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

Buet, C.

Transp. Theory Stat. Phys. 25, No. 1, 33-60 (1996).

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

Keywords:

conservative entropic discrete-velocity method; monoatomic species; discrete collision kernel; hyperbolic system; finite volume scheme; acceleration procedures of Monte Carlo type

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