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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2018, Volume 58, Number 8, Pages 83–89
DOI: https://doi.org/10.31857/S004446690002003-4 (Mi zvmmf10764) 		 
This article is cited in 6 scientific papers (total in 6 papers)

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

Yu. D. Shevelev

Institute of Computer Aided Design, Russian Academy of Sciences, Moscow, Russia
Citations (6)
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DOI: https://doi.org/10.31857/S004446690002003-4
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.
Received: 01.01.1900
English version:
Computational Mathematics and Mathematical Physics, 2018, Volume 58, Issue 8, Pages 1280–1286
DOI: https://doi.org/10.1134/S0965542518080158
Bibliographic databases:
Document Type: Article
UDC: 517.53
Language: Russian
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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    • This publication is cited in the following 6 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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