A kinetic ellipsoidal BGK model for a binary gas mixture

M. Groppi^a, S. Monica and G. Spiga

Department of Mathematics, Parma University - Parco Area delle Scienze 53/A, I-43124 Parma, Italy, EU

^a maria.groppi@unipr.it

Received: 19 September 2011
Accepted: 1 November 2011

Abstract

An ellipsoidal BGK model is proposed for a binary mixture of rarefied gases in the frame of kinetic theory. It fulfils the crucial properties of the actual Boltzmann equation (collision invariants, equilibria, entropy dissipation), and introduces a further constraint on velocity equalization of the two species. The model features two disposable relaxation parameters which can be used to fit exactly, in the continuum limit, Fick's law for diffusion velocities and Newton's law for the viscous stress in the relevant set of Navier-Stokes equations. Positivity of temperature fields is guaranteed by a physically meaningful restriction on the parameters themselves.