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 12 #ifndef blasius_h 13 #define blasius_h 14 15 #include <math.h> 16 #include <ceed.h> 17 #include "../navierstokes.h" 18 19 #ifndef blasius_context_struct 20 #define blasius_context_struct 21 typedef struct BlasiusContext_ *BlasiusContext; 22 struct BlasiusContext_ { 23 bool implicit; // !< Using implicit timesteping or not 24 bool weakT; // !< flag to set Temperature weakly at inflow 25 CeedScalar delta0; // !< Boundary layer height at inflow 26 CeedScalar Uinf; // !< Velocity at boundary layer edge 27 CeedScalar P0; // !< Pressure at outflow 28 CeedScalar theta0; // !< Temperature at inflow 29 struct NewtonianIdealGasContext_ newtonian_ctx; 30 }; 31 #endif 32 33 #ifndef M_PI 34 #define M_PI 3.14159265358979323846 35 #endif 36 37 void CEED_QFUNCTION_HELPER(BlasiusSolution)(const CeedScalar y, 38 const CeedScalar Uinf, const CeedScalar x0, const CeedScalar x, 39 const CeedScalar rho, CeedScalar *u, CeedScalar *v, CeedScalar *t12, 40 const NewtonianIdealGasContext newt_ctx) { 41 42 CeedInt nprofs = 50; 43 // *INDENT-OFF* 44 CeedScalar eta_table[] = { 45 0.000000000000000000e+00, 1.282051282051281937e-01, 2.564102564102563875e-01, 3.846153846153845812e-01, 5.128205128205127750e-01, 46 6.410256410256409687e-01, 7.692307692307691624e-01, 8.974358974358973562e-01, 1.025641025641025550e+00, 1.153846153846153744e+00, 47 1.282051282051281937e+00, 1.410256410256410131e+00, 1.538461538461538325e+00, 1.666666666666666519e+00, 1.794871794871794712e+00, 48 1.923076923076922906e+00, 2.051282051282051100e+00, 2.179487179487179294e+00, 2.307692307692307487e+00, 2.435897435897435681e+00, 49 2.564102564102563875e+00, 2.692307692307692069e+00, 2.820512820512820262e+00, 2.948717948717948456e+00, 3.076923076923076650e+00, 50 3.205128205128204844e+00, 3.333333333333333037e+00, 3.461538461538461231e+00, 3.589743589743589425e+00, 3.717948717948717618e+00, 51 3.846153846153845812e+00, 3.974358974358974006e+00, 4.102564102564102200e+00, 4.230769230769229949e+00, 4.358974358974358587e+00, 52 4.487179487179487225e+00, 4.615384615384614975e+00, 4.743589743589742724e+00, 4.871794871794871362e+00, 5.000000000000000000e+00, 53 5.500000000000000000e+00, 6.000000000000000000e+00, 6.500000000000000000e+00, 7.000000000000000000e+00, 7.500000000000000000e+00, 54 8.000000000000000000e+00, 8.500000000000000000e+00, 9.000000000000000000e+00, 9.500000000000000000e+00, 1.000000000000000000e+01}; 55 56 CeedScalar f_table[] = { 57 0.000000000000000000e+00, 2.728923405566200267e-03, 1.091524811461423369e-02, 2.455658828897525764e-02, 4.364674649279581820e-02, 58 6.817382707725749835e-02, 9.811838418932711248e-02, 1.334516294237205192e-01, 1.741337304561980659e-01, 2.201122374410622862e-01, 59 2.713206781625860375e-01, 3.276773654929600599e-01, 3.890844612583744255e-01, 4.554273387986328414e-01, 5.265742820946719416e-01, 60 6.023765522220410062e-01, 6.826688421431770237e-01, 7.672701287583111318e-01, 8.559849171804534418e-01, 9.486048570979430661e-01, 61 1.044910695686512625e+00, 1.144674516826549082e+00, 1.247662203367335465e+00, 1.353636048811749593e+00, 