NUMERICAL COMPUTATION OF SCHWARZ-CHRISTOFFEL TRANSFORMATION FOR SIMPLY CONNECTED UNBOUNDED DOMAIN

A direct numerical conformal mapping based on the modified Kantorovich method is developed to transform the upper half-plane onto a bounded or unbounded polygon in the complex domain. The 'accessary parameters' in the Schwarz-Christoffel formula are determined iteratively from solving a set of nonlinear equations which are in terms of the side-length ratios of the polygon. Both pure and compound Gauss-Jacobi quadratures are employed to evaluate the improper integrals and their first order derivatives with end-point singularities. In addition to the parameter determination, the computational schemes for forward and inverse mapping which can be applied to the numerical grid generation for computational fluid dynamics are also presented. Several examples are provided in order to demonstrate the advantage of this approach.