Coupling a lattice Boltzmann and a finite difference scheme

Abstract

We show how a lattice Boltzmann (LB) scheme can be spatially coupled with a finite difference (FD) scheme in order to solve the same problem. The typical situation we consider is a computational domain which is partitioned in two regions. The same spatio-temporal physical process extends over the full domain but a different numerical method is used over each region. At the interface of the subdomains, the LB and FD must be connected so as to ensure a perfect continuity of the physical quantities. We derive the theoretical concepts, which allow us to link both methods in the case of a diffusion process, and validate them with numerical simulations on a 2D domain. © Springer-Verlag Berlin Heidelberg 2004.