Riv. Mat. Univ. Parma, Vol. 1, No. 2, 2010

Aude Champmartin, Laurent Desvillettes and Julien Mathiaud

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

Pages: 271-305
Received: 21 October 2010   
Accepted: 5 November 2010
Mathematics Subject Classification (2010): 76P05, 76T10, 82C40.

Keywords: Sprays, inelastic Boltzmann equation, BGK model.

Abstract: We introduce a model of inelastic collisions for droplets in a spray, leading to a specific 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.

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