ABSTRACT

Boundary element method incorporated with free-surface Green’s function (FSGF) is commonly used for radiation and diffraction problems of a floating body. In the solution of the boundary integral equation, it is important to obtain the integral of FSGF over panels. However, most of the research studies focus on the numerical calculation of FSGF. In the present paper, the spatial distribution of FSGF is explicitly analysed, and its drastic oscillation on the horizontal level appears. Thus the uniformly distributed horizontal line segment source of FSGF is derived. Then a practical numerical scheme for the panel integral of FSGF is proposed, in which the panel integral is considered as the summation of integrations on several horizontal line segments. Compared with the Gauss–Legendre quadrature, numerical results indicate its superiority. Furthermore, the present approach is applied to evaluate the hydrodynamic coefficients of floating bodies. Satisfactory predictions are obtained.

摘要

结合有自由表面格林函数（FSGF）的边界元方法通常用于解决浮体的辐射和衍射问题。在边界积分方程的求解中，重要的是获得面板上FSGF的积分。但是，大多数研究集中在FSGF的数值计算上。在本文中，明确分析了FSGF的空间分布，并显示了其在水平方向上的剧烈振荡。因此，导出了FSGF的均匀分布的水平线段源。然后提出了一种实用的FSGF面板积分的数值方案，其中将面板积分视为几个水平线段上积分的总和。与高斯-勒格德勒积分相比较，数值结果表明了其优越性。此外，本方法被应用于评估浮体的流体动力系数。获得令人满意的预测。