Abstract: A fourth-order combined compact upwind (CCU) finite difference scheme with high resolving efficiency is proposed. A high-order compact difference algorithm for Navier-Stokes (NS) equations based on projection method is developed with CCU scheme on staggered grids. Convection terms are discretized by CCU scheme. Viscous terms, pressure gradient terms and pressure Poisson equations are discretized with fourth-order compact symmetric finite difference schemes. Numerical examples validate capability of the proposed approach. It is shown that the method is accurate and robust, and is applicable to complex fluid flows.

Key words: high-order accuracy, combined compact upwind scheme, projection method, directly numerical simulation