Abstract
Mapping techniques are mathematical methods which are frequently applied for solving fluid flow problems in the interior involving 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 + iv plane where \( i = \sqrt { - 1} \). 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
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
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.
Rights and permissions
Copyright information
© 2004 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Halin, H.J., Jaschke, L. (2004). Conformal Mapping of a Circle. In: Solving Problems in Scientific Computing Using Maple and MATLAB®. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-18873-2_11
Download citation
DOI: https://doi.org/10.1007/978-3-642-18873-2_11
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-21127-3
Online ISBN: 978-3-642-18873-2
eBook Packages: Springer Book Archive