A conformal mapping technique for non-symmetric flows with free-streamlines

A technique is described for efficiently solving for the potential flow past an arbitrary body with separation. The solution involves a conformal mapping using the Schwartz-Christoffel transformation generalized for curved elements. A composite integration scheme is used so that the transformation can be evaluated accurately in the regions around the singularities at the separation points and at corners in the body if they exist. Solutions are given for various cases including flows past flat plates, airfoils, and wedges. A step size study is presented which shows this technique to be second-order accurate. In addition to using the method as a potential flow solver, it may be used as a coordinate system generator. Since the mapping technique is a boundary integral method, virtually any coordinate system can be generated based on the initial mapping of a given boundary or body surface.