Continuity boundary condition

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).

sub. A      Interior boundary         sub. B

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.