Abstract
A new numerical scheme is proposed for generating an orthogonal grid in a simply-connected 2D domain. The scheme is based on the idea of decomposition of a global orthogonal transform into consecutive mappings of a conformal mapping and an auxiliary orthogonal mapping, which was suggested by Kang and Leal (J, Comput. Phys.102, 78 (1992)). The method is non-iterative and flexible in the adjustment of grid spacing The grid spacing can be controlled mainly by specification of the boundary correspondence up to three sides of the boundary. The method is also equipped with a control function that provides further degrees of freedom in the grid spacing adjustment. From a mathematical viewpoint, the proposed scheme can also be regarded as a numerical implementation of the constructive proof for the existence of a solution of the orthogonal mapping problem in an arbitrary simply-connected domain under the condition that the boundary correspondence is specified on three sides.
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