HIGHLY PRECISE APPROXIMATION OF FREE SURFACE GREEN FUNCTION AND ITS HIGH ORDER DERIVATIVES BASED ON REFINED SUBDOMAINS
The infinite depth free surface Green function (GF) and its high order derivatives for diffraction and radiation of water waves are considered. Especially second order derivatives are essential requirements in high-order panel method. In this paper, concerning the classical representation, composed...
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Format: | Article |
Language: | English |
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Faculty of Mechanical Engineering and Naval Architecture
2018-01-01
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Series: | Brodogradnja |
Online Access: | http://hrcak.srce.hr/file/276198 |
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author | Jiameng Wu Penghao Shan |
author_facet | Jiameng Wu Penghao Shan |
author_sort | Jiameng Wu |
collection | DOAJ |
description | The infinite depth free surface Green function (GF) and its high order derivatives for diffraction and radiation of water waves are considered. Especially second order derivatives are essential requirements in high-order panel method. In this paper, concerning the classical representation, composed of a semi-infinite integral involving a Bessel function and a Cauchy singularity, not only the GF and its first order derivatives but also second order derivatives are derived from four kinds of analytical series expansion and refined division of whole calculation domain. The approximations of special functions, particularly the hypergeometric function and the algorithmic applicability with different subdomains are implemented. As a result, the computation accuracy can reach 10-9 in whole domain compared with conventional methods based on direct numerical integration. Furthermore, numerical efficiency is almost equivalent to that with the classical method. |
first_indexed | 2024-12-10T14:54:19Z |
format | Article |
id | doaj.art-36e97b85daf84f2989229b8969999bfc |
institution | Directory Open Access Journal |
issn | 0007-215X 1845-5859 |
language | English |
last_indexed | 2024-12-10T14:54:19Z |
publishDate | 2018-01-01 |
publisher | Faculty of Mechanical Engineering and Naval Architecture |
record_format | Article |
series | Brodogradnja |
spelling | doaj.art-36e97b85daf84f2989229b8969999bfc2022-12-22T01:44:21ZengFaculty of Mechanical Engineering and Naval ArchitectureBrodogradnja0007-215X1845-58592018-01-01691537010.21278/brod69104187327HIGHLY PRECISE APPROXIMATION OF FREE SURFACE GREEN FUNCTION AND ITS HIGH ORDER DERIVATIVES BASED ON REFINED SUBDOMAINSJiameng Wu0Penghao Shan1Marine Design and Research Institute of China, No.168 Zhongshan Nanyi Road, Shanghai China, 200011. School of Naval Architecture, Ocean & Civil Engineering, Shanghai Jiao Tong University, Shanghai, China.Marine Design and Research Institute of China, No.168 Zhongshan Nanyi Road, Shanghai China, 200011. School of Naval Architecture, Ocean & Civil Engineering, Shanghai Jiao Tong University, Shanghai, China.The infinite depth free surface Green function (GF) and its high order derivatives for diffraction and radiation of water waves are considered. Especially second order derivatives are essential requirements in high-order panel method. In this paper, concerning the classical representation, composed of a semi-infinite integral involving a Bessel function and a Cauchy singularity, not only the GF and its first order derivatives but also second order derivatives are derived from four kinds of analytical series expansion and refined division of whole calculation domain. The approximations of special functions, particularly the hypergeometric function and the algorithmic applicability with different subdomains are implemented. As a result, the computation accuracy can reach 10-9 in whole domain compared with conventional methods based on direct numerical integration. Furthermore, numerical efficiency is almost equivalent to that with the classical method.http://hrcak.srce.hr/file/276198 |
spellingShingle | Jiameng Wu Penghao Shan HIGHLY PRECISE APPROXIMATION OF FREE SURFACE GREEN FUNCTION AND ITS HIGH ORDER DERIVATIVES BASED ON REFINED SUBDOMAINS Brodogradnja |
title | HIGHLY PRECISE APPROXIMATION OF FREE SURFACE GREEN FUNCTION AND ITS HIGH ORDER DERIVATIVES BASED ON REFINED SUBDOMAINS |
title_full | HIGHLY PRECISE APPROXIMATION OF FREE SURFACE GREEN FUNCTION AND ITS HIGH ORDER DERIVATIVES BASED ON REFINED SUBDOMAINS |
title_fullStr | HIGHLY PRECISE APPROXIMATION OF FREE SURFACE GREEN FUNCTION AND ITS HIGH ORDER DERIVATIVES BASED ON REFINED SUBDOMAINS |
title_full_unstemmed | HIGHLY PRECISE APPROXIMATION OF FREE SURFACE GREEN FUNCTION AND ITS HIGH ORDER DERIVATIVES BASED ON REFINED SUBDOMAINS |
title_short | HIGHLY PRECISE APPROXIMATION OF FREE SURFACE GREEN FUNCTION AND ITS HIGH ORDER DERIVATIVES BASED ON REFINED SUBDOMAINS |
title_sort | highly precise approximation of free surface green function and its high order derivatives based on refined subdomains |
url | http://hrcak.srce.hr/file/276198 |
work_keys_str_mv | AT jiamengwu highlypreciseapproximationoffreesurfacegreenfunctionanditshighorderderivativesbasedonrefinedsubdomains AT penghaoshan highlypreciseapproximationoffreesurfacegreenfunctionanditshighorderderivativesbasedonrefinedsubdomains |