A numerical method for highly accelerated laminar boundary-layer flows

Abstract

A second-order-accurate implicit finite difference method is developed to study the boundary-layer flows that occur just upstream of a trailing edge which is attached to a free streamline. An important feature of this technique is the use of an asymptotic expansion to satisfy the boundary condition at the edge of the boundary layer while retaining a rapid algorithm for inverting the system of linear equations for each Newton iteration. The method is applied to the Kirchhoff-Rayleigh flow past a finite flat plate set perpendicular to a uniform stream. Computed velocity profiles are found to be in excellent agreement with those obtained from an asymptotic solution (Ackerberg (1970), (1971a), (1971b)) with pointwise differences being less than 1.2% over two-thirds of the profile. A detailed description of the method is given in Ackerberg and Phillips (1973).

This work was supported by the U.S. Army Research Office-Durham under Grant No. DA-ARO-D-31-124-71-G68.