Finite volume schemes for dispersive wave propagation and runup

Denys Dutykh; Theodoros Katsaounis; Dimitrios Mitsotakis

doi:10.1016/j.jcp.2011.01.003

Finite volume schemes for dispersive wave propagation and runup

Denys Dutykh
, Theodoros Katsaounis
, Dimitrios Mitsotakis

Mathematics

University of Crete
Institute of Petroleum Research - Foundation for Research and Technology-Hellas (IPR-FORTH)
Université Paris 11

Research output: Contribution to journal › Article › peer-review

81 Scopus citations

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.

Original language	British English
Pages (from-to)	3035-3061
Number of pages	27
Journal	Journal of Computational Physics
Volume	230
Issue number	8
DOIs	https://doi.org/10.1016/j.jcp.2011.01.003
State	Published - 20 Apr 2011

Keywords

Dispersive waves
Finite volume method
Runup
Solitary waves
Water waves

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10.1016/j.jcp.2011.01.003

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title = "Finite volume schemes for dispersive wave propagation and runup",

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.",

keywords = "Dispersive waves, Finite volume method, Runup, Solitary waves, Water waves",

author = "Denys Dutykh and Theodoros Katsaounis and Dimitrios Mitsotakis",

note = "Funding Information: 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 ). The work of D. Mitsotakis was supported by Marie Curie Fellowship No. PIEF-GA-2008-219399 of the European Commission. The authors thank also professors Diane Henderson and Costas Synolakis for providing them their experimental data and professors Jerry Bona and Vassilios Dougalis for very helpful discussions.",

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doi = "10.1016/j.jcp.2011.01.003",

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AU - Dutykh, Denys

AU - Katsaounis, Theodoros

AU - Mitsotakis, Dimitrios

N1 - Funding Information: 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 ). The work of D. Mitsotakis was supported by Marie Curie Fellowship No. PIEF-GA-2008-219399 of the European Commission. The authors thank also professors Diane Henderson and Costas Synolakis for providing them their experimental data and professors Jerry Bona and Vassilios Dougalis for very helpful discussions.

PY - 2011/4/20

Y1 - 2011/4/20

N2 - 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.

AB - 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.

KW - Dispersive waves

KW - Finite volume method

KW - Runup

KW - Solitary waves

KW - Water waves

UR - https://www.scopus.com/pages/publications/79951767730

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DO - 10.1016/j.jcp.2011.01.003

M3 - Article

AN - SCOPUS:79951767730

SN - 0021-9991

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SP - 3035

EP - 3061

JO - Journal of Computational Physics

JF - Journal of Computational Physics

IS - 8

ER -

Finite volume schemes for dispersive wave propagation and runup

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Keywords

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