A Consistency Result for a Discrete-Velocity Model of the Boltzmann Equation

Abstract

In this paper, we study the link between a certain class of discrete-velocity models (DVMs) and the Boltzmann equation. Those models possess an infinite number of velocities laying on a regular grid of step h in R3. Our aim is to prove that it is possible to construct models consistent with the Boltzmann equation, i.e., such that the discrete collision term can be seen as an approximation of the collision integral of the Boltzmann equation.