SmagorinskyForcedBGKdynamics preFactor miscalculated

[hhan]

Dear Community,

When checking SmagorinskyForcedBGKdynamics source code, I seem to have found the problem. In collisionLES.h file, struct SmagorinskyEffectiveOmega, the function computeEffectiveOmega to compute the turbulent realaxation time, is the preFactor term miscalculated and sqrt(2) redundant?

I refer to the “Application of a lattice Boltzmann method combined with a Smagorinsky turbulence model to spatially resolved heat flux inside a refrigerated vehicle “Section 2.2 of the paper.
https://doi.org/https://doi.org/10.1016/j.camwa.2018.08.018

I hope you can check this part, thank you!

[stephan]

Dear hhan,

thank you for reporting. We will have a closer look and respond here in due time.

BR
Stephan

[stephan]

Dear hhan,

sorry, it has been a while.
However, your question is interesting.

So, in our code, we make use of the model described here:
[1] https://doi.org/10.1017/jfm.2012.155
and here:
[2] https://doi.org/10.1016/j.jcp.2005.03.022

In the latter reference [2], Equation (15) has an additional sqrt(2) which should be deleted.
Nevertheless, in the same notation, let’s assume that bar(Q) := sqrt(2 sum Q_ij Q_ij).
Then we replace the Q_ij with PiNeq_ij computed in OpenLB and insert this bar(PiNeq) into Equation (15).
The sqrt(2) in our code hence resembles the prefactor of 2 when computing the magnitude of the strain rate tensor ||S|| = sqrt(2 sum S_ij S_ij) (which is a common thing to do in CFD, see [1], page 516).
All of this, also leads to same expressions as in the paper you referenced above (https://doi.org/https://doi.org/10.1016/j.camwa.2018.08.018).

Let me know if you disagree here.
Please also consider testing the tgv3d example with SmagorinskyBGKdynamics (once including the sqrt(2) and once without it in the EffectiveOmega computation) and post the results here in the forum.

Thanks again for posting and BR,
Stephan

[Author]

Posts