%0 Journal Article %A Alemani, Davide %A Chopard, Bastien %A Albuquerque, Paul %A Leone, Pierre %D 2006 %I Begell House %N 2 %P 209-219 %R 10.1615/IntJMultCompEng.v4.i2.20 %T A Hybrid Lattice Boltzmann Finite Difference Scheme for the Diffusion Equation %U https://www.dl.begellhouse.com/journals/61fd1b191cf7e96f,329fc71d60f835ec,3cbd3d7f68d44b20.html %V 4 %X We show how a lattice Boltzmann (LB) can be spatially coupled with a finite difference (FD) scheme, each method running on a separate region, to solve a given problem. The typical situation we consider is a computational domain that is partitioned into two regions. The same spatiotemporal 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 two-dimensional domain. We also consider the case of different size grids for which the coupling has to be complemented with an interpolation procedure. %8 2006-08-22