International Conference «Mathematical and Informational Technologies, MIT-2011»
(IX Conference «Computational and Informational Technologies for Science,
Engineering and Education»)

Vrnjacka Banja, Serbia, August, 27–31, 2011

Budva, Montenegro, August, 31 – September, 5, 2011

Dutykh D.   Mitsotakis D.   Dias F.   Stefanakis T.  

Dispersive wave runup and some related amplification phenomena

Reporter: Dutykh D.

Finite volume schemes are commonly used to construct approximate solutions to conservation laws. In this study we extend the framework of the finite volume methods to dispersive water wave models, in particular to Boussinesq type systems [3]. We focus mainly on the application of the method to bidirectional nonlinear, dispersive wave propagation in one space dimension. Special emphasis is given to important nonlinear phenomena such as solitary waves interactions, dispersive shock wave formation and the runup of breaking and non-breaking long waves [2]. Finally, we will assess the accuracy of several recently proposed analytical solutions [1] for the wave runup problem. Moreover, we will reveal some resonance-like phenomena during the wave runup which have not been yet known to our knowledge.

[1] I. Didenkulova and E. Pelinovsky. Run-up of long waves on a beach: the influence of the incident wave form. Oceanology, 48(1):1–6, 2008.
[2] D. Dutykh, Th. Katsaounis, and D. Mitsotakis. Finite volume methods for unidirectional dispersive wave models. Submitted,, 2010.
[3] D. Dutykh, Th. Katsaounis, and D. Mitsotakis. Finite volume schemes for dispersive wave propagation and runup. Journal of Computational Physics, 230:3035–3061, 2011.

Abstracts file: DD_DM_FD_TS-2011.pdf

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