Hybrid Burnett Equations. A New Method of Stabilizing

Authors: Söderholm,  L. H. S.
Document Type: Article
Pubstate: Published
Journal: Transport Theory and Statistical Physics
Volume: 36   495-512
Year: 2007


In the original work by Burnett the pressure tensor and the heat current contain two time derivates. Those are commonly replaced by spatial derivatives using the equations to zero order in the Knudsen number. The resulting conventional Burnett equations were shown by Bobylev to be linearly unstable. In this paper it is shown that the original equations of Burnett have a singularity. A hybrid of the original and conventional equations is constructed which is shown to be linearly stable. It contains two parameters, which have to be larger than or equal to some limit values. For any choice of the parameters, the equations agree with each other and with the Burnett equations to second order in Kn, that is to the accuracy of the Burnett equations. 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 omega_2 -> omega_3, omega_3 -> omega_3.