[j]; 51 } 52 } 53 54 CEED_QFUNCTION_HELPER void Stabilization(NewtonianIdealGasContext gas, State s, 55 CeedScalar Tau_d[3], State ds[3], CeedScalar U_dot[5], 56 const CeedScalar body_force[5], const CeedScalar x[3], CeedScalar stab[5][3]) { 57 // -- Stabilization method: none (Galerkin), SU, or SUPG 58 CeedScalar R[5] = {0}; 59 switch (gas->stabilization) { 60 case STAB_NONE: 61 break; 62 case STAB_SU: 63 FluxInviscidStrong(gas, s, ds, R); 64 break; 65 case STAB_SUPG: 66 FluxInviscidStrong(gas, s, ds, R); 67 for (CeedInt j=0; j<5; j++) R[j] += U_dot[j] - body_force[j]; 68 break; 69 } 70 StabilizationMatrix(gas, s, Tau_d, R, x, stab); 71 } 72 73 // ***************************************************************************** 74 // Helper function for computing Tau elements (stabilization constant) 75 // Model from: 76 // PHASTA 77 // 78 // Tau[i] = itau=0 which is diagonal-Shakib (3 values still but not spatial) 79 // 80 // ***************************************************************************** 81 CEED_QFUNCTION_HELPER void Tau_diagPrim(NewtonianIdealGasContext gas, State s, 82 const CeedScalar dXdx[3][3], 83 const CeedScalar dt, CeedScalar Tau_d[3]) { 84 // Context 85 const CeedScalar Ctau_t = gas->Ctau_t; 86 const CeedScalar Ctau_v = gas->Ctau_v; 87 const CeedScalar Ctau_C = gas->Ctau_C; 88 const CeedScalar Ctau_M = gas->Ctau_M; 89 const CeedScalar Ctau_E = gas->Ctau_E; 90 const CeedScalar cv = gas->cv; 91 const CeedScalar mu = gas->mu; 92 const CeedScalar u[3] = {s.Y.velocity[0], s.Y.velocity[1], s.Y.velocity[2]}; 93 const CeedScalar rho = s.U.density; 94 95 CeedScalar gijd[6]; 96 CeedScalar tau; 97 CeedScalar dts; 98 CeedScalar fact; 99 100 //*INDENT-OFF* 101 gijd[0] = dXdx[0][0] * dXdx[0][0] 102 + dXdx[1][0] * dXdx[1][0] 103 + dXdx[2][0] * dXdx[2][0]; 104 105 gijd[1] = dXdx[0][0] * dXdx[0][1] 106 + dXdx[1][0] * dXdx[1][1] 107 + dXdx[2][0] * dXdx[2][1]; 108 109 gijd[2] = dXdx[0][1] * dXdx[0][1] 110 + dXdx[1][1] * dXdx[1][1] 111 + dXdx[2][1] * dXdx[2][1]; 112 113 gijd[3] = dXdx[0][0] * dXdx[0][2] 114 + dXdx[1][0] * dXdx[1][2] 115 + dXdx[2][0] * dXdx[2][2]; 116 117 gijd[4] = dXdx[0][1] * dXdx[0][2] 118 + dXdx[1][1] * dXdx[1][2] 119 + dXdx[2][1] * dXdx[2][2]; 120 121 gijd[5] = dXdx[0][2] * dXdx[0][2] 122 + dXdx[1][2] * dXdx[1][2] 123 + dXdx[2][2] * dXdx[2][2]; 124 //*INDENT-ON* 125 126 dts = Ctau_t / dt ; 127 128 tau = rho*rho*((4. * dts * dts) 129 + u[0] * ( u[0] * gijd[0] + 2. * ( u[1] * gijd[1] + u[2] * gijd[3])) 130 + u[1] * ( u[1] * gijd[2] + 2. * u[2] * gijd[4]) 131 + u[2] * u[2] * gijd[5]) 132 + Ctau_v* mu * mu * 133 (gijd[0]*gijd[0] + gijd[2]*gijd[2] + gijd[5]*gijd[5] + 134 + 2. * (gijd[1]*gijd[1] + gijd[3]*gijd[3] + gijd[4]*gijd[4])); 135 136 fact = sqrt(tau); 137 138 Tau_d[0] = Ctau_C * fact / (rho*(gijd[0] + gijd[2] + gijd[5]))*0.125; 139 140 Tau_d[1] = Ctau_M / fact; 141 Tau_d[2] = Ctau_E / ( fact * cv ); 142 143 // consider putting back the way I initially had it Ctau_E * Tau_d[1] /cv 144 // to avoid a division if the compiler is smart enough to see that cv IS 145 // a constant that it could invert once for all elements 146 // but in that case energy tau is scaled by the product of Ctau_E * Ctau_M 147 // OR we could absorb cv into Ctau_E but this puts more burden on user to 148 // know how to change constants with a change of fluid or units. Same for 149 // Ctau_v * mu * mu IF AND ONLY IF we don't add viscosity law =f(T) 150 } 151 152 // ***************************************************************************** 153 154 #endif // stabilization_h 155