MRT+Two phase flow

Lattice Boltzmann Method LBM: Theory
#1

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.

#2

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