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

@article{Fenton1982AFM,
  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},
  year={1982},
  volume={118},
  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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