Entropic boundary conditions for 13 moment equations in rarefied gas flows

Abstract

One of the major challenges in extending hydrodynamics to far from equilibrium gas flows comes with the need of new boundary conditions for any new modeling approach. The difficulty lies in finding an accurate set of physical conditions at the boundary which simultaneously form a well-posed system of equations. In this paper, we study a system of moment equations for rarefied gas flows that comes equipped with an entropy. This allows a straightforward derivation of boundary conditions which are consistent with the mathematical requirements of the system. The complete nonlinear system is simulated in a rarefied channel flow setting and compared to standard approaches. The results exhibit most of the desired rarefaction effects, such as temperature jump and velocity slip at the wall.