An Explicit Scheme for the Calculation of Three-Dimensional Turbulent Boundary Layers

Abstract

An explicit finite-difference scheme is formulated for calculating the development of the incompressible turbulent boundary layer on an infinite yawed cylinder. The governing partial differential equations are similar to those used by the author in a previous paper [1], and the empirical content is the same. In their general form the difference equations define a two-step scheme containing two disposable parameters, and numerical experiments have been conducted to determine the stability boundaries, and the boundaries of acceptable numerical precision, in terms of these parameters. By a particular choice of one of the parameters the system reduces to a one-step, staggered-mesh scheme, and it is in this form that the method finally emerges. With 15 collocation points through the boundary layer the method has a typical precision of 2 percent, and with 20 points, 0.5 percent.