Fourth order compact differnce scheme for 3D convection diffusion equation with boundary layers on nonuniform grids

We present a fourth order compact nite diierence scheme for a general three dimensional convection diiusion equation with variable coeecients on a uniform cubic grid. This high order compact diierence scheme is used to solve convection diiusion equation with boundary layers on a three dimensional nonuniform grid. We compare the computed accuracy and computational eeciency of the fourth order compact difference scheme with that of the standard central diierence scheme and the rst order upwind diierence scheme. Several convection diiusion problems are solved numerically to validate the proposed fourth order compact scheme.