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Long Wave Interaction with a Partially Immersed Body. Part I: Mathematical Models

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

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Jan 2020Embargo end date: 01 Jan 2019 France Publisher:Global Science PressJournal:Communications in Computational Physics, volume 27, pages 321-378 (issn: 1815-2406, eissn: 1991-7120,

Authors: Khakimzyanov, Gayaz; Dutykh, Denys;

doi: 10.4208/cicp.oa-2018-0294 , 10.48550/arxiv.1903.07617

arXiv: http://arxiv.org/abs/1903.07617

Long Wave Interaction with a Partially Immersed Body. Part I: Mathematical Models

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Abstract

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.

Accepted to Comm. Comp. Phys.: 63 pages, 5 figures, 103 references, 1 appendix. Other author's papers can be downloaded at http://www.denys-dutykh.com/

Country

France

Related Organizations

French National Centre for Scientific Research
France
Institut national des sciences mathématiques et de leurs interactions
France
Université Savoie Mont Blanc
France
Laboratoire de Mathématiques
France

Keywords

[PHYS.PHYS.PHYS-FLU-DYN]Physics [physics]/Physics [physics]/Fluid Dynamics [physics.flu-dyn], [PHYS.PHYS.PHYS-CLASS-PH]Physics [physics]/Physics [physics]/Classical Physics [physics.class-ph], wave/body interaction, FOS: Physical sciences, [PHYS.PHYS.PHYS-GEO-PH]Physics [physics]/Physics [physics]/Geophysics [physics.geo-ph], Free-surface potential flows for incompressible inviscid fluids, Physics - Classical Physics, 76M20 (secondary)47.35.Bb (primary), Finite difference methods applied to problems in fluid mechanics, 510, [PHYS.PHYS.PHYS-COMP-PH]Physics [physics]/Physics [physics]/Computational Physics [physics.comp-ph], Physics - Geophysics, 47.35.Fg (secondary), [NLIN.NLIN-PS]Nonlinear Sciences [physics]/Pattern Formation and Solitons [nlin.PS], [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], [NLIN.NLIN-SI]Nonlinear Sciences [physics]/Exactly Solvable and Integrable Systems [nlin.SI], [PHYS.MECA.MEFL]Physics [physics]/Mechanics [physics]/Fluid mechanics [physics.class-ph], [PHYS.PHYS.PHYS-AO-PH]Physics [physics]/Physics [physics]/Atmospheric and Oceanic Physics [physics.ao-ph], Water waves, gravity waves; dispersion and scattering, nonlinear interaction, long waves, free surface flows, Fluid Dynamics (physics.flu-dyn), Classical Physics (physics.class-ph), Physics - Fluid Dynamics, Computational Physics (physics.comp-ph), 76B15 (primary), 76B07, Geophysics (physics.geo-ph), Physics - Atmospheric and Oceanic Physics, floating body, Atmospheric and Oceanic Physics (physics.ao-ph), nonlinear dispersive waves, free-surface flows, Physics - Computational Physics, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]

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