19 August 2018 02:18:58 PM FEM2D_NAVIER_STOKES C++ version: Compiled on Aug 19 2018 at 14:18:58. Finite element solution of the steady incompressible Navier Stokes equations on a triangulated region in 2 dimensions.' - nu * ( Uxx + Uyy ) + UUx + VUy + dPdx = F1(x,y) - nu * ( Vxx + Vyy ) + UVx + VVy + dPdy = F2(x,y) Ux + Vy = F3(x,y). Boundary conditions may be of Dirichlet type: U(x,y) = U_BC(x,y) V(x,y) = V_BC(x,y) P(x,y) = P_BC(x,y) or of Neumann type with zero right hand side: dU/dn(x,y) = 0 dV/dn(x,y) = 0 dP/dn(x,y) = 0 The finite element method uses Taylor-Hood triangular elements which are linear for pressure and quadratic for velocity. Maximum number of Newton iterations IT_MAX = 5 Quadrature order = 7 The kinematic viscosity NU = 1 Current status: * testing zero Neumann condition option. Node file is "nodes6.txt". Element file is "triangles6.txt". Number of nodes = 289 First 10 nodes Row: 1 2 Col 1 0 0 2 0 0.0625 3 0 0.125 4 0 0.1875 5 0 0.25 6 0 0.3125 7 0 0.375 8 0 0.4375 9 0 0.5 10 0 0.5625 Element order = 6 Number of elements = 128 First 10 elements Row: 1 2 3 4 5 6 Col 1 1 3 37 2 20 19 2 1 37 35 19 36 18 3 3 5 39 4 22 21 4 3 39 37 21 38 20 5 5 7 41 6 24 23 6 5 41 39 23 40 22 7 7 9 43 8 26 25 8 7 43 41 25 42 24 9 9 11 45 10 28 27 10 9 45 43 27 44 26 Dirichlet boundary condition on pressure will be applied at node 1 Number of Neumann conditions added = 0 Boundary conditions per node: Node U_cond V_cond P_cond 0 2 2 2 1 2 2 0 2 2 2 1 3 2 2 0 4 2 2 1 5 2 2 0 6 2 2 1 7 2 2 0 8 2 2 1 9 2 2 0 10 2 2 1 11 2 2 0 12 2 2 1 13 2 2 0 14 2 2 1 15 2 2 0 16 2 2 1 17 2 2 0 18 1 1 0 19 1 1 0 20 1 1 0 21 1 1 0 22 1 1 0 23 1 1 0 24 1 1 0 25 1 1 0 26 1 1 0 27 1 1 0 28 1 1 0 29 1 1 0 30 1 1 0 31 1 1 0 32 1 1 0 33 2 2 0 34 2 2 1 35 1 1 0 36 1 1 1 37 1 1 0 38 1 1 1 39 1 1 0 40 1 1 1 41 1 1 0 42 1 1 1 43 1 1 0 44 1 1 1 45 1 1 0 46 1 1 1 47 1 1 0 48 1 1 1 49 1 1 0 50 2 2 1 51 2 2 0 52 1 1 0 53 1 1 0 54 1 1 0 55 1 1 0 56 1 1 0 57 1 1 0 58 1 1 0 59 1 1 0 60 1 1 0 61 1 1 0 62 1 1 0 63 1 1 0 64 1 1 0 65 1 1 0 66 1 1 0 67 2 2 0 68 2 2 1 69 1 1 0 70 1 1 1 71 1 1 0 72 1 1 1 73 1 1 0 74 1 1 1 75 1 1 0 76 1 1 1 77 1 1 0 78 1 1 1 79 1 1 0 80 1 1 1 81 1 1 0 82 1 1 1 83 1 1 0 84 2 2 1 85 2 2 0 86 1 1 0 87 1 1 0 88 1 1 0 89 1 1 0 90 1 1 0 91 1 1 0 92 1 1 0 93 1 1 0 94 1 1 0 95 1 1 0 96 1 1 0 97 1 1 0 98 1 1 0 99 1 1 0 100 1 1 0 101 2 2 0 102 2 2 1 103 1 1 0 104 1 1 1 105 1 1 0 106 1 1 1 107 1 1 0 108 1 1 1 109 1 1 0 110 1 1 1 111 1 1 0 112 1 1 1 113 1 1 0 114 1 1 1 115 1 1 0 116 1 1 1 117 1 1 0 118 2 2 1 119 2 2 0 120 1 1 0 121 1 1 0 122 1 1 0 123 1 1 0 124 1 1 0 125 1 1 0 126 1 1 0 127 1 1 0 128 1 1 0 129 1 1 0 130 1 1 0 