thank you very much thats help.

So in general ant terms that can not be mached with the macroscopic equation considered as error.

I looked at Irena paper it is intersting.

An other question:

In D2Q9 when I do the gram schmidt orthogonalization to the folowing basis which is based on SO(2) group

[ 1, u, v, (u^2+v^2), u*v, (u^2-v^2), u* (u^2+v^2), v* (u^2+v^2), (u^2+v^2)^2]

I got the same matrix as in the orginal paper of (dHumeries 1992)

how can I get the nice simple integer matrix which is usually used in the literature?

I tried to multiply each row by its norm. I got a similar matrrix for the conserved moment, but not for the non conserved moments. i.e.

```
rho [1,1,1,1,1,1,1,1,1],
u [0,1,0,-1,0,1,-1,-1,1],
v [0,0,1,0,-1,1,1,-1,-1],
e [-4/3,-1/3,-1/3,-1/3,-1/3,2/3,2/3,2/3,2/3],
pxy [0,0,0,0,0,1,-1,1,-1],
pxx [0,1,-1,1,-1,0,0,0,0],
qx [0,-2/3,0,2/3,0,1/3,-1/3,-1/3,1/3],
qy [0,0,-2/3,0,2/3,1/3,1/3,-1/3,-1/3],
eps [8/9,-4/9,-4/9,-4/9,-4/9,2/9,2/9,2/9,2/9]
```

I think it is ok to multiply the non conserved moments by a constant to get a nice matrix. i.e.

e=e*3*

qx=qx 3

qy=qy* 3

eps=eps* 9/2

correct me if i made a mistake.

regards