Regular and multiscale expansions of a lattice Boltzmann method

摘要

In this paper we focus on the analysis of lattice Boltzmann schemes by asymptotic methods. We consider a simple lattice Boltzmann algorithm, which is used to develop and to illustrate the ideas simultaneously. Specifically, we address the following questions: How to perform a consistency analysis of numerical schemes by regular expansions? Where are the shortcomings of regular expansions? What are multiscale expansions and how do they come naturally into play, to understand numerical algorithms more accurately?