Numerical conformal mapping and mesh generation for polygonal and multiply-connected regions

Lin, B. and Chandler-Wilde, S. N. ORCID: https://orcid.org/0000-0003-0578-1283 (2000) Numerical conformal mapping and mesh generation for polygonal and multiply-connected regions. Journal of Hydroinformatics, 2 (4). pp. 255-267. ISSN 1464-7141

Abstract/Summary

Details are given of a boundary-fitted mesh generation method for use in modelling free surface flow and water quality. A numerical method has been developed for generating conformal meshes for curvilinear polygonal and multiply-connected regions. The method is based on the Cauchy-Riemann conditions for the analytic function and is able to map a curvilinear polygonal region directly onto a regular polygonal region, with horizontal and vertical sides. A set of equations have been derived for determining the lengths of these sides and the least-squares method has been used in solving the equations. Several numerical examples are presented to illustrate the method.