1.462357437868362364e+00, 62 1.573589512396551759e+00, 1.687099740622293842e+00, 1.802662313062363353e+00, 1.920060297987626230e+00, 2.039087501786055245e+00, 63 2.159549994377929050e+00, 2.281267275838891884e+00, 2.404073076539093190e+00, 2.527815798402052838e+00, 2.652358618452637540e+00, 64 2.777579287003750341e+00, 2.903369661199559637e+00, 3.029635020019957992e+00, 3.156293209307130088e+00, 3.283273665161465349e+00, 65 3.780571892998292771e+00, 4.279620922520262383e+00, 4.779322325882148448e+00, 5.279238811036782053e+00, 5.779218028455369804e+00, 66 6.279213431354994768e+00, 6.779212528163703233e+00, 7.279212370655419484e+00, 7.779212346288013613e+00, 8.279212342945751146e+00}; 67 68 CeedScalar fp_table[] = { 69 0.000000000000000000e+00, 4.257083277988830267e-02, 8.513297869782740501e-02, 1.276641169537044151e-01, 1.701271279078802878e-01, 70 2.124702831905590783e-01, 2.546276046951935212e-01, 2.965194442747576264e-01, 3.380533304776729975e-01, 3.791251204629754179e-01, 71 4.196204840172004791e-01, 4.594167322894788796e-01, 4.983849866855867838e-01, 5.363926638765821320e-01, 5.733062319885513514e-01, 72 6.089941719927144392e-01, 6.433300586189647507e-01, 6.761956584341198839e-01, 7.074839307288774970e-01, 7.371018110314454530e-01, 73 7.649726585225528064e-01, 7.910382579383948842e-01, 8.152602836158657773e-01, 8.376211573266827415e-01, 8.581242609418713307e-01, 74 8.767934976651666767e-01, 8.936722290953328374e-01, 9.088216471306606037e-01, 9.223186672607004422e-01, 9.342534510898168332e-01, 75 9.447266795705382414e-01, 9.538467037387058367e-01, 9.617266968332524035e-01, 9.684819213624265011e-01, 9.742272083384174719e-01, 76 9.790747253056680810e-01, 9.831320868743089747e-01, 9.865008381344084754e-01, 9.892753192614093249e-01, 9.915419001656551323e-01, 77 9.968788209317821503e-01, 9.989728724371175206e-01, 9.996990677381791812e-01, 9.999216041491896245e-01, 9.999818594083667023e-01, 78 9.999962745365539307e-01, 9.999993214550036980e-01, 9.999998904550418954e-01, 9.999999843329338001e-01, 9.999999980166356384e-01}; 79 80 CeedScalar fpp_table[] = { 81 3.320573362157903663e-01, 3.320379743512646420e-01, 3.319024760665882368e-01, 3.315350015070190337e-01, 3.308206767975666041e-01, 82 3.296466995822193158e-01, 3.279038639411161471e-01, 3.254884713737624113e-01, 3.223045750196085746e-01, 3.182664816607024272e-01, 83 3.133014118810801829e-01, 3.073521951089355775e-01, 3.003798556086043625e-01, 2.923659305537876785e-01, 2.833143548208253981e-01, 84 2.732527514995234941e-01, 2.622329840371728227e-01, 2.503308560706500874e-01, 2.376448876931176457e-01, 2.242941499773744018e-01, 85 2.104151994284793603e-01, 1.961582158440171031e-01, 1.816825052623964043e-01, 1.671515786102889534e-01, 1.527280512426029968e-01, 86 1.385686249977987894e-01, 1.248194106805364800e-01, 1.116118251613979206e-01, 9.905925581301598670e-02, 8.725462988794610575e-02, 87 7.626896310981794158e-02, 6.615089622448211415e-02, 5.692716644118058639e-02, 4.860390768479891377e-02, 4.116863313890323922e-02, 88 3.459272784597366285e-02, 2.883426862493499582e-02, 2.384099224121952881e-02, 1.955324839409207718e-02, 