Investigation of some finite-difference techniques for solving the boundary layer equations

Abstract

The Levy-Lees form of the laminar boundary layer equations is solved with several second-order accurate finite-difference schemes. For incompressible flow the methods investigated include three forms of the Crank-Nicolson scheme, four variations of the Keller box scheme and a modified box scheme. The number of iterations required at each step along the surface to obtain a second-order accurate scheme is studied. The accuracy of the schemes with various step-sizes is determined for the boundary layer flow with a linearly retarded edge velocity. In addition, one form of the Crank-Nicolson scheme is extended to compressible flows and its accuracy and behavior are also examined for the linearly retarded flow case. The results of this investigation show that the coupled continuity-momentum form of the Crank-Nicolson scheme is second-order with one iteration at each step and requires less time than the Keller box scheme.