Computational conformal mapping for surface grid generation
The present paper is concerned with numerical grid generation as an essential element of the numerical solution of partial differential equations on arbitrary regions. The paper is devoted to employment of conformal mapping to develop a new methodology for generation of curvilinear coordinates on arbitrary surfaces and construction of optimal grids on complex geometries. At first the authors describe basic properties and advantages of conformal mapping from two-dimensional regions to three-dimensional surfaces. The authors formulate the generation equations for the surface case, establish relationship and connection between the derived equations based on conformal mapping and those derived for planar regions based on quasi-conformal mapping. One of the purposes of the present work is to construct the desired high quality surface grids on a given geometry. To accomplish this task effectiveness of proposed strategies is represented by a number of examples that demonstrate the application of the method in practical grid construction.
scientific article; zbMATH DE number 881862