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Efficient computation of steady solitary gravity waves

Affiliation:	1. University College Dublin, School of Mathematical Sciences, Belfield, Dublin 4, Ireland;2. LAMA, UMR 5127 CNRS, Université de Savoie, Campus Scientifique, 73376 Le Bourget-du-Lac Cedex, France;3. Laboratoire J.-A. Dieudonné, Université de Nice–Sophia Antipolis, Parc Valrose, 06108 Nice Cedex 2, France;1. Ecole Centrale Nantes, LHEEA Lab. (ECN, CNRS), Nantes, France;2. Institut de Recherche Technologique Jules Verne, Bouguenais, France;1. David Taylor Model Basin – NSWCCD, 9500 Macarthur Blvd., W. Bethesda, MD, USA;2. Office of Naval Research, One Liberty Center, 875 N Randolph St., Arlington, VA, USA;1. Faculty of Mathematics, University of Vienna, Oskar-Morgenstern-Platz 1, 1090 Vienna, Austria;2. Radon Institute of Computational and Applied Mathematics, Altenberger Str. 69, 4040 Linz, Austria;3. Computational Science Center, University of Vienna, Oskar-Morgenstern-Platz 1, 1090 Vienna, Austria

Abstract:	An efficient numerical method to compute solitary wave solutions to the free surface Euler equations is reported. It is based on the conformal mapping technique combined with an efficient Fourier pseudo-spectral method. The resulting nonlinear equation is solved via the Petviashvili iterative scheme. The computational results are compared to some existing approaches, such as Tanaka’s method and Fenton’s high-order asymptotic expansion. Several important integral quantities are computed for a large range of amplitudes. The integral representation of the velocity and acceleration fields in the bulk of the fluid is also provided.

Keywords:	Surface waves Gravity waves Euler equations Solitary wave Petviashvili method
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