According to conservation laws for D2Q9 and for LBGK model;
sum(0-8) [f] = sum(0-8) [f_eq] = rho
sum(0-8) [ef] = sum(0-8) [ef_eq] = rho*u
f: distribution function
f_eq: equilibruim distribution function.
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
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?