It follows from the previous chapters that one of the key elements in the analysis of flow separation from a solid body surface is the investigation of the flow behavior in the region of boundary-layer interaction with the external inviscid flow. Although the interaction region is normally very small, it plays a major role in the separation phenomenon because of the mutual influence of the near-wall viscous flow and external inviscid flow in this region, with a sharp pressure rise prior to the separation point leading to very rapid deceleration of fluid particles near the wall and ultimately to the appearance of the reverse flow downstream of the separation. The complexity of the physical processes in the interaction region is accompanied, as might be expected, by mathematical difficulties in solving the equations that describe the flow in this region. While everywhere outside the interaction region the solution may often be obtained in analytical or at least self-similar form, the analysis of the interaction region requires that special numerical methods be used.

Numerical solution of the interaction problem serves not only to provide meaningful physical information on the development of events in the interaction region, but in many cases also appears to provide the only way of being sure that the solution for this problem really exists, and hence that the entire asymptotic structure of the flow, anticipated in the course of the asymptotic analysis of the Navier–Stokes equations, is self-consistent.