1 // Copyright (c) 2017-2024, 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 /// Operator for Navier-Stokes example using PETSc 10 #include <ceed.h> 11 12 #include "newtonian_state.h" 13 #include "newtonian_types.h" 14 #include "utils.h" 15 16 #define BLASIUS_MAX_N_CHEBYSHEV 50 17 18 typedef struct BlasiusContext_ *BlasiusContext; 19 struct BlasiusContext_ { 20 bool implicit; // !< Using implicit timesteping or not 21 bool weakT; // !< flag to set Temperature weakly at inflow 22 CeedScalar delta0; // !< Boundary layer height at inflow 23 CeedScalar U_inf; // !< Velocity at boundary layer edge 24 CeedScalar T_inf; // !< Temperature at boundary layer edge 25 CeedScalar T_wall; // !< Temperature at the wall 26 CeedScalar P0; // !< Pressure at outflow 27 CeedScalar x_inflow; // !< Location of inflow in x 28 CeedScalar n_cheb; // !< Number of Chebyshev terms 29 CeedScalar *X; // !< Chebyshev polynomial coordinate vector (CPU only) 30 CeedScalar eta_max; // !< Maximum eta in the domain 31 CeedScalar Tf_cheb[BLASIUS_MAX_N_CHEBYSHEV]; // !< Chebyshev coefficient for f 32 CeedScalar Th_cheb[BLASIUS_MAX_N_CHEBYSHEV - 1]; // !< Chebyshev coefficient for h 33 struct NewtonianIdealGasContext_ newtonian_ctx; 34 }; 35 36 // ***************************************************************************** 37 // This helper function evaluates Chebyshev polynomials with a set of coefficients with all their derivatives represented as a recurrence table. 38 // ***************************************************************************** 39 CEED_QFUNCTION_HELPER void ChebyshevEval(int N, const double *Tf, double x, double eta_max, double *f) { 40 double dX_deta = 2 / eta_max; 41 double table[4][3] = { 42 // Chebyshev polynomials T_0, T_1, T_2 of the first kind in (-1,1) 43 {1, x, 2 * x * x - 1}, 44 {0, 1, 4 * x }, 45 {0, 0, 4 }, 46 {0, 0, 0 } 47 }; 48 for (int i = 0; i < 4; i++) { 49 // i-th derivative of f 50 f[i] = table[i][0] * Tf[0] + table[i][1] * Tf[1] + table[i][2] * Tf[2]; 51 } 52 for (int i = 3; i < N; i++) { 53 // T_n(x) = 2xT_{n-1}(x) - T_{n-2}(x) 54 table[0][i % 3] = 2 * x * table[0][(i - 1) % 3] - table[0][(i - 2) % 3]; 55 // Differentiate Chebyshev polynomials with the recurrence relation 56 for (int j = 1; j < 4; j++) { 57 // T'_{n}(x)/n = 2T_{n-1}(x) + T'_{n-2}(x)/n-2 58 table[j][i % 3] = i * (2 * table[j - 1][(i - 1) % 3] + table[j][(i - 2) % 3] / (i - 2)); 59 } 60 for (int j = 0; j < 4; j++) { 61 f[j] += table[j][i % 3] * Tf[i]; 62 } 63 } 64 for (int i = 1; i < 4; i++) { 65 // Transform derivatives from Chebyshev [-1, 1] to [0, eta_max]. 66 for (int j = 0; j < i; j++) f[i] *= dX_deta; 67 } 68 } 69 70 // ***************************************************************************** 71 // This helper function computes the Blasius boundary layer solution. 72 // ***************************************************************************** 73 State CEED_QFUNCTION_HELPER(BlasiusSolution)(const BlasiusContext blasius, const CeedScalar x[3], const CeedScalar x0, const CeedScalar x_inflow, 74 const CeedScalar rho_infty, CeedScalar *t12) { 75 CeedInt N = blasius->n_cheb; 76 CeedScalar mu = blasius->newtonian_ctx.mu; 77 CeedScalar nu = mu / rho_infty; 78 CeedScalar eta = x[1] * sqrt(blasius->U_inf / (nu * (x0 + x[0] - x_inflow))); 79 CeedScalar X = 2 * (eta / blasius->eta_max) - 1.; 80 CeedScalar U_inf = blasius->U_inf; 81 CeedScalar Rd = GasConstant(&blasius->newtonian_ctx); 82 83 CeedScalar f[4], h[4]; 84 