An Analysis of the Marshak Conditions for Matching Boltzmann and Euler Equations

Domain decomposition methods based on matching the Boltzmann and Euler equations without overlapping are an important simulation technique in rarefied gas dynamics and semiconductor device modeling. Many existing codes use the Marshak boundary conditions (i.e. imposing continuity of the fluxes) at the interface between the two modeling regimes to implicitly determine the boundary data for the compressible Euler equations.

In this paper we investigate the solvability of the Marshak conditions in the four different flow situations sub-/supersonic in-/outflow in one spacial dimension and for selected cases in 2D and 3D.