where the left side is the streaming part, and the right side is the collision term, *f*_{α}(**x**, *t*) is the density distribution function along the *α* direction at location **x** and time *t*, $f\alpha eq$ is the equilibrium distribution function, *τ*_{f} is the collision–relaxation time for the flow field, and **e**_{α} is the lattice velocity vector. A D2Q9 model is used here, so **e**_{α} can be expressed asDisplay Formula

(2)$e\alpha =[(0,0),(1,0),(0,1),(\u22121,0),(0,\u22121),(1,1),(\u22121,1),(\u22121,\u22121),(1,\u22121)]$