A LATTICE BOLTZMANN MODEL FOR THE SIMULATION OF FLUID-FLOW

We set out the theory for a Lattice Boltzmann algorithm capable of mimicking the Navier-Stokes equation for fluid flow in two dimensions (2D). The solution satisfies criteria of Galilean invariance and isotropy, and viscosity is obtained by direct reference to the viscous term in the Navier-Stokes equation. It is possible to specify directly the viscosity and other hydrodynamic parameters without reference to specific collision modes. The model was tested by simulating 2D flow through a plane channel (Poiseuille flow). A parabolic flow profile was obtained, in excellent agreement with the analytical Navier-Stokes solution. We conclude that the algorithm can be used to model 2D fluid flow.