Zou/He Boundary conditions using MRT

Dear all,

I am trying to implement the Zou/He BC in my LBM code. The problem is that the results that I obtain are only OK if I use the BGK SRT collision operator or alternatively the MRT with all relaxation parameters equal to (1/tau). If the MRT model with different relaxation values is used the results are not so OK. (By the way, I know that my results are OK because I am solving a Poiseuille flow, which is an analytical solution of LBM, so I should always obtain machine accuracy results, as I obtain for SRT models).

The problem suggests me that the Zou/He BCs proposed originally for SRT model cannot be applied in their original form for a MRT collision model.
In my opinion this is due to the form of the non-equilibrium bounce-back assumption. Maybe the computation of the unknown distribution functions has to be performed in moment spaceā€¦ However, this does not make much sense to me. Does anyone ever notice the same thing? How to solve this?

Thanks in advance for the help