ChebyshevEval(N, blasius->Tf_cheb, X, blasius->eta_max, f); 85 ChebyshevEval(N - 1, blasius->Th_cheb, X, blasius->eta_max, h); 86 87 *t12 = mu * U_inf * f[2] * sqrt(U_inf / (nu * (x0 + x[0] - x_inflow))); 88 89 CeedScalar Y[5]; 90 Y[1] = U_inf * f[1]; 91 Y[2] = 0.5 * sqrt(nu * U_inf / (x0 + x[0] - x_inflow)) * (eta * f[1] - f[0]); 92 Y[3] = 0.; 93 Y[4] = blasius->T_inf * h[0]; 94 Y[0] = rho_infty / h[0] * Rd * Y[4]; 95 return StateFromY(&blasius->newtonian_ctx, Y); 96 } 97 98 // ***************************************************************************** 99 // This QFunction sets a Blasius boundary layer for the initial condition 100 // ***************************************************************************** 101 CEED_QFUNCTION(ICsBlasius)(void *ctx, CeedInt Q, const CeedScalar *const *in, CeedScalar *const *out) { 102 const CeedScalar(*X)[CEED_Q_VLA] = (const CeedScalar(*)[CEED_Q_VLA])in[0]; 103 CeedScalar(*q0)[CEED_Q_VLA] = (CeedScalar(*)[CEED_Q_VLA])out[0]; 104 105 const BlasiusContext context = (BlasiusContext)ctx; 106 const NewtonianIdealGasContext gas = &context->newtonian_ctx; 107 const CeedScalar mu = context->newtonian_ctx.mu; 108 const CeedScalar delta0 = context->delta0; 109 const CeedScalar x_inflow = context->x_inflow; 110 CeedScalar t12; 111 112 const CeedScalar Y_inf[5] = {context->P0, context->U_inf, 0, 0, context->T_inf}; 113 const State s_inf = StateFromY(gas, Y_inf); 114 115 const CeedScalar x0 = context->U_inf * s_inf.U.density / (mu * 25 / Square(delta0)); 116 117 CeedPragmaSIMD for (CeedInt i = 0; i < Q; i++) { 118 const CeedScalar x[3] = {X[0][i], X[1][i], X[2][i]}; 119 State s = BlasiusSolution(context, x, x0, x_inflow, s_inf.U.density, &t12); 120 CeedScalar q[5] = {0}; 121 122 switch (gas->state_var) { 123 case STATEVAR_CONSERVATIVE: 124 UnpackState_U(s.U, q); 125 break; 126 case STATEVAR_PRIMITIVE: 127 UnpackState_Y(s.Y, q); 128 break; 129 } 130 for (CeedInt j = 0; j < 5; j++) q0[j][i] = q[j]; 131 } 132 return 0; 133 } 134 135 // ***************************************************************************** 136 CEED_QFUNCTION(Blasius_Inflow)(void *ctx, CeedInt Q, const CeedScalar *const *in, CeedScalar *const *out) { 137 // Inputs 138 const CeedScalar(*q)[CEED_Q_VLA] = (const CeedScalar(*)[CEED_Q_VLA])in[0]; 139 const CeedScalar(*q_data_sur) = in[2]; 140 const CeedScalar(*X)[CEED_Q_VLA] = (const CeedScalar(*)[CEED_Q_VLA])in[3]; 141 142 // Outputs 143 CeedScalar(*v)[CEED_Q_VLA] = (CeedScalar(*)[CEED_Q_VLA])out[0]; 144 CeedScalar(*jac_data_sur) = out[1]; 145 146 const BlasiusContext context = (BlasiusContext)ctx; 147 const bool is_implicit = context->implicit; 148 NewtonianIdealGasContext gas = &context->newtonian_ctx; 149 const CeedScalar mu = context->newtonian_ctx.mu; 150 const CeedScalar Rd = GasConstant(&context->newtonian_ctx); 151 const CeedScalar T_inf = context->T_inf; 152 const CeedScalar P0 = context->P0; 153 const CeedScalar delta0 = context->delta0; 154 const CeedScalar U_inf = context->U_inf; 155 const CeedScalar x_inflow = context->x_inflow; 156 const bool weakT = context->weakT; 157 const CeedScalar rho_0 = P0 / (Rd * T_inf); 158 const CeedScalar x0 = U_inf * rho_0 / (mu * 25 / Square(delta0)); 159 const CeedScalar zeros[11] = {0.}; 160 161 CeedPragmaSIMD for (CeedInt i = 0; i < Q; i++) { 162 CeedScalar wdetJb, norm[3]; 163 QdataBoundaryUnpack_3D(Q, i, q_data_sur, &wdetJb, NULL, norm); 164 wdetJb *= is_implicit ? -1. : 1.; 165 166 // Calculate inflow values 167 const CeedScalar x[3] = {X[0][i], X[1][i], 0.