开尔文源格林函数数值积分方法

Evaluation Method for Kelvin Source Green's Function

分析了开尔文源格林函数近场扰动项的奇异性与远场波动项的振荡特性,分别给出了相应的积分方法;通过改变积分表达式来消除扰动项的奇异性,并对变形后的函数采用改进的梯形法进行计算;采用变量代换方法计算波动项,对变量代换后函数出现的"伪奇异点"区域进行局部加密处理;根据波动项的衰减特性,提出其积分区间上下限截断误差的控制方法.数值计算结果表明:所提出的计算方法能够同时兼顾精度与效率,适用于对单个浮体的静水航行兴波进行数值模拟及多个浮体的兴波干扰进行数值分析.

The singularities and oscillatory performance of Kelvin source Green＇s function which consisted of a local disturbance part and a far field wave-like part were analyzed and the relative numerical integral methods for the two parts were presented. A well behaved expression of local disturbance part was used to eliminate its singularities, and an improved method based on trapezoidal integration rule was used to evaluate this part. Meanwhile, variable substitution with auxiliary technique such as local refinement of integral steps in narrow zones near false singularities was applied to calculate the far-field wave-like part function. According to the attenuation performance of the wave-like part, a finite upper limit of this part was employed to improve the efficiency. The numerical test results have proved the efficiency and accuracy of these integral methods. The methods can be applied to calculate wave-making problem of floating struc tures in calm water.