# constants in mrt model

anybody know which are the “right” constants to use in the mrt model? i use d’humiere e.a. 2002, but the constants there seem magical. are there other choices? is there a general discussion of this in some paper?

First of all could you tell me what constants you are talking about?

There are two useful choices for MRT model. One is D’Humieres, Ginzburg, Luo, Lallemand - they discuss the choice of moments in the paper by Luo and Lallemand (something like LBM: dissipation, stability, …) . If you need the name exactly I will search for. The constants for moments you can easily obtain by multiplication your usual equilibrium function on eigenvector or column of their matrix (just check it). In that case you do not need any stability analysis as they did in their paper.

I use the second MRT basis which gives me more sense. The basis of matrix is taken through consequent Hermite series of equilibrium function. I think the best paper for it is Dellar, Water shallow equations or you can use old paper of Succi - Bergassola, Succi, Benzi - 1992 - they first suggest it. But I didn’t look at it thoroughly. In any case just google it.
For D2Q9 the basis is:
( 1, 1, 1, 1, 1, 1, 1, 1, 1) -rho
( 0, 1, 0, -1, 0, 1, -1, -1, 1) -cix
( 0, 0, 1, 0, -1, 1, 1, -1, -1) - ciy
(-1/3, 2/3, -1/3, 2/3, -1/3, 2/3, 2/3, 2/3, 2/3) -cixcix-1/3
( 0, 0, 0, 0, 0, 1, -1, 1, -1)- cix
ciy
(-1/3, -1/3, 2/3, -1/3, 2/3, 2/3, 2/3, 2/3, 2/3) - ciyciy - 1/3
( 1, -2, -2, -2, -2, 4, 4, 4, 4) - gi
( 0, -2, 0 , 2, 0, 4, -4, -4, 4) -gi
cix
( 0, 0, -2 , 0, 2, 4, 4, -4, -4) -gi*ciy

If you need the right weights I can send you a paper,
Alex