Journal
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS
Volume 71, Issue 6, Pages 717-736Publisher
WILEY-BLACKWELL
DOI: 10.1002/fld.3681
Keywords
finite volume method; nonlinear dispersive waves; unidirectional propagation; solitary waves; water waves
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Funding
- French Agence Nationale de la Recherche, project MathOcean [ANR-08-BLAN-0301-01]
- Ulysses Program of the French Ministry of Foreign Affairs [23725ZA]
- CNRS PICS project [5607]
- European Union FP7 Program Capacities through ACMAC [REGPOT 2009-1]
- Publishing Arts Research Council [98-1846389]
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We extend the framework of the finite volume method to dispersive unidirectional water wave propagation in one space dimension. In particular, we consider a KdVBBM-type equation. Explicit and implicitexplicit RungeKutta-type methods are used for time discretizations. The fully discrete schemes are validated by direct comparisons to analytic solutions. Invariants' conservation properties are also studied. Main applications include important nonlinear phenomena such as dispersive shock wave formation, solitary waves, and their various interactions. Copyright (C) 2012 John Wiley & Sons, Ltd.
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