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

Didier Clamond, Denys Dutykh

Research output: Contribution to journalArticlepeer-review

23 Scopus citations

Abstract

This paper describes an efficient algorithm for computing steady two-dimensional surface gravity waves in irrotational motion. The algorithm complexity is O(N log N), N being the number of Fourier modes. This feature 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, up to approximately 99 % of the maximum steepness for all wavelengths. In particular, the possibility to compute very long (cnoidal) waves accurately is a feature not shared by other algorithms and asymptotic expansions. The method is based on conformal mapping, the Babenko equation rewritten in a suitable way, the pseudo-spectral method and Petviashvili 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.

Original languageBritish English
Pages (from-to)491-518
Number of pages28
JournalJournal of Fluid Mechanics
Volume844
DOIs
StatePublished - 10 Jun 2018

Keywords

  • computational methods
  • surface gravity waves

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