A semi-analytical computation of the Kelvin kernel for potential flows with a free surface

IF 2.5 3区数学 Q1 MATHEMATICS, APPLIED

Computational & Applied Mathematics Pub Date : 2011-07-18 DOI:10.1590/S1807-03022011000200002

J. D'Elía, L. Battaglia, Mario Alberto Storti

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引用次数: 17

Abstract

A semi-analytical computation of the three dimensional Green function for seakeeping flow problems is proposed. A potential flow model is assumed with an harmonic dependence on time and a linearized free surface boundary condition. The multiplicative Green function is expressed as the product of a time part and a spatial one. The spatial part is known as the Kelvin kernel, which is the sum of two Rankine sources and a wave-like kernel, being the last one written using the Haskind-Havelock representation. Numerical efficiency is improved by an analytical integration of the two Rankine kernels and the use of a singularity subtractive technique for the Haskind-Havelock integral, where a globally adaptive quadrature is performed for the regular part and an analytic integration is used for the singular one. The proposed computation is employed in a low order panel method with flat triangular elements. As a numerical example, an oscillating floating unit hemisphere in heave and surge modes is considered, where analytical and semi-analytical solutions are taken as a reference.

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自由表面势流开尔文核的半解析计算

提出了一种三维格林函数的半解析计算方法。假设了一个随时间谐波依赖的势流模型和一个线性化的自由表面边界条件。乘法格林函数表示为时间部分和空间部分的乘积。空间部分被称为开尔文核，它是两个朗肯源和一个波状核的和，是最后一个使用Haskind-Havelock表示的。通过对两个Rankine核的解析积分和对Haskind-Havelock积分使用奇异减法技术来提高数值效率，其中正则部分使用全局自适应求积分，奇异部分使用解析积分。所提出的计算方法采用了一种具有平面三角形单元的低阶面板法。作为数值算例，考虑了浮单元半球在升沉和激波模式下的振动，并以解析解和半解析解为参考。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Computational & Applied Mathematics Mathematics-Computational Mathematics

CiteScore

4.50

自引率

11.50%

发文量

352

审稿时长

>12 weeks

期刊介绍： Computational & Applied Mathematics began to be published in 1981. This journal was conceived as the main scientific publication of SBMAC (Brazilian Society of Computational and Applied Mathematics). The objective of the journal is the publication of original research in Applied and Computational Mathematics, with interfaces in Physics, Engineering, Chemistry, Biology, Operations Research, Statistics, Social Sciences and Economy. The journal has the usual quality standards of scientific international journals and we aim high level of contributions in terms of originality, depth and relevance.