Numerical Integration of the Equations for the Steady Incompressible Boundary Layer. (Discussion of Different Approaches, Theoretical Background for a Special Form of Galerkin's Method)

摘要

The report discusses under a unifying point of view a number of different methods for solving the boundary layer equation. This is done by studying a model equation which has some of the features of the boundary layer equation. Inherent in the problem is the fact that all numerical approaches lead to systems of stiff difference or differential equations which must be solved numerically. Stiffness can cause numerical instability (even though the problem itself is stable). Different methods of solving the boundary layer equation can be regarded as different ways of coping with the stiffness problem. By this analysis the authors are led to a special form of Galerkin's method for which the resulting system of ordinary differential equations has a form in which stiffness can be handled rather easily. Important for this procedure is the representation of the solution in terms of asymptotic expressions for the eigenfunctions of the operator governing the original differential equation. In the second part the application of this idea to the incompressible boundary layer equation is discussed. (Author)