Numerical solutions of the Navier-Stokes equations for unsteady boundary-layer flows past a wavelike bulge on a flat plate

Abstract

This paper explores a two-dimensional, incompressible, viscous flow past a wavelike bulge on a flat plate. The effect of the bulge upon the laminar boundary layer, and more significantly upon its transition, is investigated by determining the flow pattern around the bulge. This is performed by numerically solving the time-dependent Navier–Stokes equations, subject to properly chosen boundary conditions. Finite-difference methods are used, and a relatively fine net is chosen to obtain reasonable resolution. The accuracy and stability of the numerical method are of primary importance for achieving meaningful results at the high Reynolds numbers relevant to the present problem. The search for an efficient method has led to the development of a new calculation procedure which has proved more economical with respect to computer time requirements than the conventional explicit methods. Subsequent paragraphs discuss this procedure as well as physical results.