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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Main Authors: Jiameng Wu, Penghao Shan
Format: Article
Language:English
Published: Faculty of Mechanical Engineering and Naval Architecture 2018-01-01
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.
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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