Finite volume schemes for dispersive wave propagation and runup

Authors:
Denys Dutykh;Theodoros Katsaounis;Dimitrios Mitsotakis
Affiliations:
LAMA UMR 5127, Université de Savoie, CNRS, Campus Scientifique, 73376 Le Bourget-du-Lac, France;Department of Applied Mathematics, University of Crete, Heraklion 71409, Greece and Inst. of App. and Comp. Math.(IACM), FORTH, Heraklion 71110, Greece;UMR de Mathématiques, Université de Paris-Sud, Bítiment 425, P.O. Box, 91405 Orsay, France
Venue:
Journal of Computational Physics
Year:
2011

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Abstract

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. 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.