Two-Dimensional Boundary-Conforming Orthogonal Grids for External and Internal Flows Using Schwarz-Christoffel Transformation

In this paper, a Schwarz-Christoffel method for generating two-dimensional grids for a variety of complex internal and external flow configurations based on the numerical integration procedure of the Schwarz-Christoffel transformation has been developed by using Mathematica, which is a general purpose symbolic-numerical-graphical mathematics software. This method is highly accurate (fifth order) with mesh size, and is highly flexible for treatment of complex internal flow geometries, for a high degree of control of mesh spacing, and for generation of either orthogonal or non-orthogonal grids. In addition, this method directly generates two-dimensional incompressible potential flow solutions for internal flow, and simply or symmetrical multiply connected external flows: it generates a C type grid for a general multiply connected two-dimensional external flow. The capabilities of this method has been shown by sample cases including external flow over symmetric and antisymmetric airfoils, a car profile, and internal flows with arbitrary shapes. To facilitate further applications, a computer program using Mathematica software has been developed.