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 /// Operator for Navier-Stokes example using PETSc 10 11 #ifndef blasius_h 12 #define blasius_h 13 14 #include <ceed.h> 15 16 #include "newtonian_state.h" 17 #include "newtonian_types.h" 18 #include "utils.h" 19 20 #define BLASIUS_MAX_N_CHEBYSHEV 50 21 22 typedef struct BlasiusContext_ *BlasiusContext; 23 struct BlasiusContext_ { 24 bool implicit; // !< Using implicit timesteping or not 25 bool weakT; // !< flag to set Temperature weakly at inflow 26 CeedScalar delta0; // !< Boundary layer height at inflow 27 CeedScalar U_inf; // !< Velocity at boundary layer edge 28 CeedScalar T_inf; // !< Temperature at boundary layer edge 29 CeedScalar T_wall; // !< Temperature at the wall 30 CeedScalar P0; // !< Pressure at outflow 31 CeedScalar x_inflow; // !< Location of inflow in x 32 CeedScalar n_cheb; // !< Number of Chebyshev terms 33 CeedScalar *X; // !< Chebyshev polynomial coordinate vector (CPU only) 34 CeedScalar eta_max; // !< Maximum eta in the domain 35 CeedScalar Tf_cheb[BLASIUS_MAX_N_CHEBYSHEV]; // !< Chebyshev coefficient for f 36 CeedScalar Th_cheb[BLASIUS_MAX_N_CHEBYSHEV - 1]; // !< Chebyshev coefficient for h 37 struct NewtonianIdealGasContext_ newtonian_ctx; 38 }; 39 40 // ***************************************************************************** 41 // This helper function evaluates Chebyshev polynomials with a set of 42 // coefficients with all their derivatives represented as a recurrence table. 43 // ***************************************************************************** 44 CEED_QFUNCTION_HELPER void ChebyshevEval(int N, const double *Tf, double x, double eta_max, double *f) { 45 double dX_deta = 2 / eta_max; 46 double table[4][3] = { 47 // Chebyshev polynomials T_0, T_1, T_2 of the first kind in (-1,1) 48 {1, x, 2 * x * x - 1}, 49 {0, 1, 4 * x }, 50 {0, 0, 4 }, 51 {0, 0, 0 } 52 }; 53 for (int i = 0; i < 4; i++) { 54 // i-th derivative of f 55 f[i] = table[i][0] * Tf[0] + table[i][1] * Tf[1] + table[i][2] * Tf[2]; 56 } 57 for (int i = 3; i < N; i++) { 58 // T_n(x) = 2xT_{n-1}(x) - T_{n-2}(x) 59 table[0][i % 3] = 2 * x * table[0][(i - 1) % 3] - table[0][(i - 2) % 3]; 60 // Differentiate Chebyshev polynomials with the recurrence relation 61 for (int j = 1; j < 4; j++) { 62 // T'_{n}(x)/n = 2T_{n-1}(x) + T'_{n-2}(x)/n-2 63 table[j][i % 3] = i * (2 * table[j - 1][(i - 1) % 3] + table[j][(i - 2) % 3] / (i - 2)); 64 } 65 for (int j = 0; j < 4; j++) { 66 f[j] += table[j][i % 3] * Tf[i]; 67 } 68 } 69 for (int i = 1; i < 4; i++) { 70 // Transform derivatives from Chebyshev [-1, 1] to [0, eta_max]. 71 for (int j = 0; j < i; j++) f[i] *= dX_deta; 72 } 73 } 74 75 // ***************************************************************************** 76 // This helper function computes the Blasius boundary layer solution. 77 // ***************************************************************************** 78 State CEED_QFUNCTION_HELPER(BlasiusSolution)(const BlasiusContext blasius, const CeedScalar x[3], const CeedScalar x0, const CeedScalar x_inflow, 79 const CeedScalar rho_infty, CeedScalar *t12) { 80 CeedInt N = blasius->n_cheb; 81 CeedScalar mu = blasius->newtonian_ctx.mu; 82 CeedScalar nu = mu / rho_infty; 83 CeedScalar eta = x[1] * sqrt(blasius->U_inf / (nu * (x0 + x[0] - x_inflow))); 84 CeedScalar X = 2 * (eta / blasius->eta_max) - 1.; 85 CeedScalar U_inf = blasius->U_inf; 86 CeedScalar Rd = GasConstant(&blasius->newtonian_ctx); 87 88 CeedScalar f[4], h[4]; 89 ChebyshevEval(N, blasius->Tf_cheb, X, blasius->eta_max, f); 90 ChebyshevEval(N - 1, blasius->Th_cheb, X, blasius->eta_max, h); 91 92 *t12 = mu * U_inf * f[2] * sqrt(U_inf / (nu * (x0 + x[0] - x_inflow))); 93 94 CeedScalar Y[5]; 95 Y[1] = U_inf * f[1]; 96 Y[2] = 0.5 * sqrt(nu * U_inf / (x0 + x[0] - x_inflow)) * (eta * f[1] - f[0]); 97 Y[3] = 0.; 98 Y[4] = blasius->T_inf * h[0]; 99 Y[0] = rho_infty / h[0] * Rd * Y[4]; 100 return StateFromY(&blasius->newtonian_ctx, Y, x); 101 } 102 103 // ***************************************************************************** 104 // This QFunction sets a Blasius boundary layer for the initial condition 105 // ***************************************************************************** 106 CEED_QFUNCTION(ICsBlasius)(void *ctx, CeedInt Q, const CeedScalar *const *in, CeedScalar *const *out) { 107 // Inputs 108 const CeedScalar(*X)[CEED_Q_VLA] = (const CeedScalar(*)[CEED_Q_VLA])in[0]; 109 110 // Outputs 111 CeedScalar(*q0)[CEED_Q_VLA] = (CeedScalar(*)[CEED_Q_VLA])out[0]; 112 113 const BlasiusContext context = (BlasiusContext)ctx; 114 const CeedScalar cv = context->newtonian_ctx.cv; 115 const CeedScalar mu = context->newtonian_ctx.mu; 116 const CeedScalar T_inf = context->T_inf; 117 const CeedScalar P0 = context->P0; 118 const CeedScalar delta0 = context->delta0; 119 const CeedScalar U_inf = context->U_inf; 120 const CeedScalar x_inflow = context->x_inflow; 121 const CeedScalar gamma = HeatCapacityRatio(&context->newtonian_ctx); 122 const CeedScalar e_internal = cv * T_inf; 123 const CeedScalar rho = P0 / ((gamma - 1) * e_internal); 124 const CeedScalar x0 = U_inf * rho / (mu * 25 / (delta0 * delta0)); 125 CeedScalar t12; 126 127 // Quadrature Point Loop 128 CeedPragmaSIMD for (CeedInt i = 0; i < Q; i++) { 129 const CeedScalar x[3] = {X[0][i], X[1][i], 0.}; 130 State s = BlasiusSolution(context, x, x0, x_inflow, rho, &t12); 131 CeedScalar q[5] = {0}; 132 UnpackState_U(s.U, q); 133 for (CeedInt j = 0; j < 5; j++) q0[j][i] = q[j]; 134 135 } // End of Quadrature Point Loop 136 return 0; 137 } 138 139 // ***************************************************************************** 140 CEED_QFUNCTION(Blasius_Inflow)(void *ctx, CeedInt Q, const CeedScalar *const *in, CeedScalar *const *out) { 141 // *INDENT-OFF* 142 // Inputs 143 const CeedScalar(*q)[CEED_Q_VLA] = (const CeedScalar(*)[CEED_Q_VLA])in[0], (*q_data_sur)[CEED_Q_VLA] = (const CeedScalar(*)[CEED_Q_VLA])in[2], 144 (*X)[CEED_Q_VLA] = (const CeedScalar(*)[CEED_Q_VLA])in[3]; 145 146 // Outputs 147 CeedScalar(*v)[CEED_Q_VLA] = (CeedScalar(*)[CEED_Q_VLA])out[0]; 148 // *INDENT-ON* 149 const BlasiusContext context = (BlasiusContext)ctx; 150 const bool implicit = context->implicit; 151 NewtonianIdealGasContext gas = &context->newtonian_ctx; 152 const CeedScalar mu = context->newtonian_ctx.mu; 153 const CeedScalar Rd = GasConstant(&context->newtonian_ctx); 154 const CeedScalar T_inf = context->T_inf; 155 const CeedScalar P0 = context->P0; 156 const CeedScalar delta0 = context->delta0; 157 const CeedScalar U_inf = context->U_inf; 158 const CeedScalar x_inflow = context->x_inflow; 159 const bool weakT = context->weakT; 160 const CeedScalar rho_0 = P0 / (Rd * T_inf); 161 const CeedScalar x0 = U_inf * rho_0 / (mu * 25 / Square(delta0)); 162 163 CeedPragmaSIMD 164 // Quadrature Point Loop 165 for (CeedInt i = 0; i < Q; i++) { 166 // Setup 167 // -- Interp-to-Interp q_data 168 // For explicit mode, the surface integral is on the RHS of ODE q_dot = f(q). 169 // For implicit mode, it gets pulled to the LHS of implicit ODE/DAE g(q_dot, q). 170 // We can effect this by swapping the sign on this weight 171 const CeedScalar wdetJb = (implicit ? -1. : 1.) * q_data_sur[0][i]; 172 173 // Calculate inflow values 174 const CeedScalar x[3] = {X[0][i], X[1][i], 0.