Derivation of a BGK model for mixtures

The aim of this article is to construct a BGK operator for gas mixtures starting from the true Navier–Stokes equations. That is the ones with transport coefficients given by the hydrodynamic limit of the Boltzmann equation(s). Here the same hydrodynamic limit is obtained by introducing relaxation coefficients on certain moments of the distribution functions. Next the whole model is set by using entropy minimization under moment constraints as in Brull and Schneider (2008, 2009) [23] and [24]. In our case the BGK operator allows to recover the exact Fick and Newton laws and satisfy the classical properties of the Boltzmann equations for inert gas mixtures.