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International Journal for Multiscale Computational Engineering
IF: 1.016 5-Year IF: 1.194 SJR: 0.554 SNIP: 0.82 CiteScore™: 2

ISSN Print: 1543-1649
ISSN Online: 1940-4352

International Journal for Multiscale Computational Engineering

DOI: 10.1615/IntJMultCompEng.v4.i2.20
pages 209-219

A Hybrid Lattice Boltzmann Finite Difference Scheme for the Diffusion Equation

Paul Albuquerque
Computer Science Department, University of Geneva, 1211 Geneva 4, Switzerland; and LII, Ecole d'Ingénieurs de Genéve, HES-SO, 1202 Geneva, Switzerland
Davide Alemani
CABE, University of Geneva, 1211 Geneva 4, Switzerland
Bastien Chopard
Computer Science Department, University of Geneva, 1211 Geneva 4, Switzerland
Pierre Leone
Computer Science Department, University of Geneva, 1211 Geneva 4, Switzerland

ABSTRACT

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.


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