Continuity boundary condition

Lattice Boltzmann Method LBM: Theory
#1

Is there a strait way to implement continuity boundary condition in Thermal Lattice Boltzmann Method ? I have two subdomains with different properties (different relaxation time) I need to transfer heat between those subdomains without any resistance (so the heat flux is equivalent at both sides).

#2 

                     I
---------------------I------------------------
                     I
sub. A      Interior boundary         sub. B
                     q[sub]A[/sub]=q[sub]B[/sub]

So in other words… if I simply stream DF from other subdomain (the difference is only in collision term due to different relaxation time) its leads to significant error. I need a simple way to implement open interior boundary for TLBM BGK scheme.