1## libCEED: Navier-Stokes Example 2 3This page provides a description of the Navier-Stokes example for the libCEED library, based on PETSc. 4PETSc v3.17 or a development version of PETSc at commit 0e95d842 or later is required. 5 6The Navier-Stokes problem solves the compressible Navier-Stokes equations in three dimensions using an explicit time integration. 7The state variables are mass density, momentum density, and energy density. 8 9The main Navier-Stokes solver for libCEED is defined in [`navierstokes.c`](navierstokes.c) with different problem definitions according to the application of interest. 10 11Build by using: 12 13`make` 14 15and run with: 16 17``` 18./navierstokes -ceed [ceed] -problem [problem type] -degree [degree] 19``` 20 21## Runtime options 22 23% inclusion-fluids-marker 24 25The Navier-Stokes mini-app is controlled via command-line options. 26The following options are common among all problem types: 27 28:::{list-table} Common Runtime Options 29:header-rows: 1 30 31* - Option 32 - Description 33 - Default value 34 35* - `-ceed` 36 - CEED resource specifier 37 - `/cpu/self/opt/blocked` 38 39* - `-test` 40 - Run in test mode 41 - `false` 42 43* - `-compare_final_state_atol` 44 - Test absolute tolerance 45 - `1E-11` 46 47* - `-compare_final_state_filename` 48 - Test filename 49 - 50 51* - `-problem` 52 - Problem to solve (`advection`, `advection2d`, `density_current`, or `euler_vortex`) 53 - `density_current` 54 55* - `-implicit` 56 - Use implicit time integartor formulation 57 - 58 59* - `-degree` 60 - Polynomial degree of tensor product basis (must be >= 1) 61 - `1` 62 63* - `-q_extra` 64 - Number of extra quadrature points 65 - `2` 66 67* - `-viz_refine` 68 - Use regular refinement for visualization 69 - `0` 70 71* - `-output_freq` 72 - Frequency of output, in number of steps. `0` has no output, `-1` outputs final state only 73 - `10` 74 75* - `-continue` 76 - Continue from previous solution 77 - `0` 78 79* - `-output_dir` 80 - Output directory 81 - `.` 82 83* - `-bc_wall` 84 - Use wall boundary conditions on this list of faces 85 - 86 87* - `-wall_comps` 88 - An array of constrained component numbers for wall BCs 89 - 90 91* - `-bc_slip_x` 92 - Use slip boundary conditions, for the x component, on this list of faces 93 - 94 95* - `-bc_slip_y` 96 - Use slip boundary conditions, for the y component, on this list of faces 97 - 98 99* - `-bc_slip_z` 100 - Use slip boundary conditions, for the z component, on this list of faces 101 - 102 103* - `-bc_inflow` 104 - Use inflow boundary conditions on this list of faces 105 - 106 107* - `-bc_outflow` 108 - Use outflow boundary conditions on this list of faces 109 - 110 111* - `-snes_view` 112 - View PETSc `SNES` nonlinear solver configuration 113 - 114 115* - `-log_view` 116 - View PETSc performance log 117 - 118 119* - `-help` 120 - View comprehensive information about run-time options 121 - 122::: 123 124For the case of a square/cubic mesh, the list of face indices to be used with `-bc_wall`, `bc_inflow`, `bc_outflow` and/or `-bc_slip_x`, `-bc_slip_y`, and `-bc_slip_z` are: 125 126:::{list-table} 2D Face ID Labels 127:header-rows: 1 128* - PETSc Face Name 129 - Cartesian direction 130 - Face ID 131 132* - faceMarkerBottom 133 - -z 134 - 1 135 136* - faceMarkerRight 137 - +x 138 - 2 