Interacting supersonic laminar wake calculations by a finite difference method.

An implicit finite difference method is used to study the interaction of a laminar viscous wake with a supersonic, external, inviscid flow downstream of the wake stagnation point. The boundary-layer equations are used to describe the subsonic portion of the flow, with the effect of transverse pressure gradients in the supersonic viscous region included through the use of an inviscid transverse momentum equation. The von Mises coordinate system is used for simplicity in applying boundary conditions. Calculations indicate that for any oneparameter family of initial profiles, the solution proceeds downstream in a physically meaningful manner for only certain discrete values of the parameter. All other values of the parameter produce solutions of one of two types: either the centerline velocity reaches a maximum and then decreases until a second wake stagnation point is reached, or the centerline pressure drops rapidly toward zero at some downstream point. These results agree qualitatively with the Crocco-Lees theory and with previous investigations of interacting wakes using boundary-layer equations solved by integral methods.