A Noniterative Method for the Generation of Orthogonal Coordinates in Doubly-Connected Regions

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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.