A BGK model for a suspension of inelastic spheres

This paper deals with the kinetic modelling of a suspension of colliding spheres. The collisions are supposed to be instantaneous, binary and inelastic. Moreover, we take the diameter of the spheres into account. These assumptions allow us to obtain a Boltzmann-like modelling of a suspension, presented in [1]. Because of the complexity of the nonlinear structure of the collision integral, this kinetic equation is very difficult to analyse. It is therefore interesting to introduce a BGK model equation. In order to be physically realistic and consistent with the assumptions related to the collisions, a collision frequency depending on the particle velocities is chosen. Taking this into account, a BGK model is written. All the basic properties of the original operator are retained.