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Finite volume methods for unidirectional dispersive wave models

Denys Dutykh 1, 2, 3 Theodoros Katsaounis 4 Dimitrios Mitsotakis 5
1 LAMA - Laboratoire de Mathématiques
2 INSMI - Institut National des Sciences Mathématiques et de leurs Interactions
3 USMB [Université de Savoie] [Université de Chambéry] - Université Savoie Mont Blanc
4 Department of Applied Mathematics [Heraklion]
5 IMA - Institute for Mathematics and its Applications
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 IMEX 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.
Keywords : solitary waves unidirectional propagation nonlinear dispersive waves finite volume method water waves
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Submitted on : Friday, February 3, 2012 - 8:59:43 PM
Last modification on : Friday, November 6, 2020 - 3:28:53 AM
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UNIV-SAVOIE | CNRS | INSMI | LAMA | TDS-MACS | UGA

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Denys Dutykh, Theodoros Katsaounis, Dimitrios Mitsotakis. Finite volume methods for unidirectional dispersive wave models. International Journal for Numerical Methods in Fluids, Wiley, 2012, 71 (6), pp.717-736. ⟨10.1002/fld.3681⟩. ⟨hal-00538043v3⟩

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