Computation of flows including strong viscous interactions with coupling methods

The approximation levels and concepts are outlined, as well as the generalized formulations of the viscous displacement for inviscid flow. The strongly interacting methods that are based on thin viscous layers approximations are discussed. A matching formulation of the viscous flow, calculated as a difference of the inviscid overlaying flow, is presented in order to approximate the normal pressure gradient inside of the layers, as well as to eliminate the supercritical behaviors, in the Crocco-Lees sense. This analysis uses simple viscous integral equations. Numerical techniques presently available for the coupling problem are reviewed. Results are presented for trailing-edge separation, and an approximation method is presented to numerically analyze the viscous interaction under shock waves.