Application of Three-Dimensional Quasi-Conformal Mappings to Grid Construction
- Authors: Shevelev Y.D.1
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Affiliations:
- Institute of Computer Aided Design, Russian Academy of Sciences
- Issue: Vol 58, No 8 (2018)
- Pages: 1280-1286
- Section: Article
- URL: https://journal-vniispk.ru/0965-5425/article/view/179773
- DOI: https://doi.org/10.1134/S0965542518080158
- ID: 179773
Cite item
Abstract
Two-dimensional conformal mappings are a powerful and elegant tool for solving many mathematical and physical problems. The conformal mapping method is suitable for constructing two-dimensional grids. The quasi-conformal mappings constructed in this paper naturally generalize the application of conformal mappings to grid construction in the three-dimensional case. For a steady irrotational flow of an ideal incompressible fluid, in addition to the velocity potential, two stream functions are introduced. Generalized Cauchy–Riemann conditions from which three-dimensional quasi-conformal mappings follow are presented. The mappings constructed can be represented as a sequence of two-dimensional conformal mappings. Examples of grid construction using the theory of quasi-conformal mappings are given. The best proof of these results is their visualization.
About the authors
Yu. D. Shevelev
Institute of Computer Aided Design, Russian Academy of Sciences
Author for correspondence.
Email: shevelev@icad.org.ru
Russian Federation, Moscow, 123065
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