Fourth order 'Mehrstellen'-integration for three-dimensional turbulent boundary layers

A new finite difference solution for Prandtl's boundary-layer equations is described in detail for steady, incompressible laminar and turbulent flows. Only boundary sheets will be considered and curvature effects in the direction normal to the wall will be neglected. The governing equations are presented in form of a vector equation. Their numerical stability is discussed for an elementary finite difference molecule. Improved finite-difference approximations with a truncation error of fourth order are then introduced to enable either increased accuracy or shortened calculation times, in particular, for three-dimensional problems. Detailed studies of the behavior of the overall error of the solution and several applications to real flow situations supplement the general considerations.