139 140* - faceMarkerTop 141 - +z 142 - 3 143 144* - faceMarkerLeft 145 - -x 146 - 4 147::: 148 149:::{list-table} 2D Face ID Labels 150:header-rows: 1 151* - PETSc Face Name 152 - Cartesian direction 153 - Face ID 154 155* - faceMarkerBottom 156 - -z 157 - 1 158 159* - faceMarkerTop 160 - +z 161 - 2 162 163* - faceMarkerFront 164 - -y 165 - 3 166 167* - faceMarkerBack 168 - +y 169 - 4 170 171* - faceMarkerRight 172 - +x 173 - 5 174 175* - faceMarkerLeft 176 - -x 177 - 6 178::: 179 180### Advection 181 182For testing purposes, there is a reduced mode for pure advection, which holds density $\rho$ and momentum density $\rho \bm u$ constant while advecting "total energy density" $E$. 183These are available in 2D and 3D. 184 185#### 2D advection 186 187For the 2D advection problem, the following additional command-line options are available: 188 189:::{list-table} Advection2D Runtime Options 190:header-rows: 1 191 192* - Option 193 - Description 194 - Default value 195 - Unit 196 197* - `-rc` 198 - Characteristic radius of thermal bubble 199 - `1000` 200 - `m` 201 202* - `-units_meter` 203 - 1 meter in scaled length units 204 - `1E-2` 205 - 206 207* - `-units_second` 208 - 1 second in scaled time units 209 - `1E-2` 210 - 211 212* - `-units_kilogram` 213 - 1 kilogram in scaled mass units 214 - `1E-6` 215 - 216 217* - `-strong_form` 218 - Strong (1) or weak/integrated by parts (0) residual 219 - `0` 220 - 221 222* - `-stab` 223 - Stabilization method (`none`, `su`, or `supg`) 224 - `none` 225 - 226 227* - `-CtauS` 228 - Scale coefficient for stabilization tau (nondimensional) 229 - `0` 230 - 231 232* - `-wind_type` 233 - Wind type in Advection (`rotation` or `translation`) 234 - `rotation` 235 - 236 237* - `-wind_translation` 238 - Constant wind vector when `-wind_type translation` 239 - `1,0,0` 240 - 241 242* - `-E_wind` 243 - Total energy of inflow wind when `-wind_type translation` 244 - `1E6` 245 - `J` 246::: 247 248An example of the `rotation` mode can be run with: 249 250``` 251./navierstokes -problem advection2d -dm_plex_box_faces 20,20 -dm_plex_box_lower 0,0 -dm_plex_box_upper 1000,1000 -bc_wall 1,2,3,4 -wall_comps 4 -wind_type rotation -implicit -stab supg 252``` 253 254and the `translation` mode with: 255 256``` 257./navierstokes -problem advection2d -dm_plex_box_faces 20,20 -dm_plex_box_lower 0,0 -dm_plex_box_upper 1000,1000 -units_meter 1e-4 -wind_type translation -wind_translation 1,-.5 -bc_inflow 1,2,3,4 258``` 259Note the lengths in `-dm_plex_box_upper` are given in meters, and will be nondimensionalized according to `-units_meter`. 260 261#### 3D advection 262 263For the 3D advection problem, the following additional command-line options are available: 264 265:::{list-table} Advection3D Runtime Options 266:header-rows: 1 267 268* - Option 269 - Description 270 - Default value 271 - Unit 272 273* - `-rc` 274 - Characteristic radius of thermal bubble 275 - `1000` 276 - `m` 277 278* - `-units_meter` 279 - 1 meter in scaled length units 280 - `1E-2` 281 - 282 283* - `-units_second` 284 - 1 second in scaled time units 285 - `1E-2` 286 - 287 288* - `-units_kilogram` 289 - 1 kilogram in scaled mass units 290 - `1E-6` 291 - 292 293* - `-strong_form` 294 - Strong (1) or weak/integrated by parts (0) residual 295 - `0` 296 - 297 298* - `-stab` 299 - Stabilization method (`none`, `su`, or `supg`) 300 - `none` 301 - 302 303* - `-CtauS` 304 - Scale coefficient for stabilization tau (nondimensional) 305 - `0` 306 - 307 308* - `-wind_type` 309 - Wind type in Advection (`rotation` or `translation`) 310 - `rotation` 311 - 312 313* - `-wind_translation` 314 - Constant wind vector when `-wind_type translation` 315 - `1,0,0` 316 - 317 318* - `-E_wind` 319 - Total energy of inflow wind when `-wind_type translation` 320 - `1E6` 321 - `J` 322 323* - `-bubble_type` 324 - `sphere` (3D) or `cylinder` (2D) 325 - `shpere` 326 - 327 328* - `-bubble_continuity` 329 - `smooth`, `back_sharp`, or `thick` 330 - `smooth` 331 - 332::: 333 334An example of the `rotation` mode can be run with: 335 336``` 337./navierstokes -problem advection -dm_plex_box_faces 10,10,10 -dm_plex_dim 3 -dm_plex_box_lower 0,0,0 -dm_plex_box_upper 8000,8000,8000 -bc_wall 1,2,3,4,5,6 -wall_comps 4 -wind_type rotation -implicit -stab su 338``` 339 340and the `translation` mode with: 341 342``` 343./navierstokes -problem advection -dm_plex_box_faces 10,10,10 -dm_plex_dim 3 -dm_plex_box_lower 0,0,0 -dm_plex_box_upper 8000,8000,8000 -wind_type translation -wind_translation .5,-1,0 -bc_inflow 1,2,3,4,5,6 344``` 345 346### Inviscid Ideal Gas 347 348#### Isentropic Euler vortex 349 350For the Isentropic Vortex problem, the following additional command-line options are available: 351 352:::{list-table} Isentropic Vortex Runtime Options 353:header-rows: 1 354 355* - Option 356 - Description 357 - Default value 358 - Unit 359 360* - `-center` 361 - Location of vortex center 362 - `(lx,ly,lz)/2` 363 - `(m,m,m)` 364 365* - `-units_meter` 366 - 1 meter in scaled length units 367 - `1E-2` 368 - 369 370* - `-units_second` 371 - 1 second in scaled time units 372 - `1E-2` 373 - 374 375* - `-mean_velocity` 376 - Background velocity vector 377 - `(1,1,0)` 378 - 379 380* - `-vortex_strength` 381 - Strength of vortex < 10 382 - `5` 383 - 384 385* - `-c_tau` 386 - Stabilization constant 387 - `0.5` 388 - 389::: 390 391This problem can be run with: 392 393``` 394./navierstokes -problem euler_vortex -dm_plex_box_faces 20,20,1 -dm_plex_box_lower 0,0,0 -dm_plex_box_upper 1000,1000,50 -dm_plex_dim 3 -bc_inflow 4,6 -bc_outflow 3,5 -bc_slip_z 1,2 -mean_velocity .5,-.8,0. 395``` 396 397#### Sod shock tube 398 399For the Shock Tube problem, the following additional command-line options are available: 400 401:::{list-table} Shock Tube Runtime Options 402:header-rows: 1 403 404* - Option 405 - Description 406 - Default value 407 - Unit 408 409* - `-units_meter` 410 - 1 meter in scaled length units 411 - `1E-2` 412 - 413 414* - `-units_second` 415 - 1 second in scaled time units 416 - `1E-2` 417 - 418 419* - `-yzb` 420 - Use YZB discontinuity capturing 421 - `none` 422 - 423 424* - `-stab` 425 - Stabilization method (`none`, `su`, or `supg`) 426 - `none` 427 - 428::: 429 430This problem can be run with: 431 432``` 433./navierstokes -problem shocktube -yzb -stab su -bc_slip_z 3,4 -bc_slip_y 1,2 -bc_wall 5,6 -dm_plex_dim 3 -dm_plex_box_lower 0,0,0 -dm_plex_box_upper 1000,100,100 -dm_plex_box_faces 200,1,1 -units_second 0.1 434``` 435 436### Newtonian viscosity, Ideal Gas 437 438For the Density Current, Channel, and Blasius problems, the following common command-line options