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

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.

Keywords

Bibliographic record

BibTeX Citation

@article{Khakimzyanov2020longwave,
  author = {Khakimzyanov, G. and Dutykh, D.},
  title = {Long wave interaction with a partially immersed body. Part I: Mathematical models},
  journal = {Commun. Comput. Phys.},
  year = {2020},
  volume = {27},
  number = {2},
  pages = {321--378},
  doi = {10.4208/cicp.OA-2018-0294},
  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.},
  keywords = {wave-body interaction, mathematical modeling, nonlinear dispersive waves, nonlinear waves, free surface flows, partially immersed body, floating body, weakly dispersive waves, physical conservation laws, wave/body interaction, inner and outer domains, long waves, boundary conditions}
}