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Volume 27, Issue 2
Long Wave Interaction with a Partially Immersed Body. Part I: Mathematical Models

Gayaz Khakimzyanov & Denys Dutykh

DOI: 10.4208/cicp.OA-2018-0294

Commun. Comput. Phys., 27 (2020), pp. 321-378.

Published online: 2019-12

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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 paid 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 approaches to the gluing of solutions at the boundary are discussed as well. We propose several strategies which ensure the global conservation or continuity of some important physical quantities.

  • Keywords

Floating body, wave/body interaction, nonlinear dispersive waves, free surface flows, long waves.

  • AMS Subject Headings

76B15, 76B07, 76M20

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

Khak@ict.nsc.ru (Gayaz Khakimzyanov)

Denys.Dutykh@univ-smb.fr (Denys Dutykh)

  • BibTex
  • RIS
  • TXT
@Article{CiCP-27-321, author = {Khakimzyanov , Gayaz and Dutykh , Denys}, title = {Long Wave Interaction with a Partially Immersed Body. Part I: Mathematical Models}, journal = {Communications in Computational Physics}, year = {2019}, volume = {27}, number = {2}, pages = {321--378}, 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 paid 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 approaches to the gluing of solutions at the boundary are discussed as well. We propose several strategies which ensure the global conservation or continuity of some important physical quantities.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2018-0294}, url = {http://global-sci.org/intro/article_detail/cicp/13450.html} }
TY - JOUR T1 - Long Wave Interaction with a Partially Immersed Body. Part I: Mathematical Models AU - Khakimzyanov , Gayaz AU - Dutykh , Denys JO - Communications in Computational Physics VL - 2 SP - 321 EP - 378 PY - 2019 DA - 2019/12 SN - 27 DO - http://doi.org/10.4208/cicp.OA-2018-0294 UR - https://global-sci.org/intro/article_detail/cicp/13450.html KW - Floating body, wave/body interaction, nonlinear dispersive waves, free surface flows, long waves. AB -

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 paid 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 approaches to the gluing of solutions at the boundary are discussed as well. We propose several strategies which ensure the global conservation or continuity of some important physical quantities.

Khakimzyanov , Gayaz and Dutykh , Denys. (2019). Long Wave Interaction with a Partially Immersed Body. Part I: Mathematical Models. Communications in Computational Physics. 27 (2). 321-378. doi:10.4208/cicp.OA-2018-0294
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