1.590679868531958210e-02, 89 6.578593141419011685e-03, 2.402039843751689954e-03, 7.741093231657678389e-04, 2.201689553063347941e-04, 5.526217815680267893e-05, 90 1.224092624232004387e-05, 2.392841910090350858e-06, 4.127879363882133676e-07, 6.284244603762621373e-08, 8.442944409712819646e-09}; 91 // *INDENT-ON* 92 93 CeedScalar nu = newt_ctx->mu / rho; 94 CeedScalar eta = y*sqrt(Uinf/(nu*(x0+x))); 95 CeedInt idx=-1; 96 97 for(CeedInt i=0; i<nprofs; i++) { 98 if (eta < eta_table[i]) { 99 idx = i; 100 break; 101 } 102 } 103 CeedScalar f, fp, fpp; 104 105 if (idx > 0) { // eta within the bounds of eta_table 106 CeedScalar coeff = (eta - eta_table[idx-1]) / (eta_table[idx] - eta_table[idx 107 -1]); 108 109 f = f_table[idx-1] + coeff*( f_table[idx] - f_table[idx-1] ); 110 fp = fp_table[idx-1] + coeff*( fp_table[idx] - fp_table[idx-1] ); 111 fpp = fpp_table[idx-1] + coeff*( fpp_table[idx] - fpp_table[idx-1] ); 112 } else { // eta outside bounds of eta_table 113 f = f_table[nprofs-1]; 114 fp = fp_table[nprofs-1]; 115 fpp = fpp_table[nprofs-1]; 116 eta = eta_table[nprofs-1]; 117 } 118 119 *u = Uinf*fp; 120 *t12 = rho*nu*Uinf*fpp*sqrt(Uinf/(nu*(x0+x))); 121 *v = 0.5*sqrt(nu*Uinf/(x0+x))*(eta*fp - f); 122 } 123 124 // ***************************************************************************** 125 // This QFunction sets a Blasius boundary layer for the initial condition 126 // ***************************************************************************** 127 CEED_QFUNCTION(ICsBlasius)(void *ctx, CeedInt Q, 128 const CeedScalar *const *in, CeedScalar *const *out) { 129 // Inputs 130 const CeedScalar (*X)[CEED_Q_VLA] = (const CeedScalar(*)[CEED_Q_VLA])in[0]; 131 132 // Outputs 133 CeedScalar (*q0)[CEED_Q_VLA] = (CeedScalar(*)[CEED_Q_VLA])out[0]; 134 135 const BlasiusContext context = (BlasiusContext)ctx; 136 const CeedScalar cv = context->newtonian_ctx.cv; 137 const CeedScalar cp = context->newtonian_ctx.cp; 138 const CeedScalar gamma = cp/cv; 139 const CeedScalar mu = context->newtonian_ctx.mu; 140 141 const CeedScalar theta0 = context->theta0; 142 const CeedScalar P0 = context->P0; 143 const CeedScalar delta0 = context->delta0; 144 const CeedScalar Uinf = context->Uinf; 145 146 const CeedScalar e_internal = cv * theta0; 147 const CeedScalar rho = P0 / ((gamma - 1) * e_internal); 148 const CeedScalar x0 = Uinf*rho / (mu*25/ (delta0*delta0) ); 149 CeedScalar u, v, t12; 150 151 // Quadrature Point Loop 152 CeedPragmaSIMD 153 for (CeedInt i=0; i<Q; i++) { 154 const CeedScalar x[] = {X[0][i], X[1][i], X[2][i]}; 155 156 BlasiusSolution(x[1], Uinf, x0, x[0], rho, &u, &v, &t12, 157 &context->newtonian_ctx); 158 159 q0[0][i] = rho; 160 q0[1][i] = u * rho; 161 q0[2][i] = v * rho; 162 q0[3][i] = 0.; 163 q0[4][i] = rho * e_internal + 0.5*(u*u + v*v)*rho; 164 } // End of Quadrature Point Loop 165 return 0; 166 } 167 168 // ***************************************************************************** 169 CEED_QFUNCTION(Blasius_Inflow)(void *ctx, CeedInt Q, 170 const CeedScalar *const *in, 171 CeedScalar *const *out) { 172 // *INDENT-OFF* 173 // Inputs 174 const CeedScalar (*q)[CEED_Q_VLA] = (const