GENERALIZED DISCRETE VELOCITY MODELS

Abstract

Starting from a mesoscopic principle of moment conservation, discrete Boltzmann collision operators Jh are constructed, which both converge to bounded collision operators JΩ and have the same collision invariants as the original Boltzmann collision operator J. The crucial point of this construction is the application of a weak formulation of the gain operator to remove the post-collision velocities from it as well as the development of moment conserving integration formulas for the approximation of surface integrals over the unit sphere. Finally two applications for the discrete operators are presented.