A new method of numerical integration of the equations of the laminar boundary layer

Abstract

A new method for the numerical soiution of the boundary-layer equations is described. This rests in essence on the fact that the equations of steady flow are special cases of the equations of general motion. The velocity profiles are found at successive sections across the boundary layer. Trial values of the velocity are assumed at any section; from these, space derivatives of the velocity are deduced by using finite differences, and time derivatives by using the equations of motion. The trial values are then adjusted to give zero time derivatives of the velocity at the section. The method in some respects resembles Southwell's relaxation method. The method has been applied to two problems already discussed numerically by Hartree. It is not suitable for use with a differential analyser, though the development of new calculating machines may bring it within the range of machine integration; but rather less labour was required to achieve manually with it results rather more accurate than obtained by Hartree with the differential analyser. The results did not, however, differ greatly from Hartree's.