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Zh. Vychisl. Mat. Mat. Fiz., 2018, Volume 58, Number 8, Pages 83–89 (Mi zvmmf10764)  

Application of three-dimensional quasi-conformal mappings to grid construction

Yu. D. Shevelev

Institute of Computer Aided Design, Russian Academy of Sciences, Moscow, Russia

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.

Key words: conformal mappings, Lavrentiev-harmonic mappings, generalized Cauchy–Riemann conditions, grid construction, visualization.

DOI: https://doi.org/10.31857/S004446690002003-4

References: PDF file   HTML file

English version:
Computational Mathematics and Mathematical Physics, 2018, 58:8, 1280–1286

Bibliographic databases:

UDC: 517.53
Received: 01.01.1900

Citation: Yu. D. Shevelev, “Application of three-dimensional quasi-conformal mappings to grid construction”, Zh. Vychisl. Mat. Mat. Fiz., 58:8 (2018), 83–89; Comput. Math. Math. Phys., 58:8 (2018), 1280–1286

Citation in format AMSBIB
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