An operator expansion method for computing nonlinear surface waves on a ferrofluid jet

Philippe Guyenne, Emilian I. Parau

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We present a new numerical method to simulate the time evolution of axisym- metric nonlinear waves on the surface of a ferrofluid jet. It is based on the reduction of this problem to a lower-dimensional computation involving surface variables alone. To do so, we describe the associated Dirichlet–Neumann op- erator in terms of a Taylor series expansion where each term can be efficiently computed by a pseudo-spectral scheme using the fast Fourier transform. We show detailed numerical tests on the convergence of this operator and, to illus- trate the performance of our method, we simulate the long-time propagation and pairwise collisions of axisymmetric solitary waves. Both depression and elevation waves are examined by varying the magnetic field. Comparisons with weakly nonlinear predictions are also provided.
Original languageEnglish
Pages (from-to)414–434
Number of pages21
JournalJournal of Computational Physics
Early online date31 May 2016
Publication statusPublished - 15 Sep 2016


  • Dirichlet–Neumann operator
  • Ferrofluid jet
  • Pseudo-spectral method
  • Series expansion
  • Solitary waves

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