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Theoretical and Applied Mechanics Japan
Vol. 61 (2013) p. 195-200

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http://doi.org/10.11345/nctam.61.195

V APPLICATION OF MATHEMATICS AND VARIOUS NUMERICAL MODELS

It is shown that an equation derived by Van Gorder (2012) denoting a motion of a locally induced vortex filament in a coordinate representation can be transformed directly into an equation described in Umeki (2010) for a temporal evolution of a complex variable denoting a tangential vector of the filament. Analytical and numerical solutions using the equation in a coordinate representation are shown for some examples. A first-order exponential integrator for the Serret-Frenet formula is derived, which is useful when an information of the curvature and the torsion is available for computation of the shape of the filament.

Copyright © 2013 by National Committee for IUTAM

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