An error analysis of finite-difference approximations for the boundary-layer equations

A description is presented of an approach for determining the truncation error by a compact discretization procedure, taking into account the case of a finite-difference solution for a two-dimensional, steady, incompressible laminar boundary layer. The derivations can be extended to three-dimensional as well as unsteady and compressible flows. The main difficulty concerning the determination of the error is related to the achievement of a satisfactory accuracy. The different formulation of the truncation error is discussed, and the implementation of the considered procedure is illustrated with the aid of examples, giving attention to three typical boundary-layer flows. The selected flows include uniform, accelerated, and retarded flows. The step sizes can be adapted in such a way that the calculation time is kept as much as possible at a minimum.