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A noniterative method for the generation of orthogonal coordinates in doubly-connected regions

Authors: Z. U. A. Warsi and J. F. Thompson
Journal: Math. Comp. 38 (1982), 501-516
MSC: Primary 65N50; Secondary 30C60, 31A05
MathSciNet review: 645666
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Abstract: In this paper a noniterative method for the numerical generation of orthogonal curvilinear coordinates for plane annular regions between two arbitrary smooth closed curves has been developed. The basic generating equation is the Gaussian equation for a Euclidean space under the constraint of orthogonality. The resulting equation has been solved analytically for the case of isothermic coordinates. A coordinate transformation then yields nonisothermic coordinates in which the outgoing coordinate can be distributed in any desired manner. The method has been applied in many cases and these test results demonstrate that the proposed method can be readily applied in a variety of problems.

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Keywords: Grid generation, mappings, potential theory
Article copyright: © Copyright 1982 American Mathematical Society