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

Authors

  • Gayaz Khakimzyanov Institute of Computational Technologies of Siberian Branch of the Russian Academy of Sciences, Novosibirsk 630090, Russia
  • Denys Dutykh Univ. Grenoble Alpes, Univ. Savoie Mont Blanc, CNRS, LAMA, 73000 Chambéry, France

DOI:

https://doi.org/10.4208/cicp.OA-2018-0294

Keywords:

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

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.

Published

2019-12-07

Issue

Section

Articles