An exact NtD artificial boundary condition for three-dimensional water wave interaction with bottom-fixed bodies

Recently, Rim (2023a) proposed an exact artificial DtN (Dirichlet-to-Neumann) artificial boundary condition for three-dimensional water wave interaction with bottom-fixed bodies over an undulated seafloor. This paper suggests another type of artificial boundary condition, so-called Neumann-to-Dirichlet (NtD) boundary condition to solve the same problem as above. A virtual circular cylindrical surface which envelopes the bodies and undulated seafloor region is chosen as an artificial boundary by which the entire water domain is separated into an interior subregion and an exterior subregion. An exact Neumann-to-Dirichlet (NtD) map on the virtual cylindrical surface is derived analytically from a solution for the exterior subregion, which is chosen as an NtD boundary condition to focus on wave–structure interaction in the interior subregion. Based on comparison with the DtN approach in case of a rounded-rectangular cylinder, the present NtD approach is escalated to the cases of four cylinders bottom-fixed on a flat seafloor and two cylinders bottom-fixed on an undulated seafloor with a paraboloidal shoal.