Long wave interaction with a partially immersed body. Part I: Mathematical models

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

1 ICT - 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 article we consider the problem of wave interaction with a partially immersed, but floating body. We assume that the motion of the body is prescribed. The general mathematical formulation for this problem is presented in the framework of a hierarchy of mathematical models. Namely, in this first part we formulate the problem at every hierarchical level. The special attention is payed to fully nonlinear and weakly dispersive models since they are most likely to be used in practice. For this model we have to consider separately the inner (under the body) and outer domains. Various approached to the gluing of solutions at the boundary is discussed as well. We propose several strategies which ensure the global conservation or continuity of some important physical quantities.

Mots clés: floating body; wave/body interaction; nonlinear dispersive waves; free surface flows; long waves

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

Gayaz Khakimzyanov, Denys Dutykh. Long wave interaction with a partially immersed body. Part I: Mathematical models. Communications in Computational Physics, 2020, 27 (2), pp.321-378. ⟨10.4208/cicp.OA-2018-0294⟩. ⟨hal-02070055⟩