are available: 439 440:::{list-table} Newtonian Ideal Gas problems Runtime Options 441:header-rows: 1 442 443* - Option 444 - Description 445 - Default value 446 - Unit 447 448* - `-units_meter` 449 - 1 meter in scaled length units 450 - `1` 451 - 452 453* - `-units_second` 454 - 1 second in scaled time units 455 - `1` 456 - 457 458* - `-units_kilogram` 459 - 1 kilogram in scaled mass units 460 - `1` 461 - 462 463* - `-units_Kelvin` 464 - 1 Kelvin in scaled temperature units 465 - `1` 466 - 467 468* - `-stab` 469 - Stabilization method (`none`, `su`, or `supg`) 470 - `none` 471 - 472 473* - `-c_tau` 474 - Stabilization constant, $c_\tau$ 475 - `0.5` 476 - 477 478* - `-Ctau_t` 479 - Stabilization time constant, $C_t$ 480 - `1.0` 481 - 482 483* - `-Ctau_v` 484 - Stabilization viscous constant, $C_v$ 485 - `36.0` 486 - 487 488* - `-Ctau_C` 489 - Stabilization continuity constant, $C_c$ 490 - `1.0` 491 - 492 493* - `-Ctau_M` 494 - Stabilization momentum constant, $C_m$ 495 - `1.0` 496 - 497 498* - `-Ctau_E` 499 - Stabilization energy constant, $C_E$ 500 - `1.0` 501 - 502 503* - `-cv` 504 - Heat capacity at constant volume 505 - `717` 506 - `J/(kg K)` 507 508* - `-cp` 509 - Heat capacity at constant pressure 510 - `1004` 511 - `J/(kg K)` 512 513* - `-g` 514 - Gravitational acceleration 515 - `9.81` 516 - `m/s^2` 517 518* - `-lambda` 519 - Stokes hypothesis second viscosity coefficient 520 - `-2/3` 521 - 522 523* - `-mu` 524 - Shear dynamic viscosity coefficient 525 - `75` 526 - `Pa s` 527 528* - `-k` 529 - Thermal conductivity 530 - `0.02638` 531 - `W/(m K)` 532 533* - `-newtonian_unit_tests` 534 - Developer option to test properties 535 - `false` 536 - boolean 537 538* - `-primitive` 539 - Use primitive variables (pressure, velocity, temperature) instead of conservative variables (density, momentum, total energy) 540 - `false` 541 - boolean 542::: 543 544 545#### Density current 546 547The Density Current problem the following command-line options are available in addition to the Newtonian Ideal Gas options: 548 549:::{list-table} Density Current Runtime Options 550:header-rows: 1 551 552* - Option 553 - Description 554 - Default value 555 - Unit 556 557* - `-center` 558 - Location of bubble center 559 - `(lx,ly,lz)/2` 560 - `(m,m,m)` 561 562* - `-dc_axis` 563 - Axis of density current cylindrical anomaly, or `(0,0,0)` for spherically symmetric 564 - `(0,0,0)` 565 - 566 567* - `-rc` 568 - Characteristic radius of thermal bubble 569 - `1000` 570 - `m` 571 572* - `-theta0` 573 - Reference potential temperature 574 - `300` 575 - `K` 576 577* - `-thetaC` 578 - Perturbation of potential temperature 579 - `-15` 580 - `K` 581 582* - `-P0` 583 - Atmospheric pressure 584 - `1E5` 585 - `Pa` 586 587* - `-N` 588 - Brunt-Vaisala frequency 589 - `0.01` 590 - `1/s` 591::: 592 593This problem can be run with: 594 595``` 596./navierstokes -problem density_current -dm_plex_box_faces 16,1,8 -degree 1 -dm_plex_box_lower 0,0,0 -dm_plex_box_upper 2000,125,1000 -dm_plex_dim 3 -rc 400. -bc_wall 1,2,5,6 -wall_comps 1,2,3 -bc_slip_y 3,4 -mu 75 597``` 598 599#### Channel flow 600 601The Channel problem the following command-line options are available in addition to the Newtonian Ideal Gas options: 602 603:::{list-table} Channel Runtime Options 604:header-rows: 1 605 606* - Option 