CeedScalar(*)[CEED_Q_VLA])in[0], 175 (*q_data_sur)[CEED_Q_VLA] = (const CeedScalar(*)[CEED_Q_VLA])in[1], 176 (*X)[CEED_Q_VLA] = (const CeedScalar(*)[CEED_Q_VLA])in[2]; 177 178 // Outputs 179 CeedScalar (*v)[CEED_Q_VLA] = (CeedScalar(*)[CEED_Q_VLA])out[0]; 180 // *INDENT-ON* 181 const BlasiusContext context = (BlasiusContext)ctx; 182 const bool implicit = context->implicit; 183 const CeedScalar mu = context->newtonian_ctx.mu; 184 const CeedScalar cv = context->newtonian_ctx.cv; 185 const CeedScalar cp = context->newtonian_ctx.cp; 186 const CeedScalar Rd = cp - cv; 187 const CeedScalar gamma = cp/cv; 188 189 const CeedScalar theta0 = context->theta0; 190 const CeedScalar P0 = context->P0; 191 const CeedScalar delta0 = context->delta0; 192 const CeedScalar Uinf = context->Uinf; 193 const bool weakT = context->weakT; 194 const CeedScalar rho_0 = P0 / (Rd * theta0); 195 const CeedScalar x0 = Uinf*rho_0 / (mu*25/ (delta0*delta0) ); 196 197 CeedPragmaSIMD 198 // Quadrature Point Loop 199 for (CeedInt i=0; i<Q; i++) { 200 // Setup 201 // -- Interp-to-Interp q_data 202 // For explicit mode, the surface integral is on the RHS of ODE q_dot = f(q). 203 // For implicit mode, it gets pulled to the LHS of implicit ODE/DAE g(q_dot, q). 204 // We can effect this by swapping the sign on this weight 205 const CeedScalar wdetJb = (implicit ? -1. : 1.) * q_data_sur[0][i]; 206 207 // Calculate inflow values 208 const CeedScalar x[3] = {X[0][i], X[1][i], X[2][i]}; 209 CeedScalar velocity[3] = {0.}; 210 CeedScalar t12; 211 BlasiusSolution(x[1], Uinf, x0, x[0], rho_0, &velocity[0], &velocity[1], 212 &t12, &context->newtonian_ctx); 213 214 // enabling user to choose between weak T and weak rho inflow 215 CeedScalar rho,E_internal, P, E_kinetic; 216 if (weakT) { 217 // rho should be from the current solution 218 rho = q[0][i]; 219 // Temperature is being set weakly (theta0) and for constant cv this sets E_internal 220 E_internal = rho * cv * theta0; 221 // Find pressure using 222 P=rho*Rd*theta0; // interior rho with exterior T 223 E_kinetic = .5 * rho * (velocity[0]*velocity[0] + 224 velocity[1]*velocity[1] + 225 velocity[2]*velocity[2]); 226 } else { 227 // Fixing rho weakly on the inflow to a value consistent with theta0 and P0 228 rho = rho_0; 229 E_kinetic = .5 * rho * (velocity[0]*velocity[0] + 230 velocity[1]*velocity[1] + 231 velocity[2]*velocity[2]); 232 E_internal = q[4][i] - E_kinetic; // uses set rho and u but E from solution 233 P = E_internal * (gamma - 1.); 234 } 235 const CeedScalar E = E_internal + E_kinetic; 236 // ---- Normal vect 237 const CeedScalar norm[3] = {q_data_sur[1][i], 238 q_data_sur[2][i], 239 q_data_sur[3][i] 240 }; 241 242 // The Physics 243 // Zero v so all future terms can safely sum into it 244 for (int j=0; j<5; j++) v[j][i] = 0.; 245 246 const CeedScalar u_normal = norm[0]*velocity[0] + 247 norm[1]*velocity[1] + 248 norm[2]*velocity[2]; 249 250 // The Physics 251 // -- Density 252 v[0][i] -= wdetJb * rho * u_normal; // interior rho 253 254 // -- Momentum 255 for (int j=0; j<3; j++) 256 v[j+1][i] -= wdetJb * (rho * u_normal * velocity[j] + // interior rho 257 norm[j] * P); // mixed