Finite volume methods for unidirectional dispersive wave models

Denys Dutykh (1) , Theodoros Katsaounis (2) , Dimitrios Mitsotakis (3)

1 LAMA - Laboratoire de Mathématiques
2 Department of Applied Mathematics [Heraklion]
3 IMA - Institute for Mathematics and its Applications

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.

Mots clés: finite volume method; nonlinear dispersive waves; unidirectional propagation; solitary waves; water waves

Domaines: Mécanique des fluides [physics.class-ph]; Mécanique des fluides [physics.class-ph]; Physique Numérique [physics.comp-ph]; Analyse numérique [math.NA]; Equations aux dérivées partielles [math.AP]

Denys Dutykh, Theodoros Katsaounis, Dimitrios Mitsotakis. Finite volume methods for unidirectional dispersive wave models. 2010. ⟨hal-00538043v1⟩