Electronic Resource
Chichester, West Sussex
:
Wiley-Blackwell
Mathematical Methods in the Applied Sciences
18 (1995), S. 615-625
ISSN:
0170-4214
Keywords:
Mathematics and Statistics
;
Applied Mathematics
Source:
Wiley InterScience Backfile Collection 1832-2000
Topics:
Mathematics
Notes:
A thin shear layer moving from the trailing edge of a two-dimensional aerofoil section downstream can be interpreted as a curve of discontinuity for the tangential velocity and may be approximated by a vortex sheet in inviscid, incompressible fluid flow. It is well known that vortex sheets are subject to instabilities of Kelvin-Helmholtz type which lead to roll-up phenomena in the wake. The motion of such sheets is governed by the Birkhoff-Rott equation. In the case of Kelvin-Helmholtz instability it seems clear that a curvature singularity occurs at a certain critical time and that consistent discretizations of the Birkhoff-Rott equation may fail to yield reliable results even before the time of occurrence of a singularity. We discuss the modification of the Biot-Savart kernel in the sense of Krasny who regularized the kernel by means of a global parameter. Using discrete Fourier transform we show the damping influence of this regularization technique. We modify the kernel carefully by introducing a regularization found in ordinary vortex methods and show that reliable results may be obtained up to and slightly after the singularity formation without increasing the accuracy of the computation.
Additional Material:
10 Ill.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1002/mma.1670180804
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