A Hamiltonian approach to fairly low and fairly long gravity waves |
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Authors: | W A van der Veen F W Wubs |
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Affiliation: | (1) Centre for Mathematics and Computer Science, P.O. Box 4079, 1009 AB Amsterdam, The Netherlands;(2) Department of Mathematics, University of Groningen, P.O. Box 800, 9700 AV Groningen, The Netherlands |
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Abstract: | The propagation of nonlinear dispersive gravity waves in an inviscid irrotational fluid can be described by a Hamiltonian system. The canonical equations contain a boundary integral which is computationally expensive. However, for fairly low and fairly long waves an approximation can be made that gives rise to the solution of computationally more attractive Helmholtz-type equations. In an earlier attempt by Broer et al. 4, 6] canonical equations were derived that are stable for all wavenumbers. However, two Helmholtz-type equations need to be solved per right-hand side evaluation. In this paper, canonical equations are presented with the same qualities, but now only once per right-hand side evaluation a Helmholz-type equation needs to be solved, which is optimal. |
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