Numerical experiments with the lid driven cavity flow problem

The centerline velocity profiles obtained from the solution of the two- and three-dimensional representations of the lid driven cavity flow problem are compared for different Reynolds numbers. Two configurations were used in this study: a unit cavity and a cavity with an aspect ratio of 2. The Reynolds numbers ranged from 100 to 5000 for all of the configurations studied. A new method of extending the Jacobi collocation technique called spectral difference is developed in this paper together with a unique computational grid. In addition, an iterative method for solving the pressure problem is also developed. This new numerical method allowed the calculation of three-dimensional Navier-Stokes equations to be performed in computers with very modest computational capabilities such as workstations.