Asymptotic Approximation and Perturbation Stream Functions in Viscous Flow Calculations

An asymptotic approximation technique is shown to substantially decrease the number of interations necessary for the accurate computation of steady solutions for viscous incompressible flows. A numerical study of flows exterior to a circular cylinder indicates that the technique reduces the required number of iterations by a factor of 10. The flux formulation of the vorticity stream function solution for the flow of a viscous incompressible fluid external to a circular cylinder requires the solution of the Poisson equation for the stream function. The use of the FACR (1), fast direct Poisson equation solver leads to serious errors in the computation of the stream function near the cylinder. However it is shown that these errors are eliminated through the introduction of a perturbation stream function.