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

Gayaz Khakimzyanov, Denys Dutykh

Research output: Contribution to journalArticlepeer-review

10 Scopus citations


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 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.

Original languageBritish English
Pages (from-to)321-378
Number of pages58
JournalCommunications in Computational Physics
Issue number2
StatePublished - 2020


  • Floating body
  • Free surface flows
  • Long waves
  • Nonlinear dispersive waves
  • Wave/body interaction


Dive into the research topics of 'Long wave interaction with a partially immersed body. Part I: Mathematical models'. Together they form a unique fingerprint.

Cite this