A semi-direct method for calculating flows with viscous-inviscid interaction

A new 'semi-direct' method for solving viscous-inviscid interaction problem s for high-Reynolds-number separated flows is developed. Both supersonic an d subsonic flow separation may be studied using this technique. The method is based upon the vorticity and streamfunction formulation. It is fully imp licit with respect to the vorticity equation and 'interaction law', which d escribes the mutual interdependence of the viscous layer near the body surf ace and the rest of the flow. The main idea of this approach consists of ta king advantage of the particular structure of the governing equations, whic h allows the entire flow field to be solved simultaneously by using the Tho mas matrix technique. The method had better numerical stability characteris tics 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 b oundary-layer separation in compression ramp flow. Supersonic and subsonic versions of the problem have been studied. In both cases the semi-direct me thod allows calculation of flow regimes with extended separation regions co rresponding to large ramp angles that could not be analysed using other met hods.