A Second-Order Combined Compact Upwind Difference Scheme for the Navier-Stokes Equations

Based on the developed thirdand fourth-order upwind compact finite difference(FD) schemes, a new high-order weighted upwind FD approach, which is called combined compact upwind FD method, is proposed for decreasing dispersive(phase) and dissipative errors of the finite difference approximations. The newly proposed combined compact upwind FD schemes have the characters of group velocity control scheme which can obtain a large group velocity control range. In this paper the optimum combined scheme is proposed by applying the dispersion-relationpreserving (DRP) idea. Furthermore a second-order projection algorithm which has at least third-order accuracy in spatial direction is developed for solving the incompressible, two-dimensional Navier-Stokes equations. Numerical examples are given to validate the performance and efficiency of the new projection algorithm proposed. The results show that the present method has desired accuracy and resolution. The proposed method can be extended to the solution of the complex fluid flow problems. Key-Words: high-order accuracy, combined compact upwind scheme, projection method, directly numerical simulation