A simple lattice-Boltzmann code for 2D flow resolutions. All the tools are contained in the lattice.py file, and separate cases are built on top of this library.
This LBM code includes:
- D2Q9 lattice
- TRT collision operator
- Zou-He on all boundary conditions
- Drag/lift computation using interpolated bounce-back
- Core routines are deferred to Numba
Below are some examples ran with the code. The related cases are available in the repository.
A simple driven cavity in unit square. Launch it by running python3 cavity.py.
Below are the computed time-domain velocity norms and final streamlines at Re=100 (left) and Re=1000 (right).
A comparison of u_x = f(y) at the center of the domain with reference data from "U. Ghia, K. N. Ghia, C. T. Shin, High-Re solutions for incompressible flow using Navier-Stokes equations and multigrid method."
The Turek cylinder benchmark CFD case is described in "Schafer, M., Turek, S. Benchmark Computations of Laminar Flow Around a Cylinder". The 2D case consists in a circular cylinder in a channel with top and bottom no-slip conditions, and with a Poiseuille flow at the inlet (these cases are named 2D-1 and 2D-2 in the aforementionned reference). The cylinder is voluntarily not centered to trigger instability at sufficient Reynolds number. Here, we explore the accuracy of the drag and lift computation.
ny |
2D-1 (Re=20) Cd | 2D-1 (Re=20) Cl | 2D-2 (Re=100) Cd | 2D-2 (Re=100) Cl | |
|---|---|---|---|---|---|
| Turek | --- | 5.5800 | 0.0107 | 3.2300 | 1.0000 |
| lbm | 100 | 5.6300 | 0.0862 | 3.0411 | 0.5834 |
| lbm | 200 | 5.5804 | 0.0371 | 3.2582 | 1.2047 |
| lbm | 300 | 5.5846 | 0.0261 | 3.2152 | 1.0987 |
Below are videos of the 2D-1 and 2D-2 cases:
It is possible to run a Poiseuille flow with random obstacles in the domain. Below is an example.
To run a simulation, adjust the parameters in the related python file, then run python3 case.py. A results folder will be generated in ./results/ with the current date and time. The png/ folder will contain outputs of the velocity norm over the domain. To generate a video out of the png files, you can use the convert command as follows:
convert -delay 10 -resize 50% -loop 0 'u_norm_%d.png'[0-100] animation.gif
To optimize and resize gifs, use gifsicle :
gifsicle -i animation.gif --scale 0.6 -O3 --colors 256 -o anim-opt.gif