A numerical treatment of two dimensional Navier-Stokes equations

A one parameter family of central difference and upwind difference schemes are derived for the solution of two-dimensional Navier-Stokes equations by taking weighted average of its convective and divergence forms. Resulting system of equations is solved by a direct solver. The schemes are tested on four examples whose exact solutions are known, to obtain the value of optimal parameter and make a comparison between central and upwind difference schemes. The results are reported.