A Fourier method for solving nonlinear water-wave problems: application to solitary-wave interactions

  title={A Fourier method for solving nonlinear water-wave problems: application to solitary-wave interactions},
  author={John D. Fenton and Michele M. Rienecker},
  journal={Journal of Fluid Mechanics},
  pages={411 - 443}
A numerical method is developed for solution of the full nonlinear equations governing irrotational flow with a free surface and variable bed topography. It is applied to the unsteady motion of non-breaking water waves of arbitrary magnitude over a horizontal bed. All horizontal variation is approximated by truncated Fourier series. This and finite-difference representation of the time variation are the only necessary approximations. Although the method loses accuracy if the waves become sharp… 

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  • J. Fenton
  • Mathematics, Physics
    Journal of Fluid Mechanics
  • 1972
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    Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences
  • 1978
An efficient numerical method is developed for solving nonlinear wave equations typified by the Korteweg-de Vries equation and its generalizations. The method uses a pseudospectral (Fourier

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