A mixed Boltzmann-BGK model for inert gas mixtures (Q6586962)

In this paper, the authors propose a new mixed-type model of the Boltzmann and the BGK equations for gas mixtures. Traditionally, several models were suggested to describe the dynamics of gas mixtures; well-known approaches are via the use of the Boltzmann operators for multi-species interactions or the use of the BGK operators for multi-species interactions, but not using both at the same time. In this paper, the authors use both operators at the same time; namely, the collision operators between the same species are written as the Boltzmann operators while the collision operators between different species are written as the BGK relaxation operators. The authors claim in the rest of the paper that this approach allows one ``to rigorously justify that the species collisions play the dominant role (as in mixtures with very disparate particle masses)''. The authors prove that the model has the conservation laws of momentum and energy, and preserves positivity of all temperatures and the validity of Boltzmann H-theorem.