131 1 1 0 132 1 1 0 133 1 1 0 134 1 1 0 135 2 2 0 136 2 2 1 137 1 1 0 138 1 1 1 139 1 1 0 140 1 1 1 141 1 1 0 142 1 1 1 143 1 1 0 144 1 1 1 145 1 1 0 146 1 1 1 147 1 1 0 148 1 1 1 149 1 1 0 150 1 1 1 151 1 1 0 152 2 2 1 153 2 2 0 154 1 1 0 155 1 1 0 156 1 1 0 157 1 1 0 158 1 1 0 159 1 1 0 160 1 1 0 161 1 1 0 162 1 1 0 163 1 1 0 164 1 1 0 165 1 1 0 166 1 1 0 167 1 1 0 168 1 1 0 169 2 2 0 170 2 2 1 171 1 1 0 172 1 1 1 173 1 1 0 174 1 1 1 175 1 1 0 176 1 1 1 177 1 1 0 178 1 1 1 179 1 1 0 180 1 1 1 181 1 1 0 182 1 1 1 183 1 1 0 184 1 1 1 185 1 1 0 186 2 2 1 187 2 2 0 188 1 1 0 189 1 1 0 190 1 1 0 191 1 1 0 192 1 1 0 193 1 1 0 194 1 1 0 195 1 1 0 196 1 1 0 197 1 1 0 198 1 1 0 199 1 1 0 200 1 1 0 201 1 1 0 202 1 1 0 203 2 2 0 204 2 2 1 205 1 1 0 206 1 1 1 207 1 1 0 208 1 1 1 209 1 1 0 210 1 1 1 211 1 1 0 212 1 1 1 213 1 1 0 214 1 1 1 215 1 1 0 216 1 1 1 217 1 1 0 218 1 1 1 219 1 1 0 220 2 2 1 221 2 2 0 222 1 1 0 223 1 1 0 224 1 1 0 225 1 1 0 226 1 1 0 227 1 1 0 228 1 1 0 229 1 1 0 230 1 1 0 231 1 1 0 232 1 1 0 233 1 1 0 234 1 1 0 235 1 1 0 236 1 1 0 237 2 2 0 238 2 2 1 239 1 1 0 240 1 1 1 241 1 1 0 242 1 1 1 243 1 1 0 244 1 1 1 245 1 1 0 246 1 1 1 247 1 1 0 248 1 1 1 249 1 1 0 250 1 1 1 251 1 1 0 252 1 1 1 253 1 1 0 254 2 2 1 255 2 2 0 256 1 1 0 257 1 1 0 258 1 1 0 259 1 1 0 260 1 1 0 261 1 1 0 262 1 1 0 263 1 1 0 264 1 1 0 265 1 1 0 266 1 1 0 267 1 1 0 268 1 1 0 269 1 1 0 270 1 1 0 271 2 2 0 272 2 2 1 273 2 2 0 274 2 2 1 275 2 2 0 276 2 2 1 277 2 2 0 278 2 2 1 279 2 2 0 280 2 2 1 281 2 2 0 282 2 2 1 283 2 2 0 284 2 2 1 285 2 2 0 286 2 2 1 287 2 2 0 288 2 2 1 Total number of variables is 659 Variable indices per node: Node U_index V_index P_index 1 1 2 3 2 4 5 -1 3 6 7 8 4 9 10 -1 5 11 12 13 6 14 15 -1 7 16 17 18 8 19 20 -1 9 21 22 23 10 24 25 -1 11 26 27 28 12 29 30 -1 13 31 32 33 14 34 35 -1 15 36 37 38 16 39 40 -1 17 41 42 43 18 44 45 -1 19 46 47 -1 20 48 49 -1 21 50 51 -1 22 52 53 -1 23 54 55 -1 24 56 57 -1 25 58 59 -1 26 60 61 -1 27 62 63 -1 28 64 65 -1 29 66 67 -1 30 68 69 -1 31 70 71 -1 32 72 73 -1 33 74 75 -1 34 76 77 -1 35 78 79 80 36 81 82 -1 37 83 84 85 38 86 87 -1 39 88 89 90 40 91 92 -1 41 93 94 95 42 96 97 -1 43 98 99 100 44 101 102 -1 45 103 104 105 46 106 107 -1 47 108 109 110 48 111 112 -1 49 113 114 115 50 116 117 -1 51 118 119 120 52 121 122 -1 53 123 124 -1 54 125 126 -1 55 127 128 -1 56 129 130 -1 57 131 132 -1 58 133 134 -1 59 135 136 -1 60 137 138 -1 61 139 140 -1 62 141 142 -1 63 143 144 -1 64 145 146 -1 65 147 148 -1 66 149 150 -1 67 151 152 -1 68 153 154 -1 69 155 156 157 70 158 159 -1 71 160 161 162 72 163 164 -1 73 165 166 167 74 168 169 -1 75 170 171 172 76 173 174 -1 77 175 