A new ‘semi–direct’ method for solving viscous–inviscid interaction problems for high–Reynolds–number separated flows is developed. Both supersonic and subsonic flow separation may be studied using this technique. The method is based upon the vorticity and streamfunction formulation. It is fully implicit with respect to the vorticity equation and ‘interaction law’, which describes the mutual interdependence of the viscous layer near the body surface and the rest of the flow. The main idea of this approach consists of taking advantage of the particular structure of the governing equations, which allows the entire flow field to be solved simultaneously by using the Thomas matrix technique. The method had better numerical stability characteristics than most of the traditional techniques and was also faster than many other techniques developed before.
In this paper the method is used for solving the classical problem of the boundarylayer separation in compression ramp flow. Supersonic and subsonic versions of the problem have been studied. In both cases the semi–direct method allows calculation of flow regimes with extended separation regions corresponding to large ramp angles that could not be analysed using other methods.