ANALYTICAL SOLUTIONS OF THE LATTICE BOLTZMANN BGK MODEL

Analytical solutions of the two-dimensional triangular and square latt ice Boltzmann BGK models have been obtained for the plane Poiseuille f low and the plane Couette flow. The analytical solutions are written i n terms of the characteristic velocity of the flow, the single relaxat ion time tau, and the lattice spacing. The analytic solutions are the exact representation of these two flows without any approximation. Usi ng the analytical solution, it is shown that in Poiseuille flow the bo unce-back boundary condition introduces an error of first order in the lattice spacing. The boundary condition used by Kadanoff et nl. in la ttice gas automata to simulate Poiseuille flow is also considered for the triangular lattice Boltzmann BGK model. An analytical solution is obtained and used to show that the boundary condition introduces an er ror of second order in the lattice spacing.