1## libCEED: Navier-Stokes Example 2 3This page provides a description of the Navier-Stokes example for the libCEED library, based on PETSc. 4 5The Navier-Stokes problem solves the compressible Navier-Stokes equations in three dimensions using an explicit time integration. 6The state variables are mass density, momentum density, and energy density. 7 8The main Navier-Stokes solver for libCEED is defined in [`navierstokes.c`](navierstokes.c) with different problem definitions according to the application of interest. 9 10Build by using: 11 12`make` 13 14and run with: 15 16``` 17./navierstokes -ceed [ceed] -problem [problem type] -degree [degree] 18``` 19 20## Runtime options 21 22% inclusion-fluids-marker 23 24The Navier-Stokes mini-app is controlled via command-line options. 25The following options are common among all problem types: 26 27:::{list-table} Common Runtime Options 28:header-rows: 1 29 30* - Option 31 - Description 32 - Default value 33 34* - `-ceed` 35 - CEED resource specifier 36 - `/cpu/self/opt/blocked` 37 38* - `-test` 39 - Run in test mode 40 - `false` 41 42* - `-compare_final_state_atol` 43 - Test absolute tolerance 44 - `1E-11` 45 46* - `-compare_final_state_filename` 47 - Test filename 48 - 49 50* - `-problem` 51 - Problem to solve (`advection`, `advection2d`, `density_current`, or `euler_vortex`) 52 - `density_current` 53 54* - `-implicit` 55 - Use implicit time integartor formulation 56 - 57 58* - `-degree` 59 - Polynomial degree of tensor product basis (must be >= 1) 60 - `1` 61 62* - `-qextra` 63 - Number of extra quadrature points 64 - `2` 65 66* - `-viz_refine` 67 - Use regular refinement for visualization 68 - `0` 69 70* - `-output_freq` 71 - Frequency of output, in number of steps 72 - `10` 73 74* - `-continue` 75 - Continue from previous solution 76 - `0` 77 78* - `-output_dir` 79 - Output directory 80 - `.` 81 82* - `-dm_plex_box_faces` 83 - Number of faces in each linear direction 84 - `3,3,3` 85 86* - `-snes_view` 87 - View PETSc `SNES` nonlinear solver configuration 88 - 89 90* - `-log_view` 91 - View PETSc performance log 92 - 93 94* - `-help` 95 - View comprehensive information about run-time options 96 - 97::: 98 99For the 2D advection problem, the following additional command-line options are available: 100 101:::{list-table} Advection2D Runtime Options 102:header-rows: 1 103 104* - Option 105 - Description 106 - Default value 107 - Unit 108 109* - `-lx` 110 - Length scale in x direction 111 - `8000` 112 - `m` 113 114* - `-ly` 115 - Length scale in y direction 116 - `8000` 117 - `m` 118 119* - `-rc` 120 - Characteristic radius of thermal bubble 121 - `1000` 122 - `m` 123 124* - `-units_meter` 125 - 1 meter in scaled length units 126 - `1E-2` 127 - 128 129* - `-units_second` 130 - 1 second in scaled time units 131 - `1E-2` 132 - 133 134* - `-units_kilogram` 135 - 1 kilogram in scaled mass units 136 - `1E-6` 137 - 138 139* - `-strong_form` 140 - Strong (1) or weak/integrated by parts (0) residual 141 - `0` 142 - 143 144* - `-stab` 145 - Stabilization method (`none`, `su`, or `supg`) 146 - `none` 147 - 148 149* - `-CtauS` 150 - Scale coefficient for stabilization tau (nondimensional) 151 - `0` 152 - 153 154* - `-wind_type` 155 - Wind type in Advection (`rotation` or `translation`) 156 - `rotation` 157 - 158 159* - `-wind_translation` 