1 static char help[] = "Variable-Viscosity Stokes Problem in 2d.\n\ 2 Exact solutions provided by Mirko Velic.\n\n\n"; 3 4 #include <petsc.h> 5 6 #include "ex75.h" 7 8 typedef struct { 9 PetscBool fem; /* Flag for FEM tests */ 10 } AppCtx; 11 12 PetscErrorCode ProcessOptions(MPI_Comm comm, AppCtx *options) 13 { 14 PetscFunctionBeginUser; 15 options->fem = PETSC_FALSE; 16 PetscOptionsBegin(comm, "", "Stokes Problem Options", "DMPLEX"); 17 PetscCall(PetscOptionsBool("-fem", "Run FEM tests", "ex75.c", options->fem, &options->fem, NULL)); 18 PetscOptionsEnd(); 19 PetscFunctionReturn(0); 20 } 21 22 /* 23 SolKxSolution - Exact Stokes solutions for exponentially varying viscosity 24 25 Input Parameters: 26 + x - The x coordinate at which to evaluate the solution 27 . z - The z coordinate at which to evaluate the solution 28 . kn - The constant defining the x-dependence of the forcing function 29 . km - The constant defining the z-dependence of the forcing function 30 - B - The viscosity coefficient 31 32 Output Parameters: 33 + vx - The x-velocity at (x,z) 34 . vz - The z-velocity at (x,z) 35 . p - The pressure at (x,z) 36 . sxx - The stress sigma_xx at (x,z) 37 . sxz - The stress sigma_xz at (x,z) 38 - szz - The stress sigma_zz at (x,z) 39 40 Note: 41 $ The domain is the square 0 <= x,z <= 1. We solve the Stokes equation for incompressible flow with free-slip boundary 42 $ conditions everywhere. The forcing term f is given by 43 $ 44 $ fx = 0 45 $ fz = sigma*sin(km*z)*cos(kn*x) 46 $ 47 $ where 48 $ 49 $ km = m*Pi (m may be non-integral) 50 $ kn = n*Pi 51 $ 52 $ meaning that the density rho is -sigma*sin(km*z)*cos(kn*x). The viscosity eta is exp(2*B*x). 53 */ 54 PetscErrorCode SolKxSolution(PetscReal x, PetscReal z, PetscReal kn, PetscReal km, PetscReal B, PetscScalar *vx, PetscScalar *vz, PetscScalar *p, PetscScalar *sxx, PetscScalar *sxz, PetscScalar *szz) 55 { 56 PetscScalar sigma; 57 PetscScalar _C1, _C2, _C3, _C4; 58 PetscScalar Rp, UU, VV; 59 PetscScalar a, b, r, _aa, _bb, AA, BB, Rm; 60 PetscScalar num1, num2, num3, num4, den1; 61 62 PetscScalar t1, t2, t3, t4, t5, t6, t7, t8, t9, t10; 63 PetscScalar t11, t12, t13, t14, t15, t16, t17, t18, t19, t20, t21; 64 PetscScalar t22, t23, t24, t25, t26, t28, t29, t30, t31, t32; 65 PetscScalar t33, t34, t35, t36, t37, t38, t39, t40, t41, t42; 66 PetscScalar t44, t45, t46, t47, t48, t49, t51, t52, t53, t54; 67 PetscScalar t56, t58, t61, t62, t63, t64, t65, t66, t67, t68; 68 PetscScalar t69, t70, t71, t72, t73, t74, t75, t76, t77, t78; 69 PetscScalar t79, t80, t81, t82, t83, t84, t85, t86, t87, t88; 70 PetscScalar t89, t90, t91, t92, t93, t94, t95, t96, t97, t98; 71 PetscScalar t99, t100, t101, t103, t104, t105, t106, t107, t108, t109; 