P 258 v[2][i] -= wdetJb * t12 ; 259 260 // -- Total Energy Density 261 v[4][i] -= wdetJb * u_normal * (E + P); 262 v[4][i] -= wdetJb * t12 * velocity[1]; 263 264 } // End Quadrature Point Loop 265 return 0; 266 } 267 268 // ***************************************************************************** 269 CEED_QFUNCTION(Blasius_Outflow)(void *ctx, CeedInt Q, 270 const CeedScalar *const *in, 271 CeedScalar *const *out) { 272 // *INDENT-OFF* 273 // Inputs 274 const CeedScalar (*q)[CEED_Q_VLA] = (const CeedScalar(*)[CEED_Q_VLA])in[0], 275 (*q_data_sur)[CEED_Q_VLA] = (const CeedScalar(*)[CEED_Q_VLA])in[1], 276 (*X)[CEED_Q_VLA] = (const CeedScalar(*)[CEED_Q_VLA])in[2]; 277 // Outputs 278 CeedScalar (*v)[CEED_Q_VLA] = (CeedScalar(*)[CEED_Q_VLA])out[0]; 279 // *INDENT-ON* 280 281 const BlasiusContext context = (BlasiusContext)ctx; 282 const bool implicit = context->implicit; 283 const CeedScalar mu = context->newtonian_ctx.mu; 284 const CeedScalar cv = context->newtonian_ctx.cv; 285 const CeedScalar cp = context->newtonian_ctx.cp; 286 const CeedScalar Rd = cp - cv; 287 288 const CeedScalar theta0 = context->theta0; 289 const CeedScalar P0 = context->P0; 290 const CeedScalar rho_0 = P0 / (Rd*theta0); 291 const CeedScalar delta0 = context->delta0; 292 const CeedScalar Uinf = context->Uinf; 293 const CeedScalar x0 = Uinf*rho_0 / (mu*25/ (delta0*delta0) ); 294 295 CeedPragmaSIMD 296 // Quadrature Point Loop 297 for (CeedInt i=0; i<Q; i++) { 298 // Setup 299 // -- Interp in 300 const CeedScalar rho = q[0][i]; 301 const CeedScalar u[3] = {q[1][i] / rho, 302 q[2][i] / rho, 303 q[3][i] / rho 304 }; 305 const CeedScalar E = q[4][i]; 306 307 // -- Interp-to-Interp q_data 308 // For explicit mode, the surface integral is on the RHS of ODE q_dot = f(q). 309 // For implicit mode, it gets pulled to the LHS of implicit ODE/DAE g(q_dot, q). 310 // We can effect this by swapping the sign on this weight 311 const CeedScalar wdetJb = (implicit ? -1. : 1.) * q_data_sur[0][i]; 312 313 // ---- Normal vect 314 const CeedScalar norm[3] = {q_data_sur[1][i], 315 q_data_sur[2][i], 316 q_data_sur[3][i] 317 }; 318 319 // The Physics 320 // Zero v so all future terms can safely sum into it 321 for (int j=0; j<5; j++) v[j][i] = 0.; 322 323 // Implementing outflow condition 324 const CeedScalar P = P0; // pressure 325 const CeedScalar u_normal = norm[0]*u[0] + norm[1]*u[1] + 326 norm[2]*u[2]; // Normal velocity 327 328 // Calculate prescribed outflow traction values 329 const CeedScalar x[3] = {X[0][i], X[1][i], X[2][i]}; 330 CeedScalar velocity[3] = {0.}; 331 CeedScalar t12; 332 BlasiusSolution(x[1], Uinf, x0, x[0], rho_0, &velocity[0], &velocity[1], 333 &t12, &context->newtonian_ctx); 334 // The Physics 335 // -- Density 336 v[0][i] -= wdetJb * rho * u_normal; 337 338 // -- Momentum 339 for (int j=0; j<3; j++) 340 v[j+1][i] -= wdetJb *(rho * u_normal * u[j] + norm[j] * P); 341 v[2][i] += wdetJb * t12 ; 342 343 // -- Total Energy Density 344 v[4][i] -= wdetJb * u_normal * (E + P); 345 v[4][i] += wdetJb * t12 * velocity[1]; 346 347 } // End Quadrature Point Loop 348 return 0; 349 } 350 #endif // blasius_h 351