Finite volume schemes for Boussinesq type equations

Denys Dutykh (1, 2, 3) , Theodoros Katsaounis (4) , Dimitrios Mitsotakis (5)

1 LAMA - Laboratoire de Mathématiques
2 INSMI-CNRS - Institut National des Sciences Mathématiques et de leurs Interactions - CNRS Mathématiques
3 USMB [Université de Savoie] [Université de Chambéry] - Université Savoie Mont Blanc
4 Department of Applied Mathematics [Heraklion]
5 IMA - Institute for Mathematics and its Applications

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.

Mots clés: solitary waves; runup; water waves; finite volume method; dispersive waves

Domaines: Mécanique des fluides [physics.class-ph]; Mécanique des fluides [physics.class-ph]; Dynamique des Fluides [physics.flu-dyn]; Physique Numérique [physics.comp-ph]; Physique Atmosphérique et Océanique [physics.ao-ph]; Formation de Structures et Solitons [nlin.PS]; Analyse numérique [math.NA]; Equations aux dérivées partielles [math.AP]; Milieux fluides et réactifs

Denys Dutykh, Theodoros Katsaounis, Dimitrios Mitsotakis. Finite volume schemes for Boussinesq type equations. Colloque EDP-Normandie, Christian Dogbé, Oct 2010, Caen, France. ⟨hal-00553754⟩