72 PetscScalar t110, t111, t112, t113, t114, t115, t116, t117, t118, t119; 73 PetscScalar t120, t121, t123, t125, t127, t128, t130, t131, t132, t133; 74 PetscScalar t135, t136, t138, t140, t141, t142, t143, t152, t160, t162; 75 76 PetscFunctionBegin; 77 /*************************************************************************/ 78 /*************************************************************************/ 79 /* rho = -sin(km*z)*cos(kn*x) */ 80 /* viscosity Z= exp(2*B*z) */ 81 /* solution valid for km not zero -- should get trivial solution if km=0 */ 82 sigma = 1.0; 83 /*************************************************************************/ 84 /*************************************************************************/ 85 a = B * B + km * km; 86 b = 2.0 * km * B; 87 r = sqrt(a * a + b * b); 88 Rp = sqrt((r + a) / 2.0); 89 Rm = sqrt((r - a) / 2.0); 90 UU = Rp - B; 91 VV = Rp + B; 92 93 /*******************************************/ 94 /* calculate the constants */ 95 /*******************************************/ 96 t1 = kn * kn; 97 t4 = km * km; 98 t6 = t4 * t4; 99 t7 = B * B; 100 t9 = 0.4e1 * t7 * t4; 101 t12 = 0.8e1 * t7 * kn * km; 102 t14 = 0.4e1 * t7 * t1; 103 t16 = 0.2e1 * t4 * t1; 104 t17 = t1 * t1; 105 _aa = -0.4e1 * B * t1 * sigma * (t4 + t1) / (t6 + t9 + t12 + t14 + t16 + t17) / (t6 + t9 - t12 + t14 + t16 + t17); 106 107 t2 = kn * kn; 108 t3 = t2 * t2; 109 t4 = B * B; 110 t6 = 0.4e1 * t4 * t2; 111 t7 = km * km; 112 t9 = 0.4e1 * t7 * t4; 113 t10 = t7 * t7; 114 t12 = 0.2e1 * t7 * t2; 115 t16 = 0.8e1 * t4 * kn * km; 116 _bb = sigma * kn * (t3 - t6 + t9 + t10 + t12) / (t10 + t9 + t16 + t6 + t12 + t3) / (t10 + t9 - t16 + t6 + t12 + t3); 117 118 AA = _aa; 119 BB = _bb; 120 121 t1 = Rm * Rm; 122 t2 = B - Rp; 123 t4 = Rp + B; 124 t6 = UU * x; 125 t9 = exp(t6 - 0.4e1 * Rp); 126 t13 = kn * kn; 127 t15 = B * B; 128 t18 = Rp * Rp; 129 t19 = t18 * B; 130 t20 = t15 * Rp; 131 t22 = t1 * Rp; 132 t24 = B * t1; 133 t32 = 0.8e1 * t15 * BB * kn * Rp; 134 t34 = 0.2e1 * Rm; 135 t35 = cos(t34); 136 t37 = Rm * Rp; 137 t49 = sin(t34); 138 t63 = exp(t6 - 0.2e1 * Rp); 139 t65 = Rm * t2; 140 t67 = 0.2e1 * B * kn; 141 t68 = B * Rm; 142 t69 = t67 + t68 + t37; 143 t73 = 0.3e1 * t15; 144 t75 = 0.2e1 * B * Rp; 145 t76 = t73 - t75 + t1 - t13 - t18; 146 t78 = t65 * t76 * BB; 147 t80 = Rm - kn; 148 t81 = cos(t80); 149 t83 = t68 - t67 + t37; 150 t88 = Rm + kn; 151 t89 = cos(t88); 152 t92 = t65 * t76 * AA; 153 t97 = sin(t80); 154 t103 = sin(t88); 155 t108 = exp(t6 - 0.3e1 * Rp - B); 156 t110 = Rm * t4; 157 t111 = t67 + t68 - t37; 158 t115 = t73 + t75 + t1 - t13 - t18; 159 t117 = t110 * t115 * BB; 160 t120 = -t67 + t68 - t37; 161 t127 = t110 * t115 * AA; 162 t140 = exp(t6 - Rp - B); 163 num1 = -0.4e1 * t1 * t2 * t4 * AA * t9 + ((0.2e1 * Rp * (-B * t13 + 0.3e1 * t15 * B - t19 - 0.2e1 * t20 - 0.2e1 * t22 - t24) * AA - t32) * t35 + (0.2e1 * t37 * (t1 - t13 + 0.5e1 * t15 - t18) * AA - 0.8e1 * B * BB * kn * Rm * Rp) * t49 - 0.2e1 * B * (0.3e1 * t20 - t18 * Rp - 0.2e1 * t19 - Rp * t13 - t22 - 0.2e1 * t24) * AA + t32) * t63 + ((0.2e1 * t65 * t69 * AA + t78) * t81 + (0.2e1 * t65 * t83 * AA - t78) * t89 + (t92 - 0.2e1 * t65 * t69 * BB) * t97 + (t92 + 0.2e1 * t65 * t83 * BB) * t103) * t108 + ((-0.2e1 * t110 * t111 * AA - t117) * t81 + (-0.2e1 * t110 * t120 * AA + t117) * t89 + (-t127 + 0.2e1 * t110 * t111 * BB) * t97 + (-t127 - 0.2e1 * t110 * t120 * BB) * t103) * t140; 164 165 t1 = Rp + B; 166 t2 = Rm * t1; 167 t3 = B * B; 168 t4 = 0.3e1 * t3; 169 t5 = B * Rp; 170 t7 = Rm * Rm; 171 t8 = kn * kn; 172 t9 = Rp * Rp; 173 t10 = t4 + 0.2e1 * t5 + t7 - t8 - t9; 174 t12 = t2 * t10 * AA; 175 t14 = B * Rm; 176 t20 = UU * x; 177 t23 = exp(t20 - 0.4e1 * Rp); 178 t25 = Rm * Rp; 179 t32 = Rm * kn; 180 t37 = 0.2e1 * Rm; 181 t38 = cos(t37); 182 t41 = t3 * B; 183 t44 = t3 * Rp; 184 t48 = B * t7; 185 t53 = t3 * BB; 186 t54 = kn * Rp; 187 t58 = sin(t37); 188 t69 = exp(t20 - 0.2e1 * Rp); 189 t71 = t9 * Rp; 190 t72 = Rm * t71; 191 t73 = t3 * Rm; 192 t75 = 0.5e1 * t73 * Rp; 193 t77 = 0.8e1 * t44 * kn; 194 t78 = t25 * t8; 195 t79 = t7 * Rm; 196 t80 = B * t79; 197 t81 = t14 * t8; 198 t82 = t79 * Rp; 199 t84 = 0.3e1 * t41 * Rm; 200 t85 = t14 * t9; 201 t86 = -t72 + t75 + t77 - t78 + t80 - t81 + t82 + t84 + t85; 202 t88 = t7 * t9; 203 t89 = t5 * t8; 204 t90 = t7 * t3; 205 t91 = B * t71; 206 t92 = t48 * Rp; 207 t94 = 0.2e1 * t14 * t54; 208 t96 = 0.3e1 * Rp * t41; 209 t98 = 0.2e1 * t73 * kn; 210 t100 = 0.2e1 * t9 * t3; 211 t101 = -t88 - t89 - t90 - t91 - t92 - t94 + t96 - t98 - t100; 212 t105 = Rm - kn; 213 t106 = cos(t105); 214 t108 = t75 - t77 - t78 + t85 - t72 - t81 + t80 + t84 + t82; 215 t110 = -t100 + t96 - t91 + t94 + t98 - t92 - t89 - t88 - t90; 216 t114 = Rm + kn; 217 t115 = cos(t114); 218 t121 = sin(t105); 219 t127 = sin(t114); 220 t132 = exp(t20 - 0.3e1 * Rp - B); 221 t135 = 0.2e1 * B * kn; 222 t136 = t135 + t14 - t25; 223 t142 = -t135 + t14 - t25; 224 t152 = t2 * t10 * BB; 225 t162 = exp(t20 - Rp - B); 226 num2 = (0.2e1 * t12 - 0.8e1 * t14 * kn * t1 * BB) * t23 + ((-0.2e1 * t25 * (t7 - t8 + 0.5e1 * t3 - t9) * AA + 0.8e1 * B * BB * t32 * Rp) * t38 + (0.2e1 * Rp * (-B * t8 + 0.3e1 * t41 - t9 * B - 0.2e1 * t44 - 0.2e1 * t7 * Rp - t48) * AA - 0.8e1 * t53 * t54) * t58 - 0.2e1 * t14 * (t4 + t9 - t8 + t7) * AA + 0.8e1 * t53 * t32) * t69 + ((-t86 * AA - 0.2e1 * t101 * BB) * t106 + (-t108 * AA + 0.2e1 * t110 * BB) * t115 + (-0.2e1 * t101 * AA + t86 * BB) * t121 + (-0.2e1 * t110 * AA - t108 * BB) * t127) * t132 + ((t12 - 0.2e1 * t2 * t136 * BB) * t106 + (t12 + 0.2e1 * t2 * t142 * BB) * t115 + (-0.2e1 * t2 * t136 * AA - t152) * t121 + (-0.2e1 * t2 * t142 * AA + t152) * t127) * t162; 227 228 t1 = Rm * Rm; 229 t2 = B - Rp; 230 t4 = Rp + B; 231 t6 = VV * x; 232 t7 = exp(-t6); 233 t11 = B * t1; 234 t12 = Rp * Rp; 235 t13 = t12 * B; 236 t14 = B * B; 237 t15 = t14 * Rp; 238 t19 = kn * kn; 239 t21 = t1 * Rp; 240 t30 = 0.8e1 * t14 * BB * kn * Rp; 241 t32 = 0.2e1 * Rm; 242 t33 = cos(t32); 243 t35 = Rm * Rp; 244 t47 = sin(t32); 245 t61 = exp(-t6 - 0.2e1 * Rp); 246 t63 = Rm * t2; 247 t65 = 0.2e1 * B * kn; 248 t66 = B * Rm; 249 t67 = t65 + t66 + t35; 250 t71 = 0.3e1 * t14; 251 t73 = 0.2e1 * B * Rp; 252 t74 = t71 - t73 + t1 - t19 - t12; 253 t76 = t63 * t74 * BB; 254 t78 = Rm - kn; 255 t79 = cos(t78); 256 t81 = t66 - t65 + t35; 257 t86 = Rm + kn; 258 t87 = cos(t86); 259 t90 = t63 * t74 * AA; 260 t95 = sin(t78); 261 t101 = sin(t86); 262 t106 = exp(-t6 - 0.3e1 * Rp - B); 263 t108 = Rm * t4; 264 t109 = t65 + t66 - t35; 265 t113 = t71 + t73 + t1 - t19 - t12; 266 t115 = t108 * t113 * BB; 267 t118 = -t65 + t66 - t35; 268 t125 = t108 * t113 * AA; 269 t138 = exp(-t6 - Rp - B); 270 num3 = -0.4e1 * t1 * t2 * t4 * AA * t7 + ((-0.2e1 * Rp * (-t11 - t13 + 0.2e1 * t15 + 0.3e1 * t14 * B - B * t19 + 0.2e1 * t21) * AA + t30) * t33 + (-0.2e1 * t35 * (t1 - t19 + 0.5e1 * t14 - t12) * AA + 0.8e1 * B * BB * kn * Rm * Rp) * t47 + 0.2e1 * B * (-t12 * Rp + 0.2e1 * t11 + 0.3e1 * t15 + 0.2e1 * t13 - t21 - Rp * t19) * AA - t30) * t61 + ((-0.2e1 * t63 * t67 * AA - t76) * t79 + (-0.2e1 * t63 * t81 * AA + t76) * t87 + (-t90 + 0.2e1 * t63 * t67 * BB) * t95 + (-t90 - 0.2e1 * t63 * t81 * BB) * t101) * t106 + ((0.2e1 * t108 * t109 * AA + t115) * t79 + (0.2e1 * t108 * t118 * AA - t115) * t87 + (t125 - 0.2e1 * t108 * t109 * BB) * t95 + (t125 + 0.2e1 * t108 * t118 * BB) * t101) * t138; 271 272 t1 = B - Rp; 273 t2 = Rm * t1; 274 t3 = B * B; 275 t4 = 0.3e1 * t3; 276 t5 = B * Rp; 277 t7 = Rm * Rm; 278 t8 = kn * kn; 279 t9 = Rp * Rp; 280 t10 = t4 - 0.2e1 * t5 + t7 - t8 - t9; 281 t12 = t2 * t10 * AA; 282 t14 = B * Rm; 283 t20 = VV * x; 284 t21 = exp(-t20); 285 t23 = Rm * Rp; 286 t30 = Rm * kn; 287 t35 = 0.2e1 * Rm; 288 t36 = cos(t35); 289 t38 = B * t7; 290 t40 = t3 * Rp; 291 t42 = t3 * B; 292 t51 = t3 * BB; 293 t52 = kn * Rp; 294 t56 = sin(t35); 295 t67 = exp(-t20 - 0.2e1 * Rp); 296 t70 = 0.2e1 * B * kn; 297 t71 = t70 + t14 + t23; 298 t76 = Rm - kn; 299 t77 = cos(t76); 300 t79 = t14 - t70 + t23; 301 t84 = Rm + kn; 302 t85 = cos(t84); 303 t91 = t2 * t10 * BB; 304 t93 = sin(t76); 305 t99 = sin(t84); 306 t104 = exp(-t20 - 0.3e1 * Rp - B); 307 t106 = t9 * Rp; 308 t107 = Rm * t106; 309 t108 = t3 * Rm; 310 t110 = 0.5e1 * t108 * Rp; 311 t112 = 0.8e1 * t40 * kn; 312 t113 = t23 * t8; 313 t114 = t7 * Rm; 314 t115 = B * t114; 315 t116 = t14 * t8; 316 t117 = t114 * Rp; 317 t119 = 0.3e1 * t42 * Rm; 318 t120 = t14 * t9; 319 t121 = t107 - t110 - t112 + t113 + t115 - t116 - t117 + t119 + t120; 320 t123 = t38 * Rp; 321 t125 = 0.2e1 * t14 * t52; 322 t127 = 0.3e1 * Rp * t42; 323 t128 = t7 * t3; 324 t130 = 0.2e1 * t9 * t3; 325 t131 = t7 * t9; 326 t132 = B * t106; 327 t133 = t5 * t8; 328 t135 = 0.2e1 * t108 * kn; 329 t136 = -t123 - t125 + t127 + t128 + t130 + t131 - t132 - t133 + t135; 330 t141 = -t110 + t112 + t113 + t120 + t107 - t116 + t115 + t119 - t117; 331 t143 = t125 - t132 + t130 - t135 + t127 + t131 - t123 + t128 - t133; 332 t160 = exp(-t20 - Rp - B); 333 num4 = (0.2e1 * t12 - 0.8e1 * t14 * kn * t1 * BB) * t21 + ((0.2e1 * t23 * (t7 - t8 + 0.5e1 * t3 - t9) * AA - 0.8e1 * B * BB * t30 * Rp) * t36 + (-0.2e1 * Rp * (-t38 - t9 * B + 0.2e1 * t40 + 0.3e1 * t42 - B * t8 + 0.2e1 * t7 * Rp) * AA + 0.8e1 * t51 * t52) * t56 - 0.2e1 * t14 * (t4 + t9 - t8 + t7) * AA + 0.8e1 * t51 * t30) * t67 + ((t12 - 0.2e1 * t2 * t71 * BB) * t77 + (t12 + 0.2e1 * t2 * t79 * BB) * t85 + (-0.2e1 * t2 * t71 * AA - t91) * t93 + (-0.2e1 * t2 * t79 * AA + t91) * t99) * t104 + ((-t121 * AA + 0.2e1 * t136 * BB) * t77 + (-t141 * AA - 0.2e1 * t143 * BB) * t85 + (0.2e1 * t136 * AA + t121 * BB) * t93 + (0.2e1 * t143 * AA - t141 * BB) * t99) * t160; 334 335 t1 = Rm * Rm; 336 t2 = Rp * Rp; 337 t3 = t1 * t2; 338 t4 = B * B; 339 t5 = t1 * t4; 340 t9 = exp(-0.4e1 * Rp); 341 t15 = cos(0.2e1 * Rm); 342 t22 = exp(-0.2e1 * Rp); 343 den1 = (-0.4e1 * t3 + 0.4e1 * t5) * t9 + ((0.8e1 * t1 + 0.8e1 * t4) * t2 * t15 - 0.8e1 * t5 - 0.8e1 * t2 * t4) * t22 - 0.4e1 * t3 + 0.4e1 * t5; 344 345 _C1 = num1 / den1; 346 _C2 = num2 / den1; 347 _C3 = num3 / den1; 348 _C4 = num4 / den1; 349 350 /*******************************************/ 351 /* calculate solution */ 352 /*******************************************/ 353 t1 = Rm * x; 354 t2 = cos(t1); 355 t4 = sin(t1); 356 t10 = exp(-0.2e1 * x * B); 357 t12 = kn * x; 358 t13 = cos(t12); 359 t16 = sin(t12); 360 *vx = -km * (_C1 * t2 + _C2 * t4 + _C3 * t2 + _C4 * t4 + t10 * AA * t13 + t10 * BB * t16); 361 362 t2 = Rm * x; 363 t3 = cos(t2); 364 t6 = sin(t2); 365 t22 = exp(-0.2e1 * x * B); 366 t23 = B * t22; 367 t24 = kn * x; 368 t25 = cos(t24); 369 t29 = sin(t24); 370 *vz = UU * _C1 * t3 + UU * _C2 * t6 - _C1 * t6 * Rm + _C2 * t3 * Rm - VV * _C3 * t3 - VV * _C4 * t6 - _C3 * t6 * Rm + _C4 * t3 * Rm - 0.2e1 * t23 * AA * t25 - 0.2e1 * t23 * BB * t29 - t22 * AA * t29 * kn + t22 * BB * t25 * kn; 371 372 t3 = exp(0.2e1 * x * B); 373 t4 = t3 * B; 374 t8 = km * km; 375 