Hybrid Burnett Equations. A New Method of Stabilizing

Abstract

In the Chapman & Enskog version of the Burnett equations the two time derivatives in the pressure tensor and heat current are replaced by spatial derivatives using the equations to zero order in the Knudsen number. Bobylev showed that the resulting conventional Burnett equations are linearly unstable. In this paper it is shown that if the time derivatives are instead kept, the equations. A hybrid of the two possibilities is proposed which gives equations which are shown to be linearly stable. The system contains two parameters. For the simplest choice of parameters the hybrid equations have no third derivative of the temperature but the inertia term contains second spatial derivatives. For stationary flow, when terms $Kn^2Ma^2$ can be neglected, the only difference from the conventional Burnett equations is the change of coefficients $\varpi_{2}\to \varpi_{3},\varpi_{3}\to \varpi_{3}.$