Classical free-streamline flow over a polygonal obstacle
Elcrat, Alan R. Trefethen, L.
Elcrat, Alan R.
Trefethen, L.
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1986-02
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Keywords
Cavities,Conformal mapping,Free streamline,Hodograph,Jets,Kirchhoff Flow,Schwarz-christoffel,Wakes,Mathematical techniques - Conformal mapping,Numerical conformal mapping,Polygonal obstacle
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Citation
Alan R. Elcrat, Lloyd N. Trefethen, Classical free-streamline flow over a polygonal obstacle, Journal of Computational and Applied Mathematics, Volume 14, Issues 1–2, 1986, Pages 251-265, ISSN 0377-0427, https://doi.org/10.1016/0377-0427(86)90142-1.
Abstract
In classical Kirchhoff flow, an ideal incompressible fluid flows past an obstacle and around a motionless wake bounded by free streamlines. Since 1869 it has been known that in principle, the two-dimensional Kirchhoff flow over a polygonal obstacle can be determined by constructing a conformal map onto a polygon in the log-hodograph plane. In practice, however, this idea has rarely been put to use except for very simple obstacles, because the conformal mapping problem has been too difficult. This paper presents a practical method for computing flows over arbitrary polygonal obstacles to high accuracy in a few seconds of computer time. We achieve this high speed and flexibility by working with a modified Schwarz-Christoffel integral that maps onto the flow region directly rather than onto the log-hodograph polygon. This integral and its associated parameter problem are treated numerically by methods developed earlier by Trefethen for standard Schwarz-Christoffel maps. © 1986. © 2014 Elsevier B.V., All rights reserved.
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This is an open access article under the CC BY license.
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Elsevier B.V.
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Journal of Computational and Applied Mathematics
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03770427