A physically optimum difference scheme for threedimensional boundary layers
Abstract
A new finite difference scheme has been formulated for the threedimensional 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.
 Publication:

Numerical Methods in Fluid Dynamics
 Pub Date:
 1975
 DOI:
 10.1007/BFb0019742
 Bibcode:
 1975LNP....35..144D
 Keywords:

 Boundary Layer Equations;
 Finite Difference Theory;
 Laminar Boundary Layer;
 Three Dimensional Boundary Layer;
 Angle Of Attack;
 Boundary Layer Flow;
 Convective Flow;
 Cross Flow;
 Diffusivity;
 Flow Velocity;
 Magnus Effect;
 Numerical Analysis;
 Shear Flow;
 Supersonic Flow;
 Fluid Mechanics and Heat Transfer