Abstract
Mapping techniques are mathematical methods which are frequently applied for solving fluid flow problems in the interior and about bodies of nonregular shape. Since the advent of supercomputers such techniques have become quite important in the context of numerical grid generation [1]. In introductory courses in fluid dynamics students learn how to calculate the circulation of an incompressible potential flow about a so-called “Joukowski airfoil” [3] which represent the simplest airfoils of any technical relevance. The physical plane where flow about the airfoil takes place is in a complex p ═ u + iυ plane where i ═ √–1. The advantage of a Joukowski transform consists in providing a conformal mapping of the p plane on a z ═ x + iy plane such that calculating the flow about the airfoil gets reduced to the much simpler problem of calculating the flow about a displaced circular cylinder. A special form of the mapping function p = f(z) = u(z) + iv(z) of the Joukowski transform reads
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Keywords
- Conformal Mapping
- Order Differential Equation
- Physical Plane
- Technical Relevance
- Numerical Integration Algorithm
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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References
J. HÄuser and C. Taylor, Numerical Grid Generation in Computational Fluid Dynamics, Pineridge Press, Swansea, U.K., 1986.
J. Heinhold and U. Kulisch, Analogrechnen, BI-Hochschultaschenbücher Reihe Informatik, Bibliographisches Institut Mannheim / Zürich, 168/168a, 1968.
W.F. Hughes and J.A. Brighton, Fluid Dynamics, Schaum’s Outline Series, McGraw-Hill, USA, 1967.
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© 1995 Springer-Verlag Berlin Heidelberg
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Halin, H.J. (1995). Conformal Mapping of a Circle. In: Solving Problems in Scientific Computing Using Maple and MATLAB® . Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-97619-3_11
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DOI: https://doi.org/10.1007/978-3-642-97619-3_11
Publisher Name: Springer, Berlin, Heidelberg
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