Lattice Boltzmann equation on a two-dimensional rectangular grid

sWe construct a multirelaxation lattice Boltzmann model [1] on a two-dimens ional rectangular grid. The model is partly inspired by a previous work of Koelman [2] to construct a lattice BGK model on a two-dimensional rectangul ar grid. The linearized dispersion equation is analyzed to obtain the const raints on the isotropy of the transport coefficients and Galilean invarianc e for various wave propagations in the model. The linear stability of the m odel 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 c onditions: (b) Poiseuille flow with an arbitrary inclined angle with respec t to the lattice orientation; and (c) a cylinder asymmetrically placed in a channel. The numerical results of these tests are compared with either ana lytic solutions or the results obtained by other methods. Satisfactory resu lts are obtained for the numerical simulations. (C) 2001 Academic Press.