Long Wave Interaction with a Partially Immersed Body. Part I: Mathematical Models (Communications in Computational Physics, 2019)
In the present article we consider the problem of wave interaction with apartially immersed, but floating body. We assume that the motion of the body is prescribed. The general mathematical formulation for this problem is presented in theframework 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 fullynonlinear 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) andouter domains. Various approaches to the gluing of solutions at the boundary are discussed as well. We propose several strategies which ensure the global conservation orcontinuity of some important physical quantities.
Keywords: Floating body; wave/body interaction; nonlinear dispersive waves; free surface flows; long waves.