Numerical Conformal Mappings by the Charge Simulation Method and Their Applications to Fluid Mechanics

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The numerical conformal mapping has been an important subject in computational and applied mathematics. Our major concern is to develop new methods of numerical conformal mappings by the charge simulation method (or the fundamental solution method) and apply them to potential flow problems.1.We constructed approximate mapping functions of the conformal mapping w= f(z) of an unbounded multiply connected domains D onto the unbounded canonical slit domains of Nehari (Mc-Graw Hill, 1952) under the condition f(v) = ∞, where v is a finite point given in the problem domain. They were applied to the problem of potential flows past obstacles caused by a dipole source, a pair of positive and negative vortexes or a pair of point source and sink.2.We constructed by the charge simulation method approximate mapping functions of the conformal mapping of bounded multiply connected domains onto all the unbounded and bounded canonical slit domains of Nehari.3.We proposed a new technique to apply the charge simulation method to a nonlinear compressible fluid flow problem. We also proposed a fundamental solution method for viscous flow problems with obstacles in a periodic array, which gives an approximate solution by a linear combination of periodic fundamental solutions.4.We proved the convergence of the approximate mapping function obtained by the charge simulation method.Many other interesting results were obtained in relation to methods of numerical computation and thier application to fluid mechanics.