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* - `-qextra` 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 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* 2D: 127 - faceMarkerBottom = 1 128 - faceMarkerRight = 2 129 - faceMarkerTop = 3 130 - faceMarkerLeft = 4 131* 3D: 132 - faceMarkerBottom = 1 133 - faceMarkerTop = 2 134 - faceMarkerFront = 3 135 - faceMarkerBack = 4 136 - faceMarkerRight = 5 137 - faceMarkerLeft = 6 138 139For the 2D advection problem, the following additional command-line options are available: 140 141:::{list-table} Advection2D Runtime Options 142:header-rows: 1 143 144* - Option 145 - Description 146 - Default value 147 - Unit 148 149* - `-rc` 150 - Characteristic radius of thermal bubble 151 - `1000` 152 - `m` 153 154* - `-units_meter` 155 - 1 meter in scaled length units 156 - `1E-2` 157 - 158 159* - `-units_second` 160 - 1 second in scaled time units 161 - `1E-2` 162 - 163 164* - `-units_kilogram` 165 - 1 kilogram in scaled mass units 166 - `1E-6` 167 - 168 169* - `-strong_form` 170 - Strong (1) or weak/integrated by parts (0) residual 171 - `0` 172 - 173 174* - `-stab` 175 - Stabilization method (`none`, `su`, or `supg`) 176 - `none` 177 - 178 179* - `-CtauS` 180 - Scale coefficient for stabilization tau (nondimensional) 181 - `0` 182 - 183 184* - `-wind_type` 185 - Wind type in Advection (`rotation` or `translation`) 186 - `rotation` 187 - 188 189* - `-wind_translation` 190 - Constant wind vector when `-wind_type translation` 191 - `1,0,0` 192 - 193 194* - `-E_wind` 195 - Total energy of inflow wind when `-wind_type translation` 196 - `1E6` 197 - `J` 198::: 199 200An example of the `rotation` mode can be run with: 201 202``` 203./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 204``` 205 206and the `translation` mode with: 207 208``` 209./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 1,2,3,4 210``` 211Note the lengths in `-dm_plex_box_upper` are given in meters, and will be nondimensionalized according to `-units_meter`. 212 213For the 3D advection problem, the following additional command-line options are available: 214 215:::{list-table} Advection3D Runtime Options 216:header-rows: 1 217 218* - Option 219 - Description 220 - Default value 221 - Unit 222 223* - `-rc` 224 - Characteristic radius of thermal bubble 225 - `1000` 226 - `m` 227 228* - `-units_meter` 229 - 1 meter in scaled length units 230 - `1E-2` 231 - 232 233* - `-units_second` 234 - 1 second in scaled time units 235 - `1E-2` 236 - 237 238* - `-units_kilogram` 239 - 1 kilogram in scaled mass units 240 - `1E-6` 241 - 242 243* - `-strong_form` 244 - Strong (1) or weak/integrated by parts (0) residual 245 - `0` 246 - 247 248* - `-stab` 249 - Stabilization method (`none`, `su`, or `supg`) 250 - `none` 251 - 252 253* - `-CtauS` 254 - Scale coefficient for stabilization tau (nondimensional) 255 - `0` 256 - 257 258* - `-wind_type` 259 - Wind type in Advection (`rotation` or `translation`) 260 - `rotation` 261 - 262 263* - `-wind_translation` 264 - Constant wind vector when `-wind_type translation` 265 - `1,0,0` 266 - 267 268* - `-E_wind` 269 - Total energy of inflow wind when `-wind_type translation` 270 - `1E6` 271 - `J` 272 273* - `-bubble_type` 274 - `sphere` (3D) or `cylinder` (2D) 275 - `shpere` 276 - 277 278* - `-bubble_continuity` 279 - `smooth`, `back_sharp`, or `thick` 280 - `smooth` 281 - 282::: 283 284An example of the `rotation` mode can be run with: 285 286``` 287./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 288``` 289 290and the `translation` mode with: 291 292``` 293./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 1,2,3,4,5,6 294``` 295 296For the Isentropic Vortex problem, the following additional command-line options are available: 297 298:::{list-table} Isentropic Vortex Runtime Options 299:header-rows: 1 300 301* - Option 302 - Description 303 - Default value 304 - Unit 305 306* - `-center` 307 - Location of vortex center 308 - `(lx,ly,lz)/2` 309 - `(m,m,m)` 310 311* - `-units_meter` 312 - 1 meter in scaled length units 313 - `1E-2` 314 - 315 316* - `-units_second` 317 - 1 second in scaled time units 318 - `1E-2` 319 - 320 321* - `-mean_velocity` 322 - Background velocity vector 323 - `(1,1,0)` 324 - 325 326* - `-vortex_strength` 327 - Strength of vortex < 10 328 - `5` 329 - 330 331* - `-c_tau` 332 - Stabilization constant 333 - `0.5` 334 - 335::: 336 337This problem can be run with: 338 339``` 340./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. 341``` 342 343For the Density Current problem, the following additional command-line options are available: 344 345:::{list-table} Euler Vortex Runtime Options 346:header-rows: 1 347 348* - Option 349 - Description 350 - Default value 351 - Unit 352 353* - `-center` 354 - Location of bubble center 355 - `(lx,ly,lz)/2` 356 - `(m,m,m)` 357 358* - `-dc_axis` 359 - Axis of density current cylindrical anomaly, or `(0,0,0)` for spherically symmetric 360 - `(0,0,0)` 361 - 362 363* - `-rc` 364 - Characteristic radius of thermal bubble 365 - `1000` 366 - `m` 367 368* - `-units_meter` 369 - 1 meter in scaled length units 370 - `1E-2` 371 - 372 373* - `-units_second` 374 - 1 second in scaled time units 375 - `1E-2` 376 - 377 378* - `-units_kilogram` 379 - 1 kilogram in scaled mass units 380 - `1E-6` 381 - 382 383* - `-units_Kelvin` 384 - 1 Kelvin in scaled temperature units 385 - `1` 386 - 387 388* - `-stab` 389 - Stabilization method (`none`, `su`, or `supg`) 390 - `none` 391 - 392 393* - `-c_tau` 394 - Stabilization constant 395 - `0.5` 396 - 397 398* - `-theta0` 399 - Reference potential temperature 400 - `300` 401 - `K` 402 403* - `-thetaC` 404 - Perturbation of potential temperature 405 - `-15` 406 - `K` 407 408* - `-P0` 409 - Atmospheric pressure 410 - `1E5` 411 - `Pa` 412 413* - `-N` 414 - Brunt-Vaisala frequency 415 - `0.01` 416 - `1/s` 417 418* - `-cv` 419 - Heat capacity at constant volume 420 - `717` 421 - `J/(kg K)` 422 423* - `-cp` 424 - Heat capacity at constant pressure 425 - `1004` 426 - `J/(kg K)` 427 428* - `-g` 429 - Gravitational acceleration 430 - `9.81` 431 - `m/s^2` 432 433* - `-lambda` 434 - Stokes hypothesis second viscosity coefficient 435 - `-2/3` 436 - 437 438* - `-mu` 439 - Shear dynamic viscosity coefficient 440 - `75` 441 - `Pa s` 442 443* - `-k` 444 - Thermal conductivity 445 - `0.02638` 446 - `W/(m K)` 447::: 448 449This problem can be run with: 450 451``` 452./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 -viz_refine 2 453``` 454