lbm

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

<p align="center"> <img width="800" alt="" src="lbm/save/header.gif"> </p>

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).

<p align="center"> <img width="300" alt="" src="lbm/save/driven_cavity/re_100_nx_200/anim-opt.gif"> <img width="300" alt="" src="lbm/save/driven_cavity/re_1000_nx_250/anim-opt.gif"> </p>

A comparison of u = f(y) and v = f(x) at the center of the domain with reference data from <a href="https://www.sciencedirect.com/science/article/pii/0021999182900584">"U. Ghia, K. N. Ghia, C. T. Shin, High-Re solutions for incompressible flow using Navier-Stokes equations and multigrid method"</a>.

<p align="center"> <img width="300" alt="" src="lbm/save/driven_cavity/re_100_nx_200/re_100.png"> <img width="300" alt="" src="lbm/save/driven_cavity/re_1000_nx_250/re_1000.png"> </p>

Turek benchmark

The Turek cylinder benchmark CFD case is described in <a href="https://link.springer.com/chapter/10.1007/978-3-322-89849-4_39">"Schafer, M., Turek, S. Benchmark Computations of Laminar Flow Around a Cylinder"</a>. 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:

<p align="center"> <img width="800" alt="" src="lbm/save/turek/re_100_ny_200/turek.gif"> </p>

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.

<p align="center"> <img width="800" alt="" src="lbm/save/array/array.gif"> </p>

Double step in channel

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

<p align="center"> <img width="800" alt="" src="lbm/save/step/step.gif"> </p>