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The main difficulty with the solution of the incompressible flow equations is the decoupling of the continuity and momentum equations due to the absence of the pressure (or density) term. The Artificial compressibility method is an important method for solving the incompressible Navier-Stokes Equations. In the present study, solution methods for velocity field of incompressible fluids are developed. The mathematical characteristic of governing flow equation used for incompressible fluids is changed from elliptic dominated to hyperbolic dominated, by applying artificial-compressibility concept. Since the governing equations in the Artificial Compressibility method are hyperbolic, flux difference splitting (FDS) originally developed for the compressible Euler equations can be used.In the present upwind compact schemes, the split derivatives for the convective terms at grid points are linked to the differences of split fluxes between neighboring grid points, and these differences are computed by using finite difference scheme. The viscous terms are approximated with a sixth-order central compact scheme. Comparisons with 2D benchmark solutions demonstrate that the present compact schem