Application of the boundary-value technique to singular perturbation problems at high Reynolds numbers

Abstract

The boundary-value technique, advanced by Roberts for the solution of singular pertubation problems of ordinary differential equations where the small parameter multiples the highest derivative, is extended to the solution of the Navier-Stokes equation at high Reynolds numbers. Three standard flows—uniform flow past a plate, flow with a linearly adverse external velocity, and shear flow past a flat plate—have been chosen as test problems with a view to evaluating some of the features of the boundary-value technique, particularly in comparison with coefficient matching techniques as examplified by the method of matcher asymptotic expansions.