Mathematical and Numerical Study of a Dusty Knudsen Gas Mixture

Abstract

We consider a mixture composed of a gas and dust particles in a very rarefied setting. Whereas the dust particles are individually described, the surrounding gas is treated as a Knudsen gas, in such a way that interactions occur only between gas particles and dust by means of diffuse reflection phenomena. After introducing the model, we prove existence and uniqueness of the solution and provide a numerical strategy for the study of the equations. At the numerical level, we focus our attention on the phenomenon of energy transfer between the gas and the moving dust particles.

Mathematical and Numerical Study of a Dusty Knudsen Gas Mixture: Extension to Non-spherical Dust Particles

“…We briefly recall the model introduced in [7] and generalize it to non-spherical particles. We consider a free transport equation in a open bounded spatial domain D ⊂ R d , d ∈ N * , which describe the evolution of the molecules density…”

“…In [13], the motion of a rigid body immersed in a gas is governed by the Newton-Euler equations, where the force and the torque on this body are computed from the momentum transfer of the gas molecules colliding with the body ; the gas is described by a Boltzmann equation without any effect of the body on the gas. The point of view adopted in [7] is rather different. The interaction between the gas and the particles (in finite number) is modeled by considering the evolution of the gas in a moving domain, where the boundary of the domain include the surface of the particules.…”

“…The paper is organised as follows. We first recall the model introduced in [7] for spherical particles, that we extend to any shape of particle. We then precise the proof of the existence of solutions announced in [7].…”

“…We first recall the model introduced in [7] for spherical particles, that we extend to any shape of particle. We then precise the proof of the existence of solutions announced in [7]. Finally we present a new numerical strategy, which allow to perform numerical simulations with non-spherical particles, and some scenarios of numerical simulations.…”

“…The gas is treated as a Knudsen gas, whereas the interaction between dust particles and gas molecules is modeled by considering a moving domain free transport equation (including the boundary with the particles and the boundary of the domain). We here precise the proof of existence of solutions to the initial-boundary value problem annonced in [7]. Moreover, we introduce a new numerical strategy, based on a splitting between the transport of the gas molecules and the movement of the boundary.…”