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,

Collision:

```
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.