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A discrete-velocity scheme for the Boltzmann operator of rarefied gas dynamics. (English) Zbl 0857.76079

Summary: We propose a conservative and entropic discrete-velocity method to compute the solutions of the Boltzmann equation in the case of monoatomic species. We begin by defining a discrete collision kernel on a velocity lattice which exhibits all the properties of the continuous kernel. The continuous Boltzmann equation is replaced by a Boltzmann equation for a discrete velocity gas, which is a hyperbolic system. This equation is discretized by a finite volume scheme. For the evaluation of the collision term we use acceleration procedures of the Monte Carlo type. The possibilities of our scheme are illustrated by numerical tests in one and two space dimensions.

MSC:

76P05 Rarefied gas flows, Boltzmann equation in fluid mechanics
82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics
82B40 Kinetic theory of gases in equilibrium statistical mechanics
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