Un-Ryong Rim, Hyo-Song Ko, Gum-Chon Ri

Wave diffraction and independent radiation by a buoyant body in finite-depth water by using an exact NtD boundary condition

Introduction

Wave diffraction and independent radiation by a buoyant body in finite-depth water by using an exact ntd boundary condition. Analyze wave diffraction & radiation of buoyant bodies in finite-depth water using an exact NtD boundary condition. Accurate for offshore and coastal engineering applications.

Abstract

Hydrodynamics of a floating structure is of interest from offshore and coastal engineers who develop the wave energy converters and utilize the marine space resources. Recently, Rim [1-3] proposed an exact DtN (Dirichlet-to-Neumann) artificial boundary condition in order to solve three-dimensional wave-structure interactions or wave motion over piecewise topographies numerically. This paper is concerned with another artificial boundary condition or so-called NtD (Neumann-to-Dirichlet) boundary condition in order to solve water wave diffraction and independent radiation by a buoyant body. A virtual cylindrical surface enclosing the floating body is chosen as a boundary on which an exact NtD map is analytically derived from a solution of the exterior subregion and then it is specified as a boundary condition in order to solve the interior problem. The present model shows good accuracy through the comparison with the DtN approach and suggests the escalated results for the effects of heading angle of incident wave and draft of a buoyant chamfer box.

Review

This paper presents a significant contribution to the field of offshore hydrodynamics by introducing an exact Neumann-to-Dirichlet (NtD) artificial boundary condition for solving wave diffraction and independent radiation problems involving buoyant bodies in finite-depth water. The work is motivated by the critical need for accurate and efficient modeling tools in the design of wave energy converters and other marine space resource utilization. Building upon previous efforts with Dirichlet-to-Neumann (DtN) conditions, this study rigorously develops an alternative exact boundary condition, promising enhanced analytical and computational capabilities for complex three-dimensional wave-structure interactions. The core methodology involves selecting a virtual cylindrical surface that encloses the floating structure. On this surface, an exact NtD map is analytically derived directly from the solution of the exterior fluid subregion. This analytically obtained NtD map is then precisely specified as the boundary condition for solving the hydrodynamic problem within the interior domain encompassing the buoyant body. This approach eliminates the need for arbitrary truncations or approximations at the far-field boundary, characteristic of many numerical methods, thereby ensuring high fidelity in the solution of the water wave interaction problem. The efficacy and accuracy of the developed NtD model are thoroughly validated through comparisons with established DtN approaches, demonstrating good agreement. Furthermore, the model is applied to investigate the effects of critical parameters such as the incident wave heading angle and the draft of a buoyant chamfer box, providing "escalated results" that likely refer to detailed and insightful findings. This research offers a robust and accurate numerical framework for analyzing wave-buoyant body interactions, holding substantial promise for advancing the design and optimization of offshore structures and wave energy conversion devices through its precise and computationally sound methodology.

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