The flow of lattice gas in a two-dimensional channel - The development of a Poiseuille profile

A lattice gas model is presented for the flow between two planes placed parallel to the gas flow. The model assumes a flow of particles closely resembling that of a liquid, and attention is given to flow characteristics at various points of a grid. The calculations proceed by assuming a random distribution particle on one side of the flow and a Poiseuille profile on the other. The density and velocity are sampled at points of the lattice after each iteration. Sample results indicate a monotonic increase occurs in the tangential velocity at the center of the channel, leading to a parabolic velocity profile far downstream. The results are compared with the predictions of Shlichting theory and previous experimental data. The accuracy of the method is demonstrated in both cases.