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Numerical solitary wave interaction: the order of the inelastic effect

Published online by Cambridge University Press:  17 February 2009

T. R. Marchant
T. R. Marchant
Affiliation:
School of Mathematics and Applied Statistics, University of Wollongong, Wollongong, NSW, Australia; e-mail: tim@uow.edu.au.
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Abstract

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Solitary wave interaction is examined using an extended Benjamin-Bona-Mahony (eBBM) equation. This equation includes higher-order nonlinear and dispersive effects and is is asymptotically equivalent to the extended Korteweg-de Vries (eKdV) equation. The eBBM formulation is preferable to the eKdV equation for the numerical modelling of solitary wave collisions, due to the stability of its finite-difference scheme. In particular, it allows the interaction of steep waves to be modelled, which due to numerical instability, is not possible using the eKdV equation.

Numerical simulations of a number of solitary wave collisions of varying nonlinearity are performed for two special cases corresponding to surface water waves. The mass and energy of the dispersive wavetrain generated by the inelastic collision is tabulated and used to show that the change in solitary wave amplitude after interaction is of O(α4), verifying previously obtained theoretical predictions.

Type
Research Article
Information
The ANZIAM Journal , Volume 44 , Issue 1 , July 2002 , pp. 95 - 102
Copyright
Copyright © Australian Mathematical Society 2002

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