160 - Constant wind vector when `-wind_type translation` 161 - `1,0,0` 162 - 163 164* - `-E_wind` 165 - Total energy of inflow wind when `-wind_type translation` 166 - `1E6` 167 - `J` 168::: 169 170An example of the `rotation` mode can be run with: 171 172``` 173./navierstokes -problem advection2d -wind_type rotation -implicit -stab supg 174``` 175 176and the `translation` mode with: 177 178``` 179./navierstokes -problem advection2d -wind_type translation -wind_translation 1,-.5 180``` 181 182For the 3D advection problem, the following additional command-line options are available: 183 184:::{list-table} Advection3D Runtime Options 185:header-rows: 1 186 187* - Option 188 - Description 189 - Default value 190 - Unit 191 192* - `-lx` 193 - Length scale in x direction 194 - `8000` 195 - `m` 196 197* - `-ly` 198 - Length scale in y direction 199 - `8000` 200 - `m` 201 202* - `-lz` 203 - Length scale in z direction 204 - `4000` 205 - `m` 206 207* - `-rc` 208 - Characteristic radius of thermal bubble 209 - `1000` 210 - `m` 211 212* - `-units_meter` 213 - 1 meter in scaled length units 214 - `1E-2` 215 - 216 217* - `-units_second` 218 - 1 second in scaled time units 219 - `1E-2` 220 - 221 222* - `-units_kilogram` 223 - 1 kilogram in scaled mass units 224 - `1E-6` 225 - 226 227* - `-strong_form` 228 - Strong (1) or weak/integrated by parts (0) residual 229 - `0` 230 - 231 232* - `-stab` 233 - Stabilization method (`none`, `su`, or `supg`) 234 - `none` 235 - 236 237* - `-CtauS` 238 - Scale coefficient for stabilization tau (nondimensional) 239 - `0` 240 - 241 242* - `-wind_type` 243 - Wind type in Advection (`rotation` or `translation`) 244 - `rotation` 245 - 246 247* - `-wind_translation` 248 - Constant wind vector when `-wind_type translation` 249 - `1,0,0` 250 - 251 252* - `-E_wind` 253 - Total energy of inflow wind when `-wind_type translation` 254 - `1E6` 255 - `J` 256 257* - `-bubble_type` 258 - `sphere` (3D) or `cylinder` (2D) 259 - `shpere` 260 - 261 262* - `-bubble_continuity` 263 - `smooth`, `back_sharp`, or `thick` 264 - `smooth` 265 - 266::: 267 268An example of the `rotation` mode can be run with: 269 270``` 271./navierstokes -problem advection -wind_type rotation -implicit -stab supg 272``` 273 274and the `translation` mode with: 275 276``` 277./navierstokes -problem advection -wind_type translation -wind_translation .5,-1,0 278``` 279 280For the Isentropic Vortex problem, the following additional command-line options are available: 281 282:::{list-table} Isentropic Vortex Runtime Options 283:header-rows: 1 284 285* - Option 286 - Description 287 - Default value 288 - Unit 289 290* - `-lx` 291 - Length scale in x direction 292 - `1000` 293 - `m` 294 295* - `-ly` 296 - Length scale in y direction 297 - `1000` 298 - `m` 299 300* - `-lz` 301 - Length scale in z direction 302 - `1` 303 - `m` 304 305* - `-center` 306 - Location of vortex center 307 - `(lx,ly,lz)/2` 308 - `(m,m,m)` 309 310* - `-units_meter` 311 - 1 meter in scaled length units 312 - `1E-2` 313 - 314 315* - `-units_second` 316 - 1 second in scaled time units 317 - `1E-2` 318 - 319 320* - `-mean_velocity` 321 - Background velocity vector 322 - `(1,1,0)` 323 - 324 325* - `-vortex_strength` 326 - Strength of vortex < 10 327 - `5` 328 - 329 330* - `-c_tau` 331 - Stabilization constant 332 - `0.5` 333 - 334::: 335 336This problem can be run with: 337 338``` 339./navierstokes -problem euler_vortex -mean_velocity .5,-.8,0. 