[For the entire collection see Zbl 0614.00028.]
The indirect viscous-inviscid solvers based on interacting defect integral equations do provide a Navier-Stokes-like capability in computation of massive separations. The approximate defect integral equations have been generalized for massive separations by adjusting the coordinate system where the thin-layer approximations are involved. The coordinate system linked to the displacement body is found satisfactory. The final integral equations are however projected on the directions tangent and normal to the wall, where they are simpler. The integral turbulent closure based on a velocity profile modelling has been generalized for massive separation. The guidelines are to obtain the proper mathematical domains of dependence for the integral equations, insuring the viscous upstream influence recovery in the whole reverse flow range, and to reach the description of the isobaric mixing-layer limit for infinitely-separated boundary layers.
The explicit ”semi-inverse” coupling method of the author [Viscid- inviscid coupling calculations for two- and three-dimensional flows, Lecture Series 1982-04, Von Kármán Institute, Computational Fluid Dynamics (1982)] was found to converge for massive separations of two chord lengths over airfoils at deep stall conditions, or with highly deflected spoilers. The same method is capable to solve the supersonic and transonic shock wave-boundary layer interactions. The ”Semi-Implicit” coupling method is capable to solve time-consistently the strong viscous- inviscid interaction at conditions of buffeting separation.
Very encouraging results are obtained for shock wave-boundary layer interactions, oscillating airfoils, transonic buffeting, computation of airfoils stall, and spoiler-induced separations. For most of these stiff viscous-inviscid interactions, the sensivity to the hysteresis effect of the two-equation model for turbulence is found important, even with the approach of an integral method closure.