Application of Three-Dimensional Quasi-Conformal Mappings to Grid Construction


Cite item

Full Text

Open Access Open Access
Restricted Access Access granted
Restricted Access Subscription Access

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

Supplementary files

Supplementary Files
Action
1. JATS XML

Copyright (c) 2018 Pleiades Publishing, Ltd.