Smagorinsky implementation and its effect on lattice parameters


So far, I’ve found that working with higher Re but a relatively coarse grid can be done with the use of a Smagorinsky model. I’ve been making use of the externalFlowAroundObstacle as my base code, and if I understand correctly, it makes use of the static Smagorinsky model with BGK.

Literature-wise, most I’ve come across set Cs = 0.14, with the usual range being from 0.1 to 0.2, so I think I’m sticking with that for at least the main pertinent thing for the Smagorinsky implementation. However, when it comes to setting up my simulation, I’m not quite sure how to work it out in terms of stability.

I’m aware of the compressibility limit for Ma (and u_LB) as well as the optimal values of tau. However, I’m quite lost as to how C,s should factor in when I set it up. All I know is that the tensor norm of the strain rate as well as the stress tensor itself are related to viscosity, and thus, to tau as well. But not quite sure how overall, I would work backwards for stable parameters.

Any tips or even additional references would be of great help. Thank you for your time!