有限水深Kelvin源格林函数及其导数的快速计算

应用线性船舶水动力学理论,将有限水深Kelvin移动兴波源格林函数分解成3部分:简单Rankine源集合、局部扰动项和波函数项。对各部分在亚临界和超临界航速时的快速计算分别作了讨论,其中对计算费时的局部扰动项采用了复数中的最陡下降积分法,加快了计算速度,进而引出各部分偏导数的计算。最后,比较了格林函数的差分值与偏导数值,计算了薄船兴波阻力与表面兴波,讨论了不同面元网格划分的收敛性,证实了亚临界、超临界航速兴波分别以横波、散波为主。

Fast calculation of Kelvin source green function and derivatives of steady motion in finite depth

According to the linear marine hydrodynamics theory,the Kelvin wave source Green function of steady motion was divided into three parts: array of simple Rankine sources,local disturbance and wave.Effective calculation for each part at subcritical and supercritical speed part was discussed.Especially the steepest descent integration method in the complex was used to solve the time-consuming local disturbance part,which was a most time-efficient procedure.The computation of derivatives of each part was also made.Finally,the comparison of the difference value of Green function and the partial derivatives,calculation of ship′s wave resistance and surface wave and discussion of the convergence of different panel grid division verify that the transversal and divergent waves are the key properties of subcritical and supcritical speed wave system.