numerical solution of unsteady two dimensional couette flow, using finite difference lbm

a two dimensional finite difference lattice boltzmann method (fdlbm) for computing single phase flow problems is developed here. temporal term is discretized with low dissipation-low dispersion. discretization of convective term is implemented with third order upwind method. it will be explained governing equations and numerical method. methodology of imposing boundary conditions in fdlbm is described. then for evaluation, two basic problems will be solved: taylor's vortices and unsteady couette flow. the purpose of this paper is the presentation of a robust method to solve unsteady and steady problems.