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Journal Articles International Journal for Numerical Methods in Fluids Year : 2012

Finite volume methods for unidirectional dispersive wave models

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.
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Dates and versions

hal-00538043 , version 1 (20-11-2010)
hal-00538043 , version 2 (17-11-2011)
hal-00538043 , version 3 (03-02-2012)

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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, 2012, 71 (6), pp.717-736. ⟨10.1002/fld.3681⟩. ⟨hal-00538043v3⟩
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