Regularization LBM

Dear all,

Currently I am observing some strange results in my LB simulations, which I think might be due to the influence of high order (non-hydrodynamic) terms in my hydrodynamic solution. Therefore, and in order to clarify this situation, I am thinking to implement in my BGK collision model the Regularized approach (proposed by Latt and Chopard). By suppressing the influence of f(2) and high order terms in f then I hoping to see if my guess regarding the influence of high order terms is right or not. However, before starting to implement this I would like to be sure about some theoretical issues of this model. Therefore, if anyone could explain me the following doubts I would be very much grateful.

(1) What is the difference between Latt and Chopard Regularized model and that proposed by Ladd and Verberg (2001) where a collision model in form of a matrix is used and the relaxation parameters related to the ghost (non-hydrodynamic) modes are assign to -1 so that their contribution to the hydrodynamic solution is nil. Both approaches seem to aim at the same objective but they follow different paths. Am I right? What is the difference from a theoretical point of view? and disregarding the efficiency or complexity of each model what is the one you would recommend me to use if accuracy is my only goal?

(2) Why in MRT models we do not generally choose the relaxation values of ghost modes as -1 (as Ladd and Verberg do in their work) but choose relaxation parameters for the ghost modes slightly different from -1 allowing thus a small contribution of these terms to the hydrodynamic solution. Is this justified only because of stability? Or is there something else that I am missing? Because if accuracy is my only aim I do not see any advantage!

Thank you in advance for your kind answers.


Goncalo Silva

Dear Goncalo Silva,

I have a partial answer for the second question:
The ghost relaxation parameters are totally defined by the problem you simulate (and can be different for the purpose you want to achieve: stability, accuracy of scheme, accuracy of boundary conditions).Even more, if you take the ghost relaxation parameters as -1, they are still in the play for higher orders hydrodynamic limits. In a kind of general problem those parameters are dictated by the Galilean invariance or isotropy of the equilibrium distribution function - people take them just above 1. You can find it in Lallemand and Luo paper for MRT.


Thank you Alex, your answer helped!