Finite volume methods for unidirectional dispersive wave models
Classical Physics
2020-01-09 v3 Analysis of PDEs
Numerical Analysis
Computational Physics
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 IMEX 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.
Cite
@article{arxiv.1011.4589,
title = {Finite volume methods for unidirectional dispersive wave models},
author = {Denys Dutykh and Theodoros Katsaounis and Dimitrios Mitsotakis},
journal= {arXiv preprint arXiv:1011.4589},
year = {2020}
}
Comments
25 pages, 12 figures, 51 references. Other authors papers can be downloaded at http://www.lama.univ-savoie.fr/~dutykh/