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<p>Recently, Rim(Wave Motion 116:063, 2023) and Rim(Comput Fluid Dyn 38: 75–87, 2024) have proposed an exact DtN (Dirichlet-to-Neumann) artificial boundary condition for three-dimensional wave–structure interactions or wave motion over an undulated seafloor. This paper suggests another type of artificial boundary condition, so-called Neumann-to-Dirichlet (NtD) boundary condition to analyze the motion of water wave over piecewise smooth topographies or undulated seafloor. A virtual circular cylindrical surface which envelopes the piecewise smooth topographies 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 a NtD boundary condition to focus on wave motion in the interior subregion. Based on comparison with the DtN approach, the present NtD model is escalated to consider the effects of heading angle of incident wave, wave number and submergence on an array of 2*2 rounded-rectangular cylinders and an array of 2*1 circular paraboloidal shoals.</p>

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Hydrodynamic interaction between a free surface water wave and an undulated seabed by using NtD boundary condition

  • 期刊论文

  • 发表日期：

    2025年7月14日

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  • Un-Ryong Rim,
  • Chol-Jin Kim,
  • Yong-Jae Min,
  • Hye-Ran Han,
  • Si-Bom Han

摘要

Recently, Rim(Wave Motion 116:063, 2023) and Rim(Comput Fluid Dyn 38: 75–87, 2024) have proposed an exact DtN (Dirichlet-to-Neumann) artificial boundary condition for three-dimensional wave–structure interactions or wave motion over an undulated seafloor. This paper suggests another type of artificial boundary condition, so-called Neumann-to-Dirichlet (NtD) boundary condition to analyze the motion of water wave over piecewise smooth topographies or undulated seafloor. A virtual circular cylindrical surface which envelopes the piecewise smooth topographies 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 a NtD boundary condition to focus on wave motion in the interior subregion. Based on comparison with the DtN approach, the present NtD model is escalated to consider the effects of heading angle of incident wave, wave number and submergence on an array of 2*2 rounded-rectangular cylinders and an array of 2*1 circular paraboloidal shoals.