Kinetic Modelling and Numerical Simulations using Particle Methods for the Transport of Dust in a Rarefied Gas

We present a new model for the transport of macroscopic particles such as specks of dust in a rarefied gas, based on a purely kinetic approach. Assuming that post-collision velocities are given by a diffuse reflexion on the surface of particles, we obtain a couple of two Boltzmann-type equations. Moreover, we propose an asymptotic expansion of one of the collision operators with respect to the ratio of mass between a molecule of gas and a particle which leads to another equation for the transport of dust. Starting from those models, we performed some numerical simulations using two different methods: a first one based on the initial system of equations and a second one based on the system obtained after the asymptotic expansion has been performed. Theses methods are validated thanks to an explicit formula obtained in a particular case.