Finite volume methods for unidirectional dispersive wave models |
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| Authors: | D. Dutykh Th. Katsaounis D. Mitsotakis |
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| Affiliation: | 1. LAMA UMR 5127, Université de Savoie, CNRS, Campus Scientifique, , France;2. Department of Applied Mathematics, University of Crete, , Heraklion, 71409 Greece;3. Institute of Applied Computational Mathematics (IACM), FORTH, , Heraklion, 71110 Greece;4. Institute for Mathematics and its Applications, University of Minnesota 114 Lind Hall, , MN, 55455 |
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| Abstract: | We extend the framework of the finite volume method to dispersive unidirectional water wave propagation in one space dimension. In particular, we consider a KdV–BBM‐type equation. Explicit and implicit–explicit Runge–Kutta‐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 © 2012 John Wiley & Sons, Ltd. |
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| Keywords: | finite volume method nonlinear dispersive waves unidirectional propagation solitary waves water waves |
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