Body forces in MRT

Hello, LBMers,

I’m working on force implement in MRT. I tested Luo and Lallemand’s (PRE, 2003) scheme. However, the maximum velocity is not correct in Poiseuille flow. I’m not sure where is wrong…

What I did is as follows,


relaxation paramters:
  s0=s3=s5=0.0;   s1=1.64;   s2=1.54;   s4=s6=1.7;   s7=s8=1.0/tau;

macroscopic value:
  rho=\sum f_i;
  [b]j[/b] = \sum f_i*e_i + 0.5 * [b]F[/b];  // flux, updated with half force 

equilibrium values of the moments:
  m_eq0= rho; m_eq1= -2.0*rho+3.0*(j_x^2+j_y^2)/rho; ....

transfer from population space to moment space:
  [b]m[/b] =  [b]T f[/b];  // T is the matrix

collsion in moment space:
 [b]m*[/b]= s ([b]m_eq[/b]-[b]m[/b]);

j" = j'+0.5*[b]F[/b]; // another half part of the force.

inverse transfer from moment space to population space:
  [b]f *[/b]=[b]T^{-1} m*[/b]

End of the collision step

Thank you very much.