Lattice Boltzmann Equation on a Two-Dimensional Rectangular Grid

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 transport 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.