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lbm

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.

Contents

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.

Lid-driven cavity

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."

Turek benchmark

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:

Poiseuille with random obstacles

It is possible to run a Poiseuille flow with random obstacles in the domain. Below is an example.

Running

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