Finite volume schemes for dispersive wave propagation and runup

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

1 LAMA - Laboratoire de Mathématiques
2 USMB [Université de Savoie] [Université de Chambéry] - Université Savoie Mont Blanc
3 INSMI-CNRS - Institut National des Sciences Mathématiques et de leurs Interactions - CNRS Mathématiques
4 Department of Applied Mathematics [Heraklion]
5 LM-Orsay - Laboratoire de Mathématiques d'Orsay

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, dispersive shock wave formation and the runup of breaking and non-breaking long waves.

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

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

Denys Dutykh, Theodoros Katsaounis, Dimitrios Mitsotakis. Finite volume schemes for dispersive wave propagation and runup. Journal of Computational Physics, 2011, 230 (8), pp.3035-3061. ⟨10.1016/j.jcp.2011.01.003⟩. ⟨hal-00472431v5⟩