Accounting for backflow in hydrodynamic-Boltzmann interfaces

Methods for building a consistent interface between hydrodynamic and Boltzmann modules is presented. These methods account for the backflow across the hydrodynamic-Boltzmann hypersurface. The algorithms are efficient, relatively straight-forward to implement, and exactly satisfy conservation laws across the hypersurface. The methods also account for the interactions between particles in the backflow and other particles by following the subsequent impact of such particles. Since the number of altered trajectories grows exponentially in time, a cutoff is built into the procedure so that the effects of the backflow are ignored beyond a certain number of collisions.