Generalized Lattice-Boltzmann Equations (d'Humieres' MRT)

Hi, all!
I am having some trouble with that classic '92 paper “Generalized Lattice-Boltzmann Equations” by d’Humieres.
The problems start with the Chapman-Enskog expansion of the moment-transformed lattice Boltzmann equation, eq. (5).
It is not clear to me how to derive macroscopic equations from that, espacially since it remains unclear to me what S^ is in equation (5). Shouldn’t it be equal to the matrix S of eq. (4). Even by assuming the latter, it seems impossible to derive - say Eq (13), continuity equation, from (5), i.e. in moment space.
I’d be grateful for any hints!

Figured out that S^ = T S T^(-1).


do you still have a problem with this paper? Could you please post a link to the paper so i can comment the equations you mention?

Best that I could find:
It does not seem to be available online.

I need the paper “Generalized Lattice-Boltzmann Equations (d’Humieres’ MRT)”. Can you send it to my email that is ""? Thank you very much.