t9 = t3 * t8; 376 t11 = 0.3e1 * t9 * Rm; 377 t12 = Rm * Rm; 378 t14 = t3 * t12 * Rm; 379 t15 = UU * UU; 380 t19 = 0.4e1 * t4 * UU * Rm - t11 - t14 + 0.3e1 * t3 * t15 * Rm; 381 t20 = Rm * x; 382 t21 = sin(t20); 383 t26 = 0.2e1 * t9 * B; 384 t33 = 0.2e1 * t4 * t12; 385 t36 = -t3 * t15 * UU - t26 + 0.3e1 * t9 * UU + 0.3e1 * t3 * UU * t12 + t33 - 0.2e1 * t4 * t15; 386 t37 = cos(t20); 387 t46 = VV * VV; 388 t53 = -t11 - t14 + 0.3e1 * t3 * t46 * Rm - 0.4e1 * t4 * VV * Rm; 389 t64 = -t26 + t33 + t3 * t46 * VV - 0.3e1 * t9 * VV - 0.2e1 * t4 * t46 - 0.3e1 * t3 * VV * t12; 390 t73 = kn * kn; 391 t74 = t73 * kn; 392 t79 = B * B; 393 t86 = B * t8; 394 t90 = kn * x; 395 t91 = sin(t90); 396 t106 = cos(t90); 397 *sxx = -((t19 * t21 + t36 * t37) * _C1 + (t36 * t21 - t19 * t37) * _C2 + (t53 * t21 + t64 * t37) * _C3 + (t64 * t21 - t53 * t37) * _C4 + (-AA * t74 - 0.4e1 * BB * t73 * B + 0.4e1 * t79 * AA * kn - 0.3e1 * t8 * AA * kn - 0.8e1 * t86 * BB) * t91 + (-0.8e1 * t86 * AA - 0.4e1 * AA * t73 * B - 0.4e1 * t79 * BB * kn + 0.3e1 * t8 * BB * kn + BB * t74) * t106) / km; 398 399 t3 = exp(0.2e1 * x * B); 400 t4 = km * km; 401 t5 = t3 * t4; 402 t6 = Rm * x; 403 t7 = cos(t6); 404 t8 = _C1 * t7; 405 t10 = sin(t6); 406 t11 = _C2 * t10; 407 t13 = _C3 * t7; 408 t15 = _C4 * t10; 409 t18 = kn * x; 410 t19 = cos(t18); 411 t22 = sin(t18); 412 t24 = UU * UU; 413 t25 = t3 * t24; 414 t28 = t3 * UU; 415 t38 = Rm * Rm; 416 t39 = t7 * t38; 417 t42 = t10 * t38; 418 t44 = t5 * t8 + t5 * t11 + t5 * t13 + t5 * t15 + t4 * AA * t19 + t4 * BB * t22 + t25 * t8 + t25 * t11 - 0.2e1 * t28 * _C1 * t10 * Rm + 0.2e1 * t28 * _C2 * t7 * Rm - t3 * _C1 * t39 - t3 * _C2 * t42; 419 t45 = VV * VV; 420 t46 = t3 * t45; 421 t49 = t3 * VV; 422 t62 = B * B; 423 t78 = kn * kn; 424 t82 = t46 * t13 + t46 * t15 + 0.2e1 * t49 * _C3 * t10 * Rm - 0.2e1 * t49 * _C4 * t7 * Rm - t3 * _C3 * t39 - t3 * _C4 * t42 + 0.4e1 * t62 * AA * t19 + 0.4e1 * t62 * BB * t22 + 0.4e1 * B * AA * t22 * kn - 0.4e1 * B * BB * t19 * kn - AA * t19 * t78 - BB * t22 * t78; 425 *sxz = t44 + t82; 426 427 t3 = exp(0.2e1 * x * B); 428 t4 = t3 * B; 429 t8 = km * km; 430 t9 = t3 * t8; 431 t10 = t9 * Rm; 432 t11 = Rm * Rm; 433 t13 = t3 * t11 * Rm; 434 t14 = UU * UU; 435 t18 = 0.4e1 * t4 * UU * Rm - t10 - t13 + 0.3e1 * t3 * t14 * Rm; 436 t19 = Rm * x; 437 t20 = sin(t19); 438 t25 = 0.2e1 * t9 * B; 439 t31 = 0.2e1 * t4 * t11; 440 t34 = -t3 * t14 * UU - t25 + t9 * UU + 0.3e1 * t3 * UU * t11 + t31 - 0.2e1 * t4 * t14; 441 t35 = cos(t19); 442 t44 = VV * VV; 443 t51 = -t10 - t13 + 0.3e1 * t3 * t44 * Rm - 0.4e1 * t4 * VV * Rm; 444 t61 = -t25 + t31 + t3 * t44 * VV - t9 * VV - 0.2e1 * t4 * t44 - 0.3e1 * t3 * VV * t11; 445 t70 = kn * kn; 446 t71 = t70 * kn; 447 t76 = B * B; 