Numerical modelling of surface water wave interaction with a moving wall

Gayaz Khakimzyanov (1) , Denys Dutykh (2, 3, 4)

1 Institute of Computational Technologies
2 LAMA - Laboratoire de Mathématiques
3 INSMI-CNRS - Institut National des Sciences Mathématiques et de leurs Interactions - CNRS Mathématiques
4 USMB [Université de Savoie] [Université de Chambéry] - Université Savoie Mont Blanc

In the present manuscript, we consider the practical problem of wave interaction with a vertical wall. However, the novelty here consists in the fact that the wall can move horizontally due to a system of springs. The water wave evolution is described with the free surface potential flow model. Then, a semi-analytical numerical method is presented. It is based on a mapping technique and a finite difference scheme in the transformed domain. The idea is to pose the equations on a fixed domain. This method is thoroughly tested and validated in our study. By choosing specific values of spring parameters, this system can be used to damp (or in other words to extract the energy of) incident water waves.

Mots clés: wave/body interaction; wave energy extraction; wave damping; wave run-up; movable wall; full Euler equations

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

Gayaz Khakimzyanov, Denys Dutykh. Numerical modelling of surface water wave interaction with a moving wall. Communications in Computational Physics, 2018, 23 (5), pp.1289-1354. ⟨10.4208/cicp.OA-2017-0110⟩. ⟨hal-01546833v2⟩