Numerical Conformal Mapping and Its Application to the Two-Dimensional Potential Flow Analysis

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Conformal mappings are familiar in science and engineering. But, exact mapping functions are not known except for special domains. Particularly, conformal mappings of unbounded multiply-connected domains are well known as a method of two-dimensional potential flow analysis. The mappings of a domain exterior to closed Jordan curves onto parallel, circular and radial slit domains are directly related to the problems of uniform, vortex and point-souce flows around obstacles, respectively.We presented a simple method of numerical conformal mappings of the multiply-connected domains onto the parallel, circular and radial slit domains. We reduced the mapping problems to the Dirichlet problem with a pair of conjugate harmonic functions and employed the charge simulation method, where the pair of conjugate harmonic functions are appoximated by a linear combination of complex logarithmic potentials. The method has the following features :1. Conformal mappings onto the parallel slit domains with slits parallel to the imaginary axis and parallel to the real axis constitute a dual problem and can be computed in a dual way.2. Conformal mappings onto the circular and radial slit domains constitute a dual problem and can be computed in a dual way.3. They are reformulated into a more integrated form in which the linear equations to be solved have the same coefficient matrix.