Numerical solution of the boundary-layer equations.

Abstract

The numerical solution of the boundary-layer equations by means of implicit finite-difference integration, as set forth by Fliigge-Lotz and Blottner, is examined in detail. Ting's recent analysis of the compatibility condition for the velocity components at the initial station suggests a new approach for the integration of the continuity equation. The integration scheme presented here requires only initial data for the tangential velocity component and the temperature, and can handle boundary-layer problems with discontinuities in the initial and/or boundary conditions. Although the original integration procedure for the momentum and energy equations is retained, the integration of the continuity equation is facilitated simultaneously by an iteration process. In this manner the difficulties at the start of the integration are eliminated, and no additional initial conditions for the normal velocity component or the streamwise derivatives of u and T have to be imposed. Several numerical examples are included to demonstrate the application of the method.