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Computation 2016, 4(3), 36; doi:10.3390/computation4030036

An Extremely Efficient Boundary Element Method for Wave Interaction with Long Cylindrical Structures Based on Free-Surface Green’s Function

1
Renewable Energy Center, Research Institute for Applied Mechanics, Kyushu University, Kasuga 8168580, Japan
2
State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology, Dalian 116024, China
*
Author to whom correspondence should be addressed.
Academic Editor: Qinjun Kang
Received: 8 August 2016 / Revised: 2 September 2016 / Accepted: 12 September 2016 / Published: 16 September 2016
(This article belongs to the Section Computational Engineering)
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Abstract

The present study aims to develop an efficient numerical method for computing the diffraction and radiation of water waves with horizontal long cylindrical structures, such as floating breakwaters in the coastal region, etc. A higher-order scheme is used to discretize geometry of the structure as well as the physical wave potentials. As the kernel of this method, Wehausen’s free-surface Green function is calculated by a newly-developed Gauss–Kronrod adaptive quadrature algorithm after elimination of its Cauchy-type singularities. To improve its computation efficiency, an analytical solution is derived for a fast evaluation of the Green function that needs to be implemented thousands of times. In addition, the OpenMP parallelization technique is applied to the formation of the influence coefficient matrix, significantly reducing the running CPU time. Computations are performed on wave-exciting forces and hydrodynamic coefficients for the long cylindrical structures, either floating or submerged. Comparison with other numerical and analytical methods demonstrates a good performance of the present method. View Full-Text
Keywords: long cylindrical structure; free-surface Green function; higher-order boundary element method; multipole expansion; singularity elimination; Gauss–Kronrod; numerical quadrature; OpenMP parallelization long cylindrical structure; free-surface Green function; higher-order boundary element method; multipole expansion; singularity elimination; Gauss–Kronrod; numerical quadrature; OpenMP parallelization
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Liu, Y.; Gou, Y.; Teng, B.; Yoshida, S. An Extremely Efficient Boundary Element Method for Wave Interaction with Long Cylindrical Structures Based on Free-Surface Green’s Function. Computation 2016, 4, 36.

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