# MRT+Two phase flow

Hello

I have a problem! First I coded LBM based on shan-chen method that is described on sukop’s book then because i want to simulate porous media i changed my collision operator(BGK) to Multi Relaxation Time(MRT). My problem is when i added interaction forces to distribution function after collision step by formula 3wt(exgr_x + eygr_y) in which gr_x and gr_y are interaction forces in X and Y direction, my results are very good in Poiseuille Flow by any matrix of relaxation time that the parameters have a value of 0.5-2.0 (s0,s3 and s5 =0 in Relaxation Matrix(s0 s1 s2 s3 s4 s5 s6 s7 s8 s9)) but when i want to simulate Contact angle of droplet in surface my results are not very good for some of the variables of G (adhesion coefficient) .But when I added interaction forces by shifting the velocity the results are acceptable. I guess when i add interaction forces to distribution function maybe the formula 3wt(exgr_x + eygr_y) is not comprehensive can not be used in this case or maybe some other changes should be made. Your help is appreciated.

Amir.

Hi Amir,

The formula is comprehensive but you should be really attentive with the equilibrium function. When the force population is 3wt(exgr_x+eygr_y) the equilibrium function needs to be as:
f_eq=wtrho(1+3*(exux_micro+eyuy_micro)+4.5*Q_{iab}*ux_macro,a * uy_macro,b), where ux_micro and uy_micro are the microscopic velocities calculated as \rho u_micro=\sum_i{f_i e_i} and macroscopic velocities (your output velocities) are calculated as \rho u_macro=\sum_i{f_i e_i}+Gr/2.

As well note that the shifting velocity is much more stable.

Hopefully it will help,
Alex