Boundary conditions for the upwind finite difference Lattice Boltzmann model: Evidence of slip velocity in micro-channel flow

We conduct a systematic study of the effect of various boundary conditions (bounce back and three versions of diffuse se reflection) for the two-dimensional first-order upwind finite difference Lattice Boltzmann model, Simulation of Couette flow in a micro-channel using the diffuse reflection boundary condition reveals the existence of a slip velocity that depends on the Knudsen number epsilon = lambda/L, where lambda is the mean free path and L is the channel width. For walls moving in opposite directions with speeds +/- u(w), the slip velocity satisfies u(slip) = 2/epsilon tt(wall)(1 + 2 epsilon). In the case of Poiseuille flow in a micro-channel, the slip velocity is found to depend on the lattice spacing delta s and Knudsen number E to both first and second order. The best results are obtained for diffuse reflection boundary conditions that allow thermal mixing at a wall located at half lattice spacing outside the boundary nodes. (c) 2005 Elsevier Inc. All rights reserved.