Numerical methods for the Navier-Stokes equations with reference to the driven cavity problem

A number of formulations for the solution of the Navier-Stokes equations are given with reference to steady state incompressible flow. The driven cavity problem is used as a numerical test case for the methods examined. A number of finite difference and finite element schemes have been used to reduce the problem to a form suitable for numerical computation. Convergence of the iterative procedures for the solution of the non-linear systems of equations is often difficult, frequently requiring very fine meshes and accurate starting points for the iterative techniques used.