176 177 78 178 179 -1 79 180 181 182 80 183 184 -1 81 185 186 187 82 188 189 -1 83 190 191 192 84 193 194 -1 85 195 196 197 86 198 199 -1 87 200 201 -1 88 202 203 -1 89 204 205 -1 90 206 207 -1 91 208 209 -1 92 210 211 -1 93 212 213 -1 94 214 215 -1 95 216 217 -1 96 218 219 -1 97 220 221 -1 98 222 223 -1 99 224 225 -1 100 226 227 -1 101 228 229 -1 102 230 231 -1 103 232 233 234 104 235 236 -1 105 237 238 239 106 240 241 -1 107 242 243 244 108 245 246 -1 109 247 248 249 110 250 251 -1 111 252 253 254 112 255 256 -1 113 257 258 259 114 260 261 -1 115 262 263 264 116 265 266 -1 117 267 268 269 118 270 271 -1 119 272 273 274 120 275 276 -1 121 277 278 -1 122 279 280 -1 123 281 282 -1 124 283 284 -1 125 285 286 -1 126 287 288 -1 127 289 290 -1 128 291 292 -1 129 293 294 -1 130 295 296 -1 131 297 298 -1 132 299 300 -1 133 301 302 -1 134 303 304 -1 135 305 306 -1 136 307 308 -1 137 309 310 311 138 312 313 -1 139 314 315 316 140 317 318 -1 141 319 320 321 142 322 323 -1 143 324 325 326 144 327 328 -1 145 329 330 331 146 332 333 -1 147 334 335 336 148 337 338 -1 149 339 340 341 150 342 343 -1 151 344 345 346 152 347 348 -1 153 349 350 351 154 352 353 -1 155 354 355 -1 156 356 357 -1 157 358 359 -1 158 360 361 -1 159 362 363 -1 160 364 365 -1 161 366 367 -1 162 368 369 -1 163 370 371 -1 164 372 373 -1 165 374 375 -1 166 376 377 -1 167 378 379 -1 168 380 381 -1 169 382 383 -1 170 384 385 -1 171 386 387 388 172 389 390 -1 173 391 392 393 174 394 395 -1 175 396 397 398 176 399 400 -1 177 401 402 403 178 404 405 -1 179 406 407 408 180 409 410 -1 181 411 412 413 182 414 415 -1 183 416 417 418 184 419 420 -1 185 421 422 423 186 424 425 -1 187 426 427 428 188 429 430 -1 189 431 432 -1 190 433 434 -1 191 435 436 -1 192 437 438 -1 193 439 440 -1 194 441 442 -1 195 443 444 -1 196 445 446 -1 197 447 448 -1 198 449 450 -1 199 451 452 -1 200 453 454 -1 201 455 456 -1 202 457 458 -1 203 459 460 -1 204 461 462 -1 205 463 464 465 206 466 467 -1 207 468 469 470 208 471 472 -1 209 473 474 475 210 476 477 -1 211 478 479 480 212 481 482 -1 213 483 484 485 214 486 487 -1 215 488 489 490 216 491 492 -1 217 493 494 495 218 496 497 -1 219 498 499 500 220 501 502 -1 221 503 504 505 222 506 507 -1 223 508 509 -1 224 510 511 -1 225 512 513 -1 226 514 515 -1 227 516 517 -1 228 518 519 -1 229 520 521 -1 230 522 523 -1 231 524 525 -1 232 526 527 -1 233 528 529 -1 234 530 531 -1 235 532 533 -1 236 534 535 -1 237 536 537 -1 238 538 539 -1 239 540 541 542 240 543 544 -1 241 545 546 547 242 548 549 -1 243 550 551 552 244 553 554 -1 245 555 556 557 246 558 559 -1 247 560 561 562 248 563 564 -1 249 565 566 567 250 568 569 -1 251 570 571 572 