lbm

A simple lattice-Boltzmann code for 2D flow resolutions.

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

Running simulations

Cases are described in the lbm/src/app/ repository. To run a simulation, adjust the parameters in the related python file, then run python3 start.py <app_name>. A results folder will be generated in ./results/ with the current date and time. If you wish to add a new application, you must create a new app, and register it in the factory, located in lbm/src/app/app.py. Below are some examples and benchmarks that were ran with the code. The related cases are available in the repository. The computational times are obtained on a standard laptop.

Benchmarks

Lid-driven cavity

A simple driven cavity in unit square. Below are the computed time-domain velocity norms at Re=100 (left) and Re=1000 (right).

A comparison of u = f(y) and v = f(x) 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". Here, we explore the accuracy of the drag and lift computation (using IBB). Note that for the 2D-2 case, the values correspond to the max drag and lift.

	ny	2D-1 (Re=20) Cd, Cl, CPU	2D-2 (Re=100) Cd, Cl, CPU
Turek	---	5.5800 - 0.0107 - N/A	3.2300 - 1.0000 - N/A
lbm	100	5.7111 - 0.0285 - 236 s.	3.5409 - 1.0696 - 518 s.
lbm	200	5.6250 - 0.0212 - 1367 s.	3.2959 - 1.0253 - 2762 s.

Below is a video of the 2D-2 case:

Applications

Array of obstacles

An array of square obstacles at Re=2000, with ny=200. This computation took approx 20 minutes on my laptop, although the accuracy here is questionable.

Double step in channel

Two steps in a channel at Re=500, with ny=150. This computation took approx 15 minutes on my laptop.