Hi everybody,

According to conservation laws for D2Q9 and for LBGK model;

sum(0-8) [f] = sum(0-8) [f_eq] = rho

sum(0-8) [e*f] = sum(0-8) [e*f_eq] = rho*u

f: distribution function

f_eq: equilibruim distribution function.

rho: density

u: fluid velocity

0 -8: lattice numbers (form 0 to 8)

In Multi-Chapman Enskog Analysis.

f= f_0 + eps*f_1

f_0: Equilibruim distribution function (Zeroth order distribution function)

f_1: First order distribution function

Therefore;

sum(0-8) [f_1] =0 (Eq*)

sum(0-8) [e*f_1] = 0 (Eq **)

My Question is; why do the Eq* and Eq** like this. Where do they come form?

Thank you,

Daracan