Numerical and analytical spatial coupling of a lattice Boltzmann model and a partial differential equation

Abstract

This article is concerned with the spatial coupling of a lattice Boltzmann model (LBM) and the finite difference discretization of the corresponding partial differential equation (PDE). At the interface, we have a one-to-many problem since the macroscopic PDE variables have to be mapped to more LBM variables. We show how this mapping can be done either analytically, using results from the Chapman-Enskog expansion or numerically, using a fixed point iterative scheme. The results are illustrated for different diffusive systems on a one-dimensional domain. © 2006 Springer-Verlag Berlin Heidelberg.