Numerical Conformal Mapping by the Charge Simulation Method and its Application to Potential Flow Analysis

Abstract

Conformal mappings are familiar in science and engineering. But exact mapping functions are not known except for special domains. Particularly confomal mappings of a domain exterior to closed Jordan curves onto parallel, circular and radial slit domains are well known as a method of two-dimensional potential flow analysis. But no systematic method of computation has been established for these mappings. We here present a simple method of numerical conformal mappings of the multiply-connected domains and apply it to a typical flow problem. We use the charge simulation method for computation, which is known as a rapid solver of potential problems. A pair of conjugate harmonic functions are approximated by a linear combination of complex logarithmic potentials.