252 573 574 -1 253 575 576 577 254 578 579 -1 255 580 581 582 256 583 584 -1 257 585 586 -1 258 587 588 -1 259 589 590 -1 260 591 592 -1 261 593 594 -1 262 595 596 -1 263 597 598 -1 264 599 600 -1 265 601 602 -1 266 603 604 -1 267 605 606 -1 268 607 608 -1 269 609 610 -1 270 611 612 -1 271 613 614 -1 272 615 616 -1 273 617 618 619 274 620 621 -1 275 622 623 624 276 625 626 -1 277 627 628 629 278 630 631 -1 279 632 633 634 280 635 636 -1 281 637 638 639 282 640 641 -1 283 642 643 644 284 645 646 -1 285 647 648 649 286 650 651 -1 287 652 653 654 288 655 656 -1 289 657 658 659 The matrix half bandwidth is 84 The matrix bandwidth is 169 The storage bandwidth is 253 Pressure nodes written to "nodes3.txt". Pressure triangles written to "triangles3.txt". l2-norm of FEM residual = 3.122 l2-norm of adjusted FEM residual = 0.0419437 l2-norm of Newton correction = 0.915287 l2-norm of FEM residual = 3.12195 l2-norm of adjusted FEM residual = 1.22747e-06 Convergence. Solution to the NAVIER STOKES Equations: Node U V P 0 0 0 0 1 0.75 -1.73908e-18 2 1 2.45583e-18 -0.480117 3 0.75 2.33499e-18 4 -1.25096e-18 7.28804e-18 -32.0424 5 -2.72564e-19 -4.72495e-18 6 6.95224e-19 5.91528e-19 -26.7908 7 2.12377e-18 -2.56323e-18 8 -2.30405e-18 2.66903e-18 -26.2344 9 4.58736e-18 3.56136e-18 10 -6.51824e-19 1.27686e-18 -26.2268 11 1.67125e-18 -9.23833e-21 12 -1.30106e-18 3.11743e-19 -25.9879 13 -9.75265e-19 -1.30035e-18 14 -1.12699e-23 -1.95158e-18 -25.7041 15 7.46478e-24 6.50521e-19 16 0 0 -25.6022 17 0 0 18 0.685197 0.0734907 19 0.900755 0.201504 20 0.65379 0.386089 21 0.196217 0.370895 22 0.0465541 0.174347 23 0.0147164 0.0997185 24 0.00781411 0.0844236 25 0.010092 0.0619767 26 0.00836806 0.0470204 27 0.00612977 0.0340412 28 0.00495591 0.0225344 29 0.0040875 0.0133356 30 0.00299828 0.00632721 31 0.00163597 0.00176277 32 2.3407e-05 2.3407e-05 33 0 0 34 -3.651e-19 4.3621e-19 -18.0438 35 0.539808 0.0962444 36 0.726517 0.251984 -17.4677 37 0.627515 0.393324 38 0.345947 0.412771 -23.4894 39 0.140141 0.288231 40 0.0681923 0.204321 -24.7498 41 0.0438637 0.166956 42 0.0352394 0.125911 -25.8811 43 0.0289724 0.0929612 44 0.0235931 0.0680523 -25.8301 45 0.0196081 0.0478211 46 0.0160003 0.0304219 -25.7446 47 0.0116508 0.0168568 48 0.00668035 0.00688454 -25.603 49 0.00177293 0.00167238 50 0 0 -25.4911 51 7.37706e-19 -1.66472e-20 52 0.387869 0.0781925 53 0.551357 0.206663 54 0.514253 0.335593 55 0.362338 0.374957 56 0.229938 0.320369 57 0.150798 0.262853 58 0.10304 0.217635 59 0.0742079 0.174069 60 0.0586549 0.132373 61 0.0491172 0.100083 62 0.0421503 0.0729218 63 0.035382 0.0483993 64 0.0268742 0.0282138 65 0.0169294 0.0125838 66 0.00666166 