Solution of the BGK model kinetic equation for very hard particle interaction. (English) Zbl 0589.76099

Summary: We study the Bhatnagar-Gross-Krook model kinetic equation with a velocity-dependent collision frequency. We derive the conditions that must be verified in order to keep the main physical properties of the Boltzmann equation, i.e., H-theorem and conservation laws. The particular case of the so-called VHP interaction is considered, and the resulting kinetic equation is solved for a homogeneous and isotropic gas. Overpopulation phenomena are observed and analyzed for some kinds of initial conditions. The results are compared, where possible, with the exact solution of the Boltzmann equation.


76P05 Rarefied gas flows, Boltzmann equation in fluid mechanics
82B05 Classical equilibrium statistical mechanics (general)
82B40 Kinetic theory of gases in equilibrium statistical mechanics
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