}; 175 CeedScalar t12; 176 State s = BlasiusSolution(context, x, x0, x_inflow, rho_0, &t12); 177 CeedScalar qi[5]; 178 for (CeedInt j = 0; j < 5; j++) qi[j] = q[j][i]; 179 State s_int = StateFromU(gas, qi, x); 180 181 // enabling user to choose between weak T and weak rho inflow 182 if (weakT) { // density from the current solution 183 s.U.density = s_int.U.density; 184 s.Y = StatePrimitiveFromConservative(gas, s.U, x); 185 } else { // Total energy from current solution 186 s.U.E_total = s_int.U.E_total; 187 s.Y = StatePrimitiveFromConservative(gas, s.U, x); 188 } 189 190 // ---- Normal vect 191 const CeedScalar norm[3] = {q_data_sur[1][i], q_data_sur[2][i], q_data_sur[3][i]}; 192 193 StateConservative Flux_inviscid[3]; 194 FluxInviscid(&context->newtonian_ctx, s, Flux_inviscid); 195 196 const CeedScalar stress[3][3] = { 197 {0, t12, 0}, 198 {t12, 0, 0}, 199 {0, 0, 0} 200 }; 201 const CeedScalar Fe[3] = {0}; // TODO: viscous energy flux needs grad temperature 202 CeedScalar Flux[5]; 203 FluxTotal_Boundary(Flux_inviscid, stress, Fe, norm, Flux); 204 for (CeedInt j = 0; j < 5; j++) v[j][i] = -wdetJb * Flux[j]; 205 } // End Quadrature Point Loop 206 return 0; 207 } 208 209 // ***************************************************************************** 210 CEED_QFUNCTION(Blasius_Inflow_Jacobian)(void *ctx, CeedInt Q, const CeedScalar *const *in, CeedScalar *const *out) { 211 // *INDENT-OFF* 212 // Inputs 213 const CeedScalar(*dq)[CEED_Q_VLA] = (const CeedScalar(*)[CEED_Q_VLA])in[0], (*q_data_sur)[CEED_Q_VLA] = (const CeedScalar(*)[CEED_Q_VLA])in[2], 214 (*X)[CEED_Q_VLA] = (const CeedScalar(*)[CEED_Q_VLA])in[3]; 215 216 // Outputs 217 CeedScalar(*v)[CEED_Q_VLA] = (CeedScalar(*)[CEED_Q_VLA])out[0]; 218 // *INDENT-ON* 219 const BlasiusContext context = (BlasiusContext)ctx; 220 const bool implicit = context->implicit; 221 const CeedScalar mu = context->newtonian_ctx.mu; 222 const CeedScalar cv = context->newtonian_ctx.cv; 223 const CeedScalar Rd = GasConstant(&context->newtonian_ctx); 224 const CeedScalar gamma = HeatCapacityRatio(&context->newtonian_ctx); 225 const CeedScalar T_inf = context->T_inf; 226 const CeedScalar P0 = context->P0; 227 const CeedScalar delta0 = context->delta0; 228 const CeedScalar U_inf = context->U_inf; 229 const bool weakT = context->weakT; 230 const CeedScalar rho_0 = P0 / (Rd * T_inf); 231 const CeedScalar x0 = U_inf * rho_0 / (mu * 25 / (delta0 * delta0)); 232 233 CeedPragmaSIMD 234 // Quadrature Point Loop 235 for (CeedInt i = 0; i < Q; i++) { 236 // Setup 237 // -- Interp-to-Interp q_data 238 // For explicit mode, the surface integral is on the RHS of ODE q_dot = f(q). 239 // For implicit mode, it gets pulled to the LHS of implicit ODE/DAE g(q_dot, q). 240 // We can effect this by swapping the sign on this weight 241 const CeedScalar wdetJb = (implicit ? -1. : 1.) * q_data_sur[0][i]; 242 243 // Calculate inflow values 244 const CeedScalar x[3] = {X[0][i], X[1][i], X[2][i]}; 245 CeedScalar t12; 246 State s = BlasiusSolution(context, x, x0, 0, rho_0, &t12); 247 248 // enabling user to choose between weak T and weak rho inflow 249 CeedScalar drho, dE, dP; 250 if (weakT) { 251 // rho should be from the current solution 252 drho = dq[0][i]; 253 CeedScalar dE_internal = drho * cv * T_inf; 254 CeedScalar dE_kinetic = .5 * drho * Dot3(s.Y.velocity, s.Y.velocity); 255 dE = dE_internal + dE_kinetic; 256 dP = drho * Rd * T_inf; // interior rho with exterior T 257 } else { // rho specified, E_internal from solution 258 drho = 0; 259 dE = dq[4][i]; 260 dP = dE * (gamma - 1.); 261 } 262 const CeedScalar norm[3] = {q_data_sur[1][i], q_data_sur[2][i], q_data_sur[3][i]}; 263 264 const CeedScalar u_normal = Dot3(norm, s.Y.velocity); 265 266 v[0][i] = -wdetJb * drho * u_normal; 267 for (int j = 0; j < 3; j++) { 268 v[j + 1][i] = -wdetJb * (drho * u_normal * s.Y.velocity[j] + norm[j] * dP); 269 } 270 v[4][i] = -wdetJb * u_normal * (dE + dP); 271 } // End Quadrature Point Loop 272 return 0; 273 } 274 275 #endif // blasius_h 276