0.00328024 67 0 0 68 1.32613e-18 9.15002e-19 -24.2889 69 0.286301 0.0506235 70 0.422961 0.154218 -22.2533 71 0.43941 0.257243 72 0.362116 0.310444 -23.2613 73 0.266402 0.309226 74 0.197669 0.280112 -24.8773 75 0.148118 0.239929 76 0.113811 0.200649 -25.435 77 0.0937475 0.161253 78 0.0809689 0.126654 -25.5466 79 0.0710164 0.0956261 80 0.0606417 0.0656466 -25.613 81 0.0477484 0.0395156 82 0.0317946 0.0184645 -25.4658 83 0.0147839 0.0049134 84 0 0 -25.1906 85 3.21848e-18 1.24187e-18 86 0.203266 0.0335435 87 0.326088 0.108892 88 0.36214 0.196691 89 0.333672 0.252226 90 0.276981 0.274582 91 0.221197 0.268521 92 0.178181 0.243417 93 0.14728 0.214752 94 0.128232 0.181607 95 0.115688 0.148134 96 0.104429 0.115116 97 0.091376 0.0815119 98 0.0741516 0.0503133 99 0.0518751 0.0240528 100 0.0258486 0.00650708 101 0 0 102 0 -1.18149e-18 -25.4745 103 0.149029 0.0241367 104 0.249531 0.0809072 -24.3409 105 0.296389 0.150452 106 0.294294 0.203328 -24.4624 107 0.265689 0.234954 108 0.229132 0.245055 -24.948 109 0.197239 0.236198 110 0.173851 0.219701 -25.2746 111 0.158457 0.195703 112 0.148578 0.166167 -25.5686 113 0.139047 0.132957 114 0.125623 0.0969179 -25.6377 115 0.105671 0.061496 116 0.0764949 0.0301543 -25.4417 117 0.0401434 0.00830252 118 0 0 -24.9973 119 0 -4.43556e-19 120 0.110909 0.0175045 121 0.192848 0.0604949 122 0.237316 0.116967 123 0.248954 0.165554 124 0.239521 0.201373 125 0.220996 0.221443 126 0.203523 0.226084 127 0.190596 0.220658 128 0.182743 0.20593 129 0.178347 0.182459 130 0.173506 0.151332 131 0.16303 0.114148 132 0.142169 0.0746724 133 0.107122 0.037221 134 0.0580856 0.0104316 135 0 0 136 0 -1.89203e-18 -25.8853 137 0.0815695 0.0135865 138 0.145988 0.0473521 -25.2141 139 0.188129 0.092474 140 0.206552 0.13649 -25.0199 141 0.209904 0.173767 142 0.204935 0.200724 -25.1532 143 0.19893 0.215984 144 0.196455 0.220935 -25.4603 145 0.197773 0.215432 146 0.202733 0.199743 -25.7637 147 0.20694 0.172625 148 0.203285 0.135498 -25.8883 149 0.185172 0.0918279 150 0.143886 0.047052 -25.6969 151 0.0805854 0.0135292 152 0 0 -25.032 153 0 -1.07711e-18 154 0.0589637 0.0104676 155 0.108942 0.0374514 156 0.144771 0.0751841 157 0.166047 0.114963 158 0.176462 0.152351 159 0.180825 0.183451 160 0.184421 0.206604 161 0.191216 0.220825 162 0.202919 0.225624 163 0.219148 0.220374 164 0.236589 0.199993 165 0.2454 0.164238 166 0.233912 0.116042 167 0.190356 0.0600603 168 0.109761 0.0174058 169 0 0 170 0 1.30109e-18 -25.9147 171 0.0409184 0.00834574 172 0.0780682 0.0303903 -25.4653 173 0.107931 0.0620088 174 0.128333 0.0977469 -25.2684 175 0.141875 0.134052 176 0.151204 0.16737 -25.3452 177 0.160558 0.196696 178 