Abstract
In this paper a number of topics that arise in application of Chebyshev expansion methods to the solution of the Navier-Stokes equations are addressed. These include the equivalence of finite differences and finite elements approaches, a new velocity-pressure formulation that permits easy extension to three dimensions, evaluation of the importance of pressure boundary conditions and the virtues of collocation over the tau method for satisfying boundary conditions. Example results from the velocity-pressure formulation which eliminate a non-linear momentum equation in favor of the linear continuity equation are presented. The results are for a 2-D unsteady flow on a flat plate at large Reynolds numbers. The behavior of an unsteady disturbance in such a flow is examined and compared with previous stream-function vorticity results of Murdock.
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