有限水深格林函数及其导数的改进Gauss-Laguerre算法

文中对计算有限水深自由面格林函数及其导数主值积分的Gauss-Laguerre算法进行了两点改进,一是通过约分从被积函数中分离出可由公式直接求解的部分,降低了被积函数其余部分中积分变量的阶数,二是采用无限水深格林函数的主值积分和指数积分相结合的方式来消除被积函数的奇异性,这两点改进不仅极大地改善了被积函数的收敛性,使获得满意精度所需要的高斯积分点数目大大降低,计算效率显著提高,而且解决了传统方法中计算频率较高时计算结果失真的问题.计算结果表明,该改进方法求得的水动力系数和法国BV船级社的Hydrostar软件的计算结果吻合良好.

An improved Gauss-Laguerre method for finite water depth Green function and its derivatives

Two improvements were made to the Gauss-Laguerre method which is used to calculate the principal value integrals of the finite water depth free-surface Green function and its derivatives. The first one is to use a reduction of fraction to separate the parts that can be calculated by formulas from the integral functions,and this decreases the integral variable's order of the rest of the integral functions; the second one is to remove the singularity of the integral function by using the infinite Green function together with the exponential integral.These two improvements not only greatly improve the convergence of the integrals,therefore,the required number of the integral points for the satisfied accurate results is reduced and the calculation becomes more efficient,but also solve the problem of numerical distortion when the computational frequencies are high. It shows that the results of the hydrodynamic coefficients obtained by this method correspond well with those obtained by BV Hydrostar.