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Finite Volumes for Complex Applications VI Problems & Perspectives pp 389–397Cite as

Dispersive wave runup on non-uniform shores

Part of the Springer Proceedings in Mathematics book series (PROM,volume 4)

Abstract

Historically the finite volume methods have been developed for the numerical integration of conservation laws. In this study we present some recent results on the application of such schemes to dispersive PDEs. Namely, we solve numerically a representative of Boussinesq type equations in view of important applications to the coastal hydrodynamics. Numerical results of the runup of a moderate wave onto a non-uniform beach are presented along with great lines of the employed numerical method (see D. Dutykh et al. (2011) [6] for more details).

Keywords

  • dispersive wave
  • runup
  • Boussinesq equations
  • shallow water

MSC2010: 65M08, 76B15

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Acknowledgements

D. Dutykh acknowledges the support from French Agence Nationale de la Recherche, project MathOcean (Grant ANR-08-BLAN-0301-01) and Ulysses Program of the French Ministry of Foreign Affairs under the project 23725ZA. The work of Th. Katsaounis was partially supported by European Union FP7 program Capacities(Regpot 2009-1), through ACMAC (http://acmac.tem.uoc.gr).

Author information

Authors and Affiliations

  1. LAMA, UMR 5127 CNRS, Université de Savoie, Campus Scientifique, 73376, Le Bourget-du-Lac Cedex, France

    Denys Dutykh

  2. Department of Applied Mathematics, University of Crete, Heraklion, 71409 Greece Inst. of App. and Comp. Math. (IACM), FORTH, Heraklion, 71110, Greece

    Theodoros Katsaounis

  3. IMA, University of Minnesota, MN, Minneapolis, 55455, USA

    Dimitrios Mitsotakis

Authors
  1. Denys Dutykh
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  2. Theodoros Katsaounis
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  3. Dimitrios Mitsotakis
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Corresponding author

Correspondence to Denys Dutykh .

Editor information

Editors and Affiliations

  1. , Faculty of Mechanical Engineering, Czech Technical University, Karlovo náměstí 13, Prague, Czech Republic

    Jaroslav Fořt

  2. , Faculty of Mechanical Engineering, Czech Technical University, Karlovo náměstí 13, Prague, Czech Republic

    Jiří Fürst

  3. , Faculty of Mechanical Engineering, Czech Technical University, Karlovo náměstí 13, Prague, Czech Republic

    Jan Halama

  4. LATP, Laboratoire d'Analyse, Probabilités et Topologie, Université Aix-Marseille, rue Joliot Curie 39, Marseille, 13453, France

    Raphaèle Herbin

  5. LATP, Laboratoire d'Analyse, Probabilités et Topologie, Université Aix-Marseille, rue Joliot Curie 39, Marseille, 13453, France

    Florence Hubert

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Dutykh, D., Katsaounis, T., Mitsotakis, D. (2011). Dispersive wave runup on non-uniform shores. In: Fořt, J., Fürst, J., Halama, J., Herbin, R., Hubert, F. (eds) Finite Volumes for Complex Applications VI Problems & Perspectives. Springer Proceedings in Mathematics, vol 4. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-20671-9_41

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