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.
Bibliographical noteFunding 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.
- Dispersive waves
- Finite volume method
- Solitary waves
- Water waves
ASJC Scopus subject areas
- Numerical Analysis
- Modeling and Simulation
- Physics and Astronomy (miscellaneous)
- General Physics and Astronomy
- Computer Science Applications
- Computational Mathematics
- Applied Mathematics