A DIFFUSIVE LIMIT FOR NONLINEAR DISCRETE VELOCITY MODELS

Abstract

This paper is devoted to the analysis of the diffusive limit for a general discrete velocity model of the Boltzmann equation in any dimension of the physical space, for densities which remain in a suitable small neighbourhood of global Maxwellians. The scaled solutions of discrete Boltzmann equation are shown to have fluctuations that converge locally in time weakly to a limit governed by a solution of incompressible Stokes equations provided that the initial fluctuations are smooth. The weak limit becomes strong when the initial fluctuations converge to appropriate initial data. As applications the Carleman model and the one-dimensional Broadwell model are analyzed in detail.