Finite solution of the Navier Stokes equations

The solution of fluid mechanics problems defined by the Navier-Stokes equations presents such analytical difficulties that numerical methods using finite difference/finite elements appear to be the only reasonable means of solution within the foreseeable future. In this paper, a number of interesting fluid mechanics problems including the two-dimensional Navier-Stokes equations governing the steady state, viscous, incompressible flow within a cavity are solved using the finite element program TWODEPEP with automatic user-controlled mesh grading. The finite element used is the standard six-node triangle with quadratic basis functions with one edge curved when adjacent to a curved boundary according to the isoparametric method. In addition, the main principles of software package design for a preprocessor program which reads the user input describing the problem in a problem-oriented format designed to minimize the user effort is also described.