448 t82 = B * t8; 449 t86 = kn * x; 450 t87 = sin(t86); 451 t101 = cos(t86); 452 *p = ((t18 * t20 + t34 * t35) * _C1 + (t34 * t20 - t18 * t35) * _C2 + (t51 * t20 + t61 * t35) * _C3 + (t61 * t20 - t51 * t35) * _C4 + (-AA * t71 - 0.4e1 * BB * t70 * B + 0.4e1 * t76 * AA * kn - t8 * AA * kn - 0.4e1 * t82 * BB) * t87 + (-0.4e1 * t82 * AA - 0.4e1 * AA * t70 * B - 0.4e1 * t76 * BB * kn + t8 * BB * kn + BB * t71) * t101) / km; 453 454 t3 = exp(0.2e1 * x * B); 455 t4 = UU * UU; 456 t8 = km * km; 457 t9 = t3 * t8; 458 t10 = t9 * Rm; 459 t11 = Rm * Rm; 460 t13 = t3 * t11 * Rm; 461 t14 = t3 * B; 462 t18 = 0.3e1 * t3 * t4 * Rm + t10 - t13 + 0.4e1 * t14 * UU * Rm; 463 t19 = Rm * x; 464 t20 = sin(t19); 465 t23 = 0.2e1 * t9 * B; 466 t33 = 0.2e1 * t14 * t11; 467 t34 = -t23 + 0.3e1 * t3 * UU * t11 - t9 * UU - t3 * t4 * UU - 0.2e1 * t4 * t14 + t33; 468 t35 = cos(t19); 469 t47 = VV * VV; 470 t51 = t10 - 0.4e1 * t14 * VV * Rm + 0.3e1 * t3 * t47 * Rm - t13; 471 t61 = t9 * VV - t23 + t3 * t47 * VV - 0.2e1 * t14 * t47 + t33 - 0.3e1 * t3 * VV * t11; 472 t70 = B * B; 473 t74 = kn * kn; 474 t75 = t74 * kn; 475 t83 = kn * x; 476 t84 = sin(t83); 477 t96 = cos(t83); 478 *szz = -((t18 * t20 + t34 * t35) * _C1 + (t34 * t20 - t18 * t35) * _C2 + (t51 * t20 + t61 * t35) * _C3 + (t61 * t20 - t51 * t35) * _C4 + (0.4e1 * t70 * AA * kn - AA * t75 - 0.4e1 * BB * t74 * B + t8 * AA * kn) * t84 + (-t8 * BB * kn - 0.4e1 * AA * t74 * B - 0.4e1 * t70 * BB * kn + BB * t75) * t96) / km; 479 480 /* vx = Vx, vz = Vz, sxx = xx-component of stress tensor, sxz = xz-component of stress tensor, p = pressure, szz = zz-component of stress tensor */ 481 *vx *= cos(km * z); /* Vx */ 482 *vz *= sin(km * z); /* Vz */ 483 *p *= cos(km * z); /* p */ 484 *sxx *= cos(km * z); /* sxx total stress */ 485 *sxz *= sin(km * z); /* tzx stress */ 486 *szz *= cos(km * z); /* szz total stress */ 487 488 /* rho = -sigma*sin(km*z)*cos(kn*x); */ /* density */ 489 PetscFunctionReturn(0); 490 } 491 492 PetscErrorCode SolKxWrapperV(PetscInt dim, const PetscReal x[], PetscInt Nf, PetscScalar v[], void *ctx) 493 { 494 PetscReal B = 100.0; 495 PetscReal kn = 100 * M_PI; 496 PetscReal km = 100 * M_PI; 497 PetscScalar p, sxx, sxz, szz; 498 499 PetscFunctionBeginUser; 500 SolKxSolution(x[0], x[1], kn, km, B, &v[0], &v[1], &p, &sxx, &sxz, &szz); 501 PetscFunctionReturn(0); 502 } 503 504 PetscErrorCode SolKxWrapperP(PetscInt dim, const PetscReal x[], PetscInt Nf, PetscScalar v[], void *ctx) 505 { 506 PetscReal B = 100.0; 507 PetscReal kn = 100 * M_PI; 508 PetscReal km = 100 * M_PI; 509 PetscScalar vx, vz, sxx, sxz, szz; 510 511 PetscFunctionBeginUser; 512 SolKxSolution(x[0], x[1], kn, km, B, &vx, &vz, &v[0], &sxx, &sxz, &szz); 513 