A physically optimum difference scheme for three-dimensional boundary layers

A new finite difference scheme has been formulated for the three-dimensional boundary layer equations based on the physics of the convective and diffusive momentum transport in the boundary layer. It is shown that the scheme is a physically optimum one and that it is consistent with the usual specification of initial conditions. A stability analysis of the linearized equations shows that a relative restriction is necessary on the step sizes along the convective coordinates even though the difference scheme is "implicit". The method is then applied to a problem that taxes the method and the laminar boundary layer equations to their limit; that problem being the supersonic flow over a spinning sharp cone at angle of attack. The results of the spinning cone calculation also yields some very useful insight into the "Magnus" problem and to the contributions to the "Magnus" force by the boundary layer flow.