}; 168 CeedScalar t12; 169 State s = BlasiusSolution(context, x, x0, x_inflow, rho_0, &t12); 170 CeedScalar qi[5]; 171 for (CeedInt j = 0; j < 5; j++) qi[j] = q[j][i]; 172 State s_int = StateFromU(gas, qi); 173 174 // enabling user to choose between weak T and weak rho inflow 175 if (weakT) { // density from the current solution 176 s.U.density = s_int.U.density; 177 s.Y = StatePrimitiveFromConservative(gas, s.U); 178 } else { // Total energy from current solution 179 s.U.E_total = s_int.U.E_total; 180 s.Y = StatePrimitiveFromConservative(gas, s.U); 181 } 182 183 StateConservative Flux_inviscid[3]; 184 FluxInviscid(&context->newtonian_ctx, s, Flux_inviscid); 185 186 const CeedScalar stress[3][3] = { 187 {0, t12, 0}, 188 {t12, 0, 0}, 189 {0, 0, 0} 190 }; 191 const CeedScalar Fe[3] = {0}; // TODO: viscous energy flux needs grad temperature 192 CeedScalar Flux[5]; 193 FluxTotal_Boundary(Flux_inviscid, stress, Fe, norm, Flux); 194 for (CeedInt j = 0; j < 5; j++) v[j][i] = -wdetJb * Flux[j]; 195 StoredValuesPack(Q, i, 0, 11, zeros, jac_data_sur); 196 } 197 return 0; 198 } 199 200 // ***************************************************************************** 201 CEED_QFUNCTION(Blasius_Inflow_Jacobian)(void *ctx, CeedInt Q, const CeedScalar *const *in, CeedScalar *const *out) { 202 // Inputs 203 const CeedScalar(*dq)[CEED_Q_VLA] = (const CeedScalar(*)[CEED_Q_VLA])in[0]; 204 const CeedScalar(*q_data_sur) = in[2]; 205 const CeedScalar(*X)[CEED_Q_VLA] = (const CeedScalar(*)[CEED_Q_VLA])in[3]; 206 207 // Outputs 208 CeedScalar(*v)[CEED_Q_VLA] = (CeedScalar(*)[CEED_Q_VLA])out[0]; 209 210 const BlasiusContext context = (BlasiusContext)ctx; 211 const bool is_implicit = context->implicit; 212 const CeedScalar mu = context->newtonian_ctx.mu; 213 const CeedScalar cv = context->newtonian_ctx.cv; 214 const CeedScalar Rd = GasConstant(&context->newtonian_ctx); 215 const CeedScalar gamma = HeatCapacityRatio(&context->newtonian_ctx); 216 const CeedScalar T_inf = context->T_inf; 217 const CeedScalar P0 = context->P0; 218 const CeedScalar delta0 = context->delta0; 219 const CeedScalar U_inf = context->U_inf; 220 const bool weakT = context->weakT; 221 const CeedScalar rho_0 = P0 / (Rd * T_inf); 222 const CeedScalar x0 = U_inf * rho_0 / (mu * 25 / (delta0 * delta0)); 223 224 CeedPragmaSIMD for (CeedInt i = 0; i < Q; i++) { 225 CeedScalar wdetJb, norm[3]; 226 QdataBoundaryUnpack_3D(Q, i, q_data_sur, &wdetJb, NULL, norm); 227 wdetJb *= is_implicit ? -1. : 1.; 228 229 // Calculate inflow values 230 const CeedScalar x[3] = {X[0][i], X[1][i], X[2][i]}; 231 CeedScalar t12; 232 State s = BlasiusSolution(context, x, x0, 0, rho_0, &t12); 233 234 // enabling user to choose between weak T and weak rho inflow 235 CeedScalar drho, dE, dP; 236 if (weakT) { 237 // rho should be from the current solution 238 drho = dq[0][i]; 239 CeedScalar dE_internal = drho * cv * T_inf; 240 CeedScalar dE_kinetic = .5 * drho * Dot3(s.Y.velocity, s.Y.velocity); 241 dE = dE_internal + dE_kinetic; 242 dP = drho * Rd * T_inf; // interior rho with exterior T 243 } else { // rho specified, E_internal from solution 244 drho = 0; 245 dE = dq[4][i]; 246 dP = dE * (gamma - 1.); 247 } 248 249 const CeedScalar u_normal = Dot3(norm, s.Y.velocity); 250 251 v[0][i] = -wdetJb * drho * u_normal; 252 for (int j = 0; j < 3; j++) { 253 v[j + 1][i] = -wdetJb * (drho * u_normal * s.Y.velocity[j] + norm[j] * dP); 254 } 255 v[4][i] = -wdetJb * u_normal * (dE + dP); 256 } 257 return 0; 258 } 259