Finite volume methods for unidirectional dispersive wave models

D. Dutykh, Th Katsaounis, D. Mitsotakis

Research output: Contribution to journalArticlepeer-review

36 Scopus citations

Abstract

We extend the framework of the finite volume method to dispersive unidirectional water wave propagation in one space dimension. In particular, we consider a KdV-BBM-type equation. Explicit and implicit-explicit Runge-Kutta-type methods are used for time discretizations. The fully discrete schemes are validated by direct comparisons to analytic solutions. Invariants' conservation properties are also studied. Main applications include important nonlinear phenomena such as dispersive shock wave formation, solitary waves, and their various interactions.

Original languageBritish English
Pages (from-to)717-736
Number of pages20
JournalInternational Journal for Numerical Methods in Fluids
Volume71
Issue number6
DOIs
StatePublished - 28 Feb 2013

Keywords

  • Finite volume method
  • Nonlinear dispersive waves
  • Solitary waves
  • Unidirectional propagation
  • Water waves

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