Pressure methods for the approximate solution of the Navier-Stokes equations

In this paper, a family of powerful finite difference methods for the numerical solution of the Navier-Stokes equations for incompressible fluids is developed and applied. The power is derived by combining advantageous aspects of the marker-and-cell method with several special techniques for hyperbolic and parabolic equations. The stability of the methods, in the discrete L2 norm, is demonstrated to be independent of the pressure and is shown to depend only on the discretizations chosen for the convective and viscous terms. Appropriate choices of such discretizations are then suggested. A numerical example is described and discussed.