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

TL;DR

This paper develops a hierarchy of mathematical models to describe wave interaction with a partially immersed floating body, focusing on nonlinear and dispersive models, and discusses boundary conditions and conservation strategies.

Contribution

It formulates a comprehensive hierarchy of models for wave-body interaction, emphasizing nonlinear and dispersive cases, and explores boundary matching and conservation methods.

Findings

Formulated hierarchical models for wave interaction with floating bodies.

Analyzed boundary conditions and solution gluing strategies.

Ensured conservation of physical quantities across 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.