[PatrickN]

Hello Sumit,

in addition to the answer of Mathias:

(1) Exactly this is what you do in a classical way: Here a very good paper on it:
https://www.cambridge.org/core/journals/journal-of-fluid-mechanics/article/consistent-subgrid-scale-modelling-for-lattice-boltzmann-methods/7CB8A5DE28CFB82D4FFE21947F13F9C8

(2) This is tricky: It really depends on what kind of velocity and subsequent time scaling you apply. By using advective scaling, your velocity and time step increases linearly leading to a very high Mach number and, thus, initializes non-linear growing of instabilities. Diffusive scaling (delta x^2 -> delta t) on the other hand would limit the time step by just changing charU at constant latticeU. On scaling Mathias is the hardcore expert anyway.

(3) To resolve all scales like in freely decaying turbulence you need to resolve the “Kolmogorov length scale”. This is perfectly resolved. We actually did this in our recent work for isotropic turbulence. Regarding you have a wall-bounded flow. The flow is assumed to be resolved when you resolve the wall nearest turbulent energy structures by u+=y+. Let me know if you need any assistance.

Best,
Patrick

[PatrickN]

Hallo Sumit,

the problem with LBM and turbulence are the mathematics of LBM itself. The 2nd order spatial accuracy corresponding to a finite-difference scheme leads to dispersive errors at low viscosities. To suppress those dispersive errors (which also exhibit tremendous amounts of energy) we apply Navier-Stokes related turbulence models, like the Smagorinsky model, which simply increases the effective viscosity and, thus, suppresses those dispersive oscillations.

As long as you are employing an under resolved mesh at a given Reynolds number, I would suggest you use one of the Smagorinsky models or the Approximate Deconvolution Method.
If you are really considered into direct turbulence simulation I suggest a well resolved setup with a BGK approach -> which is at the hydrodynamic limit actually the solution of the Navier-Stokes equations.

I already simulated the turbulent channel flow at high Reynolds numbers and I would be happy to help you with the turbulent pipe flow and the respective forcing and mesh resolution needed for this simulation.

Best,
Patrick

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