Model Boltzmann equation for gas mixtures: Construction and numerical comparison

A new model for the nonlinear Boltzmann equation for gas mixtures is constructed by the method employed in the derivation of the McCormack model in the linearized kinetic theory [F.J. McCormack, Phys. Fluids 16 (1973) 2095]. Then it is compared numerically with other existing models proposed in [P. Andries, K. Aoki, B. Perthame, J. Stat. Phys. 106 (2002) 993] and in [L.H. Holway Jr., Phys. Fluids 9 (1966) 1658] (the so-called ES-BGK model) as well as with the original Boltzmann equation. The new model is not restricted to the Maxwell molecule, can fit to general molecular models, and reproduces well solutions of the Boltzmann equation at least in the case of weak nonequilibrium. The numerical comparison is performed in the case of a binary gas mixture consisted of the hard-sphere or pseudo Maxwell molecules, after parameters concerning the molecular interaction are adjusted appropriately.