340``` 341 342For the Density Current problem, the following additional command-line options are available: 343 344:::{list-table} Euler Vortex Runtime Options 345:header-rows: 1 346 347* - Option 348 - Description 349 - Default value 350 - Unit 351 352* - `-lx` 353 - Length scale in x direction 354 - `8000` 355 - `m` 356 357* - `-ly` 358 - Length scale in y direction 359 - `8000` 360 - `m` 361 362* - `-lz` 363 - Length scale in z direction 364 - `4000` 365 - `m` 366 367* - `-center` 368 - Location of bubble center 369 - `(lx,ly,lz)/2` 370 - `(m,m,m)` 371 372* - `-dc_axis` 373 - Axis of density current cylindrical anomaly, or `(0,0,0)` for spherically symmetric 374 - `(0,0,0)` 375 - 376 377* - `-rc` 378 - Characteristic radius of thermal bubble 379 - `1000` 380 - `m` 381 382* - `-bc_wall` 383 - Use wall boundary conditions on this list of faces 384 - `-` 385 - 386 387* - `-bc_slip_x` 388 - Use slip boundary conditions, for the x component, on this list of faces 389 - `5,6` 390 - 391 392* - `-bc_slip_y` 393 - Use slip boundary conditions, for the y component, on this list of faces 394 - `3,4` 395 - 396 397* - `-bc_slip_z` 398 - Use slip boundary conditions, for the z component, on this list of faces 399 - `1,2` 400 - 401 402* - `-units_meter` 403 - 1 meter in scaled length units 404 - `1E-2` 405 - 406 407* - `-units_second` 408 - 1 second in scaled time units 409 - `1E-2` 410 - 411 412* - `-units_kilogram` 413 - 1 kilogram in scaled mass units 414 - `1E-6` 415 - 416 417* - `-units_Kelvin` 418 - 1 Kelvin in scaled temperature units 419 - `1` 420 - 421 422* - `-stab` 423 - Stabilization method (`none`, `su`, or `supg`) 424 - `none` 425 - 426 427* - `-c_tau` 428 - Stabilization constant 429 - `0.5` 430 - 431 432* - `-theta0` 433 - Reference potential temperature 434 - `300` 435 - `K` 436 437* - `-thetaC` 438 - Perturbation of potential temperature 439 - `-15` 440 - `K` 441 442* - `-P0` 443 - Atmospheric pressure 444 - `1E5` 445 - `Pa` 446 447* - `-N` 448 - Brunt-Vaisala frequency 449 - `0.01` 450 - `1/s` 451 452* - `-cv` 453 - Heat capacity at constant volume 454 - `717` 455 - `J/(kg K)` 456 457* - `-cp` 458 - Heat capacity at constant pressure 459 - `1004` 460 - `J/(kg K)` 461 462* - `-g` 463 - Gravitational acceleration 464 - `9.81` 465 - `m/s^2` 466 467* - `-lambda` 468 - Stokes hypothesis second viscosity coefficient 469 - `-2/3` 470 - 471 472* - `-mu` 473 - Shear dynamic viscosity coefficient 474 - `75` 475 - `Pa s` 476 477* - `-k` 478 - Thermal conductivity 479 - `0.02638` 480 - `W/(m K)` 481::: 482 483For the case of a square/cubic mesh, the list of face indices to be used with `-bc_wall` and/or `-bc_slip_x`, `-bc_slip_y`, and `-bc_slip_z` are: 484 485* 2D: 486 - faceMarkerBottom = 1 487 - faceMarkerRight = 2 488 - faceMarkerTop = 3 489 - faceMarkerLeft = 4 490* 3D: 491 - faceMarkerBottom = 1 492 - faceMarkerTop = 2 493 - faceMarkerFront = 3 494 - faceMarkerBack = 4 495 - faceMarkerRight = 5 496 - faceMarkerLeft = 6 497 498This problem can be run with: 499 500``` 501./navierstokes -problem density_current -dm_plex_box_faces 16,1,8 -degree 1 -lx 2000 -ly 125 -lz 1000 -rc 400. -bc_wall 1,2,5,6 -bc_slip_y 3,4 -viz_refine 2 502``` 503