# LBM Simulation with high Reynolds numbers

Hi there!

I’m plannig to implement a 3d lattice-boltzmann solver for high Reynolds numbers on GPUs. I already have implemented a first version that seems to work for scenes like the lid-driven cavity setup. So far I compared my results to the figures presented in the paper by Povitsky (Three-dimensional flow in cavity at yaw). Does anybody know where to get more data to compare to?

Now I want to improve my solver to achieve higher Reynolds numbers. I’ve already read some literature about turbulence models (the Smagorinsky model seems to be quite easy to implement), multiple-relaxation models and adaptive grids.

Since I probably can’t try all of them I’d like to know which one is most promising for simulations with high Reynolds numbers.

Hi,

I think that the following paper answers essentially all aspects of your question:

http://dx.doi.org/10.1103/PhysRevE.79.026703

It presents LB simulations in a 3D cavity, contains links to numerical reference data, and discusses Smagorinsky-related LES models.

The summary is that although a plain Smagorinsky model is simple to implement, it is not sufficient because it does not capture the physics of the boundary layers close to the walls. As a work-around, you need to vary the Smagorinsky constant. You can do this either manually close to the walls, by incorporating some a-priori knowledge of the boundary layer (a “van Driest damping function”), or automatically with help of a dynamic Smagorinsky model.

Ah wait, the dynamic Smagorinsky model is published elsewhere; you’ll find it here:

http://dx.doi.org/10.1016/j.physa.2009.02.041

In this model, some data is averaged over nearest neighbor cells to make an estimate for the local value of the Smagorinsky constant.

It seems that the dynamic Smagorinsky model gives somewhat better results than the static one, and it doesn’t require any a-priori knowledge of the problem. But as always, it is difficult to quantify how much better it is, and if the improvement of accuracy compensates for the difficulty of the numerical implementation.

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