Journal of Computational Physics 172, 704–717 (2001) doi:10.1006/jcph.2001.6850, available online at http://www.idealibrary.com on Lattice Boltzmann Equation on a Two-Dimensional Rectangular Grid M’hamed Bouzidi, ∗ Dominique d’Humi` eres, ∗, † Pierre Lallemand, ∗ and Li-Shi Luo‡ ∗ Laboratoire C.N.R.S.-A.S.C.I., Bˆ atiment 506, Universit´ e Paris-Sud (Paris XI Orsay), 91405 Orsay Cedex, France; †Laboratoire de Physique Statistique de l’ ´ Ecole Normale Sup´ erieure, 24, Rue Lhomond, 75321 Paris Cedex 05, France; ‡ICASE, MS 132C, NASA Langley Research Center, 3 West Reid Street, Building 1152, Hampton, Virginia 23681-2199 E-mail: bouzidi@asci.fr; Dominique.Dhumieres@lps.ens.fr; lalleman@asci.fr; luo@icase.edu Received January 4, 2001; revised May 23, 2001 We construct a multirelaxation lattice Boltzmann model [1] on a two-dimensional rectangular grid. The model is partly inspired by a previous work of Koelman [2] to construct a lattice BGK model on a two-dimensional rectangular grid. The linearized dispersion equation is analyzed to obtain the constraints on the isotropy of the trans- port coefficients and Galilean invariance for various wave propagations in the model. The linear stability of the model is also studied. The model is numerically tested for three cases: (a) a vortex moving with a constant velocity on a mesh with periodic boundary conditions; (b) Poiseuille flow with an arbitrary inclined angle with respect to the lattice orientation; and (c) a cylinder asymmetrically placed in a channel. The numerical results of these tests are compared with either analytic solutions or the results obtained by other methods. Satisfactory results are obtained for the numerical simulations. c  2001 Academic Press 1. INTRODUCTION Historically originating from the lattice gas automata (LGA) introduced by Frisch, Hasslacher, and Pomeau [3], the lattice Boltzmann equation (LBE) has recently become an alternative method for computational fluid dynamics. The essential ingredients in any lattice Boltzmann models which are required to be completely specified are: (i) a discrete lattice space on which fluid particles reside; (ii) a set of discrete velocities (often going from one node to its nearest neighbors) to represent particle advection; and (iii) a set of rules for the redistribution of particles residing on a node to mimic collision processes in a real fluid. Fluid-boundary interactions are usually approximated by simple reflections of the particles by solid interfaces. 704 0021-9991/01 $35.00 Copyright c  2001 by Academic Press All rights of reproduction in any form reserved.