Dispersive wave runup on non-uniform shores

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

Historically the finite volume methods have been developed for the numerical integration of conservation laws. In this study we present some recent results on the application of such schemes to dispersive PDEs. Namely, we solve numerically a representative of Boussinesq type equations in view of important applications to the coastal hydrodynamics. Numerical results of the runup of a moderate wave onto a non-uniform beach are presented along with great lines of the employed numerical method (see D. Dutykh et al. (2011) for more details).

Mots clés: shallow water; finite volumes; dispersive wave; runup; Boussinesq equations

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]; Analyse numérique [math.NA]; Equations aux dérivées partielles [math.AP]; Océanographie; Océan, Atmosphère; Milieux fluides et réactifs

Denys Dutykh, Theodoros Katsaounis, Dimitrios Mitsotakis. Dispersive wave runup on non-uniform shores. Finite Volumes for Complex Applications VI Problems & Perspectives, 4, Springer Berlin Heidelberg, pp.389-397, 2011, 978-3-642-20671-9. ⟨10.1007/978-3-642-20671-9_41⟩. ⟨hal-00553762v3⟩