From collisional kinetic models to sprays: internal energy exchanges

Frédérique Charles (1, 2) , Laurent Desvillettes (3, 4)

1 SU - Sorbonne Université
2 LJLL (UMR_7598) - Laboratoire Jacques-Louis Lions
3 UPCité - Université Paris Cité
4 IMJ-PRG (UMR_7586) - Institut de Mathématiques de Jussieu - Paris Rive Gauche

In this paper, we present an improvement of the modeling of collisional operators introduced in [6] and [5], which are devoted to the modeling of the interaction between macroscopic dust particles and molecules of a rarefied gas. The model developed in [6] is based on the hypothesis that collisions between dust particles and gas molecules are inelastic and are given by a diffuse reflexion mechanism on the surface of dust particles. In the present work, we propose a model which preserves the total energy by introducing a new variable in the density function of macroscopic particles. We then write the equations in non-dimensional form, and establish, like in [10], a formal asymptotics to the Vlasov-Euler equation of compressible fluid when two small parameters tend to zero, namely the ratio of masses between gas molecules and dust particles on the one hand, and the Knudsen number of the gas on the other hand.

Domaines: Equations aux dérivées partielles [math.AP]

Frédérique Charles, Laurent Desvillettes. From collisional kinetic models to sprays: internal energy exchanges. 2024. ⟨hal-03840523v3⟩