Applications of numerical conformal mapping

The application of conformal mapping methods to the solution of free-surface flow problems is considered. Methods of numerical conformal mapping based on Fourier series are extended to handle efficiently problems with time-dependent boundaries. They are shown to be practicable only for moderately distorted geometries. Extensions of the Menikoff-Zemach method to "breaking" geometries are presented. These latter methods are robust at quite large distortions, but degrade prematurely in time-dependent problems at amplitudes smaller than achieved by our recent vortex methods.