A BGK-type model for inelastic Boltzmann equations with internal energy.

Aude Champmartin (1, 2) , Laurent Desvillettes (2, 3) , Julien Mathiaud (1, 2)

1 DAM/DIF - DAM Île-de-France
2 CMLA - Centre de Mathématiques et de Leurs Applications
3 IUF - Institut universitaire de France

We introduce a model of inelastic collisions for droplets in a spray, leading to a speci c Boltzmann kernel. Then, we build caricatures of this kernel of BGK type, in which the behavior of the first moments of the solution of the Boltzmann equation (that is, mass, momentum, directional temperatures, variance of the internal energy) are mimicked. The quality of these caricatures is tested numerically at the end of the paper.

Mots clés: Sprays; inelastic Boltzmann equation; BGK model

Domaines: Modélisation et simulation; Mécanique des fluides [physics.class-ph]; Mécanique des fluides [physics.class-ph]

Aude Champmartin, Laurent Desvillettes, Julien Mathiaud. A BGK-type model for inelastic Boltzmann equations with internal energy.. Rivista di Matematica della Università di Parma, 2010, 1 (2), pp.271-305. ⟨hal-00589307⟩