0.17508 0.22021 -25.652 179 0.197243 0.236006 180 0.227763 0.244085 -25.9886 181 0.262944 0.233432 182 0.290467 0.201679 -26.4656 183 0.292404 0.149196 184 0.246477 0.0802938 -26.5847 185 0.147661 0.0239878 186 0 0 -25.4604 187 0 7.73437e-19 188 0.0265165 0.00657071 189 0.0531947 0.0243411 190 0.0760612 0.0509197 191 0.0937318 0.0824958 192 0.107014 0.11648 193 0.118262 0.149812 194 0.130573 0.183232 195 0.149042 0.215921 196 0.178944 0.243909 197 0.220628 0.268219 198 0.274801 0.273362 199 0.329839 0.250398 200 0.35755 0.195161 201 0.32228 0.108153 202 0.201529 0.0334019 203 0 0 204 0 6.46158e-19 -25.7229 205 0.0152947 0.00499961 206 0.0328082 0.0188089 -25.4426 207 0.0492353 0.0402393 208 0.0625366 0.0668396 -25.2961 209 0.0732204 0.0973284 210 0.0833323 0.128902 -25.3701 211 0.0961208 0.163725 212 0.115963 0.202917 -25.5131 213 0.149794 0.241725 214 0.198565 0.28142 -26.0862 215 0.265874 0.309099 216 0.359186 0.308949 -27.7118 217 0.434678 0.255833 218 0.418535 0.15345 -28.704 219 0.284318 0.0505127 220 0 0 -26.6919 221 5.0375e-20 6.65328e-19 222 0.00698981 0.00338 223 0.0176064 0.0129495 224 0.0278921 0.0289917 225 0.0367193 0.0497256 226 0.0437789 0.0748772 227 0.0509711 0.102791 228 0.0606925 0.135628 229 0.0763441 0.177529 230 0.105157 0.221236 231 0.152547 0.266814 232 0.230409 0.322755 233 0.359751 0.374726 234 0.509045 0.335303 235 0.546212 0.20676 236 0.385682 0.0782298 237 0 0 238 0 1.94796e-18 -25.4207 239 0.00192189 0.00175327 240 0.00701697 0.00718438 -25.3054 241 0.0121741 0.0175365 242 0.016718 0.0316174 -25.1657 243 0.0205006 0.0496713 244 0.0246322 0.0706884 -25.095 245 0.0301224 0.0964076 246 0.0366274 0.129927 -25.0958 247 0.0456151 0.171812 248 0.0704267 0.210715 -26.2781 249 0.141732 0.293492 250 0.343823 0.415175 -27.7347 251 0.622795 0.396126 252 0.720802 0.254131 -33.6646 253 0.537008 0.0967701 254 0 0 -33.0481 255 0 0 256 5.26045e-05 5.26045e-05 257 0.00173067 0.00191994 258 0.00315417 0.00672267 259 0.00430747 0.0140958 260 0.00524755 0.0237376 261 0.00647565 0.0358041 262 0.00872112 0.0494499 263 0.0105367 0.0651379 264 0.00859363 0.0886266 265 0.0159167 0.10657 266 0.0483273 0.181564 267 0.195614 0.377286 268 0.651223 0.393358 269 0.899347 0.204879 270 0.684817 0.0732959 271 0 0 272 0 0 -25.306 273 0 0 274 0 0 -25.1997 275 0 0 276 0 0 -24.9131 277 0 0 278 0 0 -24.6886 279 0 0 280 0 0 -24.718 281 0 0 282 0 0 -24.2433 283 0 0 284 0 0 -19.5763 285 0.75 0 286 1 0 -51.1793 287 0.75 0 288 0 0 -51.1072 Navier Stokes pressures written to "pressure3.txt". Navier Stokes velocities written to "velocity6.txt". FEM2D_NAVIER_STOKES: Normal end of execution. 19 August 2018 02:18:58 PM