[stephan]

Hi Duldul,

thanks for your question.

In general, for the incompressible NSE the error of LBM introduced by the Mach number is computable as O(Ma^2) and vanishes in the diffusion limit.

For a discussion of the density error in particular, please have a look at Krüger et al. 2017 “The Lattice Boltzmann Method: Principles and Practice” (Section 4.3.2 Incompressible Flow).

BR
Stephan

[stephan]

Hi Duldul,

Please have a look at Krüger et al., The Lattice Boltzmann Method (2017) (https://www.springer.com/gp/book/9783319446479).
Particularly Chapter 9 (and References therein) is very helpful for a general understanding of multiphase and multicomponent LBM, e.g. Shan-Chen.

BR
Stephan

[stephan]

Hi Alex

Your implementation seems to be correct. Also the fact that setting \tau_s = \tau_a yields the BGK solution is a good sign.

The specific values for the magic parameter \Lambda = (\tau_s – 0.5)*(\tau_a – 0.5) mentioned in the literature are a typical result for certain flow types and Reynolds number regimes.

If your code is supposed to run at high Reynolds numbers, I suggest you try different (smaller or much smaller) values for \Lambda, since it is connected to the Reynolds number via \tau_s. For high Reynolds numbers, the magnitude of \tau_a is way too large with a fixed \Lambda=0.25. Maybe try a few decimal digits below that, e.g. \Lambda=0.0025 and work your way up.

With the calibration of \tau_a through a smaller \Lambda, you should obtain stable results. In case this does not work, fix \tau_a=1 and try again.

If you encounter any special results (highly increased stability, or none at all), please let me know.

Anyway, good luck with your tests.

BR,
Stephan

PS: A similar question was posted and answered about two month ago:
https://www.openlb.net/forum/topic/smagorinsky-turbulence-model-and-trt-collision-operator/

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