Numerical Methods in Boundary-Layer Theory

There is a large variety of numerical methods that are used to solve the many flow problems to which boundary-layer theory is applied. Two particular methods, the Crank-Nicolson scheme and the Box scheme, seem to dominate in most practical applications. Of course these methods are not uniquely defined and there are many variations in their formulation as well as in the procedures used to solve the resulting (nonlinear) algebraic equations. They are both implicit with respect to variation normal to the boundary layer, they can both be second-order accurate in all variables, both can be improved to yield even higher-order accuracy. However, I prefer and stress the Box scheme as it is very easy to adapt to new classes of problems. It also allows a more rapid net variation and ease in obtaining higher-order accuracy. scheme was devised in Keller (1971), for solving diffusion problems, but it has subsequently been applied to a broad class of problems. A recent survey by Blottner (1975a) has stressed the Crank-Nicolson scheme. I suggest that article as well for a presentation of various other numerical methods that have been used. A sketch of the applications of the Box scheme to a variety of boundary-layer flow problems is given in Keller (1975b). of the problems and techniques presented in this survey have been worked out with T. Cebeci. Details of some of these techniques and even listings of a few of the codes appear in a text by Cebeci & Bradshaw (1977).