On a conservative polar discretization of the Boltzmann equation

Abstract

The paper presents a discretization of the Boltzmann equation obtained by writing the collision operator in polar coordinates, discretizing the velocity moduli and introducing a suitable class of basic interpolants. The model obtained is a system of integro-differential equations with integration over suitable angular variables: one over the portion of the unit sphere between two parallels symmetric with respect to the equatorial plane perpendicular to the velocity of the field particle and one over a unit circle. The model preserves mass, momentum and energy and an H-theorem is proved.