The Artificial Compressibility approach is an important numerical method for solving the incompressible Navier-Stokes Equations. The application of high resolution numerical methods to the equations of the artificial compressibility approach is a relatively new phenomenon and deserves further investigation. In this paper we examine the performance of five Riemann solvers: an exact Riemann solver, and four approximate solvers. The application of reflective boundary conditions is investigated, as well as the way in which the artificial compressibility coefficient is chosen.CIT