The steady laminar incompressible boundary-layer problem as an integral equation in crocco variables the calculation of non-similar flows

Abstract

The steady laminar incompressible boundary-layer problem in two dimensions has been posed as an integral equation in Crocco variables in the most general case and an algorithm developed for computing the similarity flows (Mills 1966). The present report extends the algorithm to compute non-similar flows. Essentially it consists of replacing the x-derivative terms in the integral equation by finite differences so that the problem reduces to solving a non-linear integral equation across the boundary layer at successive x-stations starting from an initial solution at x = 0. To obtain convergence a double-field type of iteration with two relaxation factors has to be used. An analysis of the convergence of the process is given in the Appendix. The algorithm was found experimentally to be stable for every combination of step-sizes tried. A local matrix stability analysis of the algorithm is given in the Appendix. A large number of examples have been computed, particularly flows with discontinuous suction distributions, periodic flows and separating flows. For the standard problems the results are in agreement with the known accurate computations. Some new problems are computed.