PetscFunctionReturn(0); 514 } 515 516 /* 517 Compare the C implementation with generated data from Maple 518 */ 519 PetscErrorCode MapleTest(MPI_Comm comm, AppCtx *ctx) 520 { 521 const PetscInt n = 41; 522 PetscScalar vxMaple[41][41], vzMaple[41][41], pMaple[41][41], sxxMaple[41][41], sxzMaple[41][41], szzMaple[41][41]; 523 PetscReal x[41], z[41]; 524 PetscReal kn, km, B; 525 PetscInt i, j; 526 527 PetscFunctionBegin; 528 PetscCall(SolKxData5(x, z, &kn, &km, &B, vxMaple, vzMaple, pMaple, sxxMaple, sxzMaple, szzMaple)); 529 for (i = 0; i < n; ++i) { 530 for (j = 0; j < n; ++j) { 531 PetscScalar vx, vz, p, sxx, sxz, szz; 532 PetscReal norm; 533 534 PetscCall(SolKxSolution(x[i], z[j], kn, km, B, &vx, &vz, &p, &sxx, &sxz, &szz)); 535 norm = PetscSqrt(PetscSqr(PetscAbsScalar(vx - vxMaple[i][j])) + PetscSqr(PetscAbsScalar(vz - vzMaple[i][j]))); 536 PetscCheck(norm > -1.0e-10, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Invalid solution, %0.17e %0.17e %0.17e %0.17e %0.17e %0.17e %0.17e %0.17e %0.17e\n", (double)x[i], (double)z[j], (double)PetscAbsScalar(vx - vxMaple[i][j]), (double)PetscAbsScalar(vz - vzMaple[i][j]), (double)PetscAbsScalar(p - pMaple[i][j]), (double)PetscAbsScalar(sxx - sxxMaple[i][j]), (double)PetscAbsScalar(sxz - sxzMaple[i][j]), (double)PetscAbsScalar(szz - szzMaple[i][j]), (double)norm); 537 } 538 } 539 } 540 PetscCall(PetscPrintf(comm, "Verified Maple test 5\n")); 541 PetscFunctionReturn(0); 542 } 543 544 PetscErrorCode FEMTest(MPI_Comm comm, AppCtx *ctx) 545 { 546 DM dm; 547 Vec u; 548 PetscErrorCode (*funcs[2])(PetscInt, const PetscReal[], PetscInt, PetscScalar *, void *) = {SolKxWrapperV, SolKxWrapperP}; 549 PetscReal discError; 550 551 PetscFunctionBegin; 552 if (!ctx->fem) PetscFunctionReturn(0); 553 /* Create DM */ 554 PetscCall(DMPlexCreateBoxMesh(comm, 2, PETSC_TRUE, NULL, NULL, NULL, NULL, PETSC_FALSE, &dm)); 555 PetscCall(DMSetFromOptions(dm)); 556 /* Project solution into FE space */ 557 PetscCall(DMGetGlobalVector(dm, &u)); 558 PetscCall(DMProjectFunction(dm, 0.0, funcs, NULL, INSERT_VALUES, u)); 559 PetscCall(DMComputeL2Diff(dm, 0.0, funcs, NULL, u, &discError)); 560 PetscCall(VecViewFromOptions(u, NULL, "-vec_view")); 561 /* Cleanup */ 562 PetscCall(DMRestoreGlobalVector(dm, &u)); 563 PetscCall(DMDestroy(&dm)); 564 PetscFunctionReturn(0); 565 } 566 567 int main(int argc, char **argv) 568 { 569 AppCtx user; /* user-defined work context */ 570 571 PetscFunctionBeginUser; 572 PetscCall(PetscInitialize(&argc, &argv, NULL, help)); 573 PetscCall(ProcessOptions(PETSC_COMM_WORLD, &user)); 574 PetscCall(MapleTest(PETSC_COMM_WORLD, &user)); 575 PetscCall(FEMTest(PETSC_COMM_WORLD, &user)); 576 PetscCall(PetscFinalize()); 577 return 0; 578 } 579