what is TRT and BGK?

LBGK is simple and straight forward, compared with MRT or TRT, but is not as stable as the latter ones. LBGK is good for relaxation time equal to one, but not for lower relaxation time, which will make the simulation collapses. I am not familiar with TRT, but I think it can be considered as a simplification for MRT. So if you study laminar flow, I think LBGK is fine. But for realizing high Reynolds number, you'd better use MRT or TRT. Also, apart from this, entropic lattice boltzmann method is also very good in different kinds of complex flow, although it's more complex in coding than LBGK.

Hi everyone

My problems are simple, incompressible, laminar and they dont have large Reynolds( for now :D ).

I am using BGK for now But I was curious about MRT and TRT.

Considering MRT large number of optimization variables, I decided to check TRT and it has only one optimization variable.

Which one do you think is better? I am talking about Run time, Accuracy and Stability.

Thanks in Advance

For accuracy and stability, MRT is much better than LBGK. MRT becomes LBGK if you set all the relaxation time equal to 1. And the computation cost of MRT is about 15%-20% more than LBGK in general, which is not too much. Actually the tunable parameters you can refer to literature, it won't take much time. Sorry about TRT since I don't know much about it.

HI Feifei

Sorry for this long delay.

Can you recommend some of those literatures?

Hi Amir, since I mainly do multiphase flow, my suggestion may not very good for you because the model is more completed. But if you just need the example of relaxation time, maybe you can use them.

D2Q9: Li, Q., K. H. Luo, and X. J. Li. "Lattice Boltzmann modeling of multiphase flows at large density ratio with an improved pseudopotential model." Physical Review E 87.5 (2013): 053301.

D3Q19:Li, Zheng, Mo Yang, and Yuwen Zhang. "Lattice Boltzmann method simulation of 3-D natural convection with double MRT model." International Journal of Heat and Mass Transfer 94 (2016): 222-238.

If you want to apply 3d MRT, you have to be careful about the transformation matrix, it has to be fit for you lattice speed direction, because the lattice speed directions can be different in different papers.