Accurate fast computation of steady two-dimensional surface gravity waves in arbitrary depth

Abstract : This paper describes an efficient algorithm for computing steady two-dimensional surface gravity wave in irrotational motion. The algorithm complexity is O(N log N), N being the number of Fourier modes. The algorithm allows the arbitrary precision computation of waves in arbitrary depth, i.e., it works efficiently for Stokes, cnoidal and solitary waves, even for quite large steepnesses. The method is based on conformal mapping, Babenko equation rewritten in a suitable way, pseudo-spectral method and Petviashvili's iterations. The efficiency of the algorithm is illustrated via some relevant numerical examples. The code is open source, so interested readers can easily check the claims, use and modify the algorithm.
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https://hal.archives-ouvertes.fr/hal-01465813
Contributeur : Denys Dutykh <>
Soumis le : lundi 13 février 2017 - 10:33:42
Dernière modification le : samedi 18 février 2017 - 01:05:24

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Distributed under a Creative Commons Paternité - Pas d'utilisation commerciale - Partage selon les Conditions Initiales 4.0 International License

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  • HAL Id : hal-01465813, version 1
  • ARXIV : 1702.04132

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Didier Clamond, Denys Dutykh. Accurate fast computation of steady two-dimensional surface gravity waves in arbitrary depth. 29 pages, 5 figures, 36 references. Other author papers can be downloaded at http://www.denys-dut.. 2017. <hal-01465813>

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