607 - Description 608 - Default value 609 - Unit 610 611* - `-umax` 612 - Maximum/centerline velocity of the flow 613 - `10` 614 - `m/s` 615 616* - `-theta0` 617 - Reference potential temperature 618 - `300` 619 - `K` 620 621* - `-P0` 622 - Atmospheric pressure 623 - `1E5` 624 - `Pa` 625 626* - `-body_force_scale` 627 - Multiplier for body force (`-1` for flow reversal) 628 - 1 629 - 630::: 631 632This problem can be run with the `channel.yaml` file via: 633 634``` 635./navierstokes -options_file channel.yaml 636``` 637```{literalinclude} ../../../../../examples/fluids/channel.yaml 638:language: yaml 639``` 640 641#### Blasius boundary layer 642 643The Blasius problem the following command-line options are available in addition to the Newtonian Ideal Gas options: 644 645:::{list-table} Blasius Runtime Options 646:header-rows: 1 647 648* - Option 649 - Description 650 - Default value 651 - Unit 652 653* - `-Uinf` 654 - Freestream velocity 655 - `40` 656 - `m/s` 657 658* - `-delta0` 659 - Boundary layer height at the inflow 660 - `4.2e-4` 661 - `m` 662 663* - `-theta0` 664 - Reference potential temperature 665 - `288` 666 - `K` 667 668* - `-P0` 669 - Atmospheric pressure 670 - `1.01E5` 671 - `Pa` 672 673* - `-platemesh_refine_height` 674 - Height at which `-platemesh_Ndelta` number of elements should refined into 675 - `5.9E-4` 676 - `m` 677 678* - `-platemesh_Ndelta` 679 - Number of elements to keep below `-platemesh_refine_height` 680 - `45` 681 - 682 683* - `-platemesh_growth` 684 - Growth rate of the elements in the refinement region 685 - `1.08` 686 - 687 688* - `-platemesh_top_angle` 689 - Downward angle of the top face of the domain. This face serves as an outlet. 690 - `5` 691 - `degrees` 692 693* - `-stg_use` 694 - Whether to use stg for the inflow conditions 695 - `false` 696 - 697 698* - `-platemesh_y_node_locs_path` 699 - Path to file with y node locations. If empty, will use mesh warping instead. 700 - `""` 701 - 702::: 703 704This problem can be run with the `blasius.yaml` file via: 705 706``` 707./navierstokes -options_file blasius.yaml 708``` 709 710```{literalinclude} ../../../../../examples/fluids/blasius.yaml 711:language: yaml 712``` 713 714#### STG Inflow for Flat Plate 715 716Using the STG Inflow for the blasius problem adds the following command-line options: 717 718:::{list-table} Blasius Runtime Options 719:header-rows: 1 720 721* - Option 722 - Description 723 - Default value 724 - Unit 725 726* - `-stg_inflow_path` 727 - Path to the STGInflow file 728 - `./STGInflow.dat` 729 - 730 731* - `-stg_rand_path` 732 - Path to the STGRand file 733 - `./STGRand.dat` 734 - 735 736* - `-stg_alpha` 737 - Growth rate of the wavemodes 738 - `1.01` 739 - 740 741* - `-stg_u0` 742 - Convective velocity, $U_0$ 743 - `0.0` 744 - `m/s` 745 746* - `-stg_mean_only` 747 - Only impose the mean velocity (no fluctutations) 748 - `false` 749 - 750 751* - `-stg_strong` 752 - Strongly enforce the STG inflow boundary condition 753 - `false` 754 - 755 756::: 757 758This problem can be run with the `blasius.yaml` file via: 759 760``` 761./navierstokes -options_file blasius.yaml -stg_use true 762``` 763 764Note the added `-stg_use true` flag 765This overrides the `stg: use: false` setting in the `blasius.yaml` file, enabling the use of the STG inflow. 766