Simplification and Improvement of a Numerical Method for Navier-Stokes Problems

Abstract

Previously, a viable numerical method for the Navier-Stokes equations was developed and applied to two-dimensional, steady state problems, to three-dimensional, axially symmetric, steady state problems, and to a class of nonsteady problems which had stearly state solutions. The method applied for all Reynolds numbers. Among other things, it required the construction of a double sequence of stream and vorticity functions and an appropriate selection of smoothing parameters to assure convergence. Both these complexities are eliminated in the method of this paper. Moreover, illustrative examples show that the new method is faster than the previous one and more accurate for physically sensitive problems.