Calculations of the incompressible turbulent boundary layer on an ellipsoid in the inverse mode

The boundary layer equations for three-dimensional, incompressible, turbulent flow have been solved using the inverse formulation. In this formulation the displacement thicknesses are prescribed and the pressure distribution is the result of the calculation. The geometry used is the ellipsoid of revolution, and the turbulence model used is based on the concept of the anisotropic eddy-viscosity. A finite-difference procedure has been used in the calculations. It was found that, for the case of the ellipsoid, the inverse formulation is capable of allowing marching into regions that are inaccessible to calculations that use prescribed pressure. Therefore it seems feasible to use such a formulation for future viscous/inviscid interaction procedures, in order to study three-dimensional separation from smooth surfaces. The procedure also provides an alternative to windward differencing, for flows with reversed circumferential flow.