High Order Method for Solving Unsteady Incompressible Navier-Stokes Equations

摘要

A new combined compact upwind (CCU) finite difference(FD) schemes are proposed. Such CCU schemes have high resolving efficiency, which have better performance than that of original schemes, decreasing the dispersive(phase) and dissipative errors of the finite difference approximations. Furthermore, a second-order projection method which has at least third-order accuracy in spatial direction, second-order in time advanced 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.