## libCEED: Navier-Stokes Example This page provides a description of the Navier-Stokes example for the libCEED library, based on PETSc. The Navier-Stokes problem solves the compressible Navier-Stokes equations in three dimensions using an explicit time integration. The state variables are mass density, momentum density, and energy density. The main Navier-Stokes solver for libCEED is defined in [`navierstokes.c`](navierstokes.c) with different problem definitions according to the application of interest. Build by using: `make` and run with: ``` ./navierstokes -ceed [ceed] -problem [problem type] -degree [degree] ``` ## Runtime options % inclusion-fluids-marker The Navier-Stokes mini-app is controlled via command-line options. The following options are common among all problem types: :::{list-table} Common Runtime Options :header-rows: 1 * - Option - Description - Default value * - `-ceed` - CEED resource specifier - `/cpu/self/opt/blocked` * - `-test` - Run in test mode - `false` * - `-compare_final_state_atol` - Test absolute tolerance - `1E-11` * - `-compare_final_state_filename` - Test filename - * - `-problem` - Problem to solve (`advection`, `advection2d`, `density_current`, or `euler_vortex`) - `density_current` * - `-implicit` - Use implicit time integartor formulation - * - `-degree` - Polynomial degree of tensor product basis (must be >= 1) - `1` * - `-qextra` - Number of extra quadrature points - `2` * - `-viz_refine` - Use regular refinement for visualization - `0` * - `-output_freq` - Frequency of output, in number of steps - `10` * - `-continue` - Continue from previous solution - `0` * - `-output_dir` - Output directory - `.` * - `-dm_plex_box_faces` - Number of faces in each linear direction - `3,3,3` * - `-snes_view` - View PETSc `SNES` nonlinear solver configuration - * - `-log_view` - View PETSc performance log - * - `-help` - View comprehensive information about run-time options - ::: For the 2D advection problem, the following additional command-line options are available: :::{list-table} Advection2D Runtime Options :header-rows: 1 * - Option - Description - Default value - Unit * - `-lx` - Length scale in x direction - `8000` - `m` * - `-ly` - Length scale in y direction - `8000` - `m` * - `-rc` - Characteristic radius of thermal bubble - `1000` - `m` * - `-units_meter` - 1 meter in scaled length units - `1E-2` - * - `-units_second` - 1 second in scaled time units - `1E-2` - * - `-units_kilogram` - 1 kilogram in scaled mass units - `1E-6` - * - `-strong_form` - Strong (1) or weak/integrated by parts (0) residual - `0` - * - `-stab` - Stabilization method (`none`, `su`, or `supg`) - `none` - * - `-CtauS` - Scale coefficient for stabilization tau (nondimensional) - `0` - * - `-wind_type` - Wind type in Advection (`rotation` or `translation`) - `rotation` - * - `-wind_translation` - Constant wind vector when `-wind_type translation` - `1,0,0` - * - `-E_wind` - Total energy of inflow wind when `-wind_type translation` - `1E6` - `J` ::: An example of the `rotation` mode can be run with: ``` ./navierstokes -problem advection2d -wind_type rotation -implicit -stab supg ``` and the `translation` mode with: ``` ./navierstokes -problem advection2d -wind_type translation -wind_translation 1,-.5 ``` For the 3D advection problem, the following additional command-line options are available: :::{list-table} Advection3D Runtime Options :header-rows: 1 * - Option - Description - Default value - Unit * - `-lx` - Length scale in x direction - `8000` - `m` * - `-ly` - Length scale in y direction - `8000` - `m` * - `-lz` - Length scale in z direction - `4000` - `m` * - `-rc` - Characteristic radius of thermal bubble - `1000` - `m` * - `-units_meter` - 1 meter in scaled length units - `1E-2` - * - `-units_second` - 1 second in scaled time units - `1E-2` - * - `-units_kilogram` - 1 kilogram in scaled mass units - `1E-6` - * - `-strong_form` - Strong (1) or weak/integrated by parts (0) residual - `0` - * - `-stab` - Stabilization method (`none`, `su`, or `supg`) - `none` - * - `-CtauS` - Scale coefficient for stabilization tau (nondimensional) - `0` - * - `-wind_type` - Wind type in Advection (`rotation` or `translation`) - `rotation` - * - `-wind_translation` - Constant wind vector when `-wind_type translation` - `1,0,0` - * - `-E_wind` - Total energy of inflow wind when `-wind_type translation` - `1E6` - `J` * - `-bubble_type` - `sphere` (3D) or `cylinder` (2D) - `shpere` - * - `-bubble_continuity` - `smooth`, `back_sharp`, or `thick` - `smooth` - ::: An example of the `rotation` mode can be run with: ``` ./navierstokes -problem advection -wind_type rotation -implicit -stab supg ``` and the `translation` mode with: ``` ./navierstokes -problem advection -wind_type translation -wind_translation .5,-1,0 ``` For the Isentropic Vortex problem, the following additional command-line options are available: :::{list-table} Isentropic Vortex Runtime Options :header-rows: 1 * - Option - Description - Default value - Unit * - `-lx` - Length scale in x direction - `1000` - `m` * - `-ly` - Length scale in y direction - `1000` - `m` * - `-lz` - Length scale in z direction - `1` - `m` * - `-center` - Location of vortex center - `(lx,ly,lz)/2` - `(m,m,m)` * - `-units_meter` - 1 meter in scaled length units - `1E-2` - * - `-units_second` - 1 second in scaled time units - `1E-2` - * - `-mean_velocity` - Background velocity vector - `(1,1,0)` - * - `-vortex_strength` - Strength of vortex < 10 - `5` - * - `-c_tau` - Stabilization constant - `0.25` - ::: This problem can be run with: ``` ./navierstokes -problem euler_vortex -mean_velocity .5,-.8,0. ``` For the Density Current problem, the following additional command-line options are available: :::{list-table} Euler Vortex Runtime Options :header-rows: 1 * - Option - Description - Default value - Unit * - `-lx` - Length scale in x direction - `8000` - `m` * - `-ly` - Length scale in y direction - `8000` - `m` * - `-lz` - Length scale in z direction - `4000` - `m` * - `-center` - Location of bubble center - `(lx,ly,lz)/2` - `(m,m,m)` * - `-dc_axis` - Axis of density current cylindrical anomaly, or `(0,0,0)` for spherically symmetric - `(0,0,0)` - * - `-rc` - Characteristic radius of thermal bubble - `1000` - `m` * - `-bc_wall` - Use wall boundary conditions on this list of faces - `-` - * - `-bc_slip_x` - Use slip boundary conditions, for the x component, on this list of faces - `5,6` - * - `-bc_slip_y` - Use slip boundary conditions, for the y component, on this list of faces - `3,4` - * - `-bc_slip_z` - Use slip boundary conditions, for the z component, on this list of faces - `1,2` - * - `-units_meter` - 1 meter in scaled length units - `1E-2` - * - `-units_second` - 1 second in scaled time units - `1E-2` - * - `-units_kilogram` - 1 kilogram in scaled mass units - `1E-6` - * - `-units_Kelvin` - 1 Kelvin in scaled temperature units - `1` - * - `-stab` - Stabilization method (`none`, `su`, or `supg`) - `none` - * - `-c_tau` - Stabilization constant - `0.25` - * - `-theta0` - Reference potential temperature - `300` - `K` * - `-thetaC` - Perturbation of potential temperature - `-15` - `K` * - `-P0` - Atmospheric pressure - `1E5` - `Pa` * - `-N` - Brunt-Vaisala frequency - `0.01` - `1/s` * - `-cv` - Heat capacity at constant volume - `717` - `J/(kg K)` * - `-cp` - Heat capacity at constant pressure - `1004` - `J/(kg K)` * - `-g` - Gravitational acceleration - `9.81` - `m/s^2` * - `-lambda` - Stokes hypothesis second viscosity coefficient - `-2/3` - * - `-mu` - Shear dynamic viscosity coefficient - `75` - `Pa s` * - `-k` - Thermal conductivity - `0.02638` - `W/(m K)` ::: For 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: * 2D: - faceMarkerBottom = 1 - faceMarkerRight = 2 - faceMarkerTop = 3 - faceMarkerLeft = 4 * 3D: - faceMarkerBottom = 1 - faceMarkerTop = 2 - faceMarkerFront = 3 - faceMarkerBack = 4 - faceMarkerRight = 5 - faceMarkerLeft = 6 This problem can be run with: ``` ./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 ```