有限水深三维脉动源格林函数数值算法研究  

Numerical study of 3D pulsating source Green function in finite water depth

作　　者：杨鹏[1] 顾学康[1] 程小明[1] 丁军[1] 

机构地区：[1]中国船舶科学研究中心,江苏无锡214082

出　　处：《船舶力学》2016年第1期57-67,共11页Journal of Ship Mechanics

基　　金：国家973计划项目基金资助(2013CB036100)

摘　　要：由于柯西主值积分的奇异性和贝塞尔函数的振荡性,有限水深情况下复杂格林函数及其导数的精确数值求解一直是浅水中波浪水动力计算的难点,因此寻找格林函数的精确数值解显得非常重要。通过对格林函数奇异项进行变形推导,文中给出了一种去掉了奇点的新积分形式。另外通过改进前人推导的Gauss-Laguerre积分方法,给出了一种改进的新Gauss-Laguerre积分方法。格林函数及其导数的数值结果显示文中给出的两种新方法可以有效地计算复杂格林函数及其导数值。最后对这两种方法、级数解以及传统的Gauss-Laguerre积分方法的计算精度和效率进行了比较研究,结果显示文中给出的两种方法的计算精度高于传统的Gauss-Laguerre积分方法,但其计算效率低于级数解。但在接近于0的近场附近级数解失真,而文中提出的改进的新Gauss-Laguerre积分方法可以获得正确结果。同时当频率和水深均较大时级数解失真,而文中提出的方法也可以获得正确结果。最后针对这些方法的优缺点,该文提出了建议的策略用于计算有限水深格林函数。The accurate and efficient evaluation of the Green function and its derivatives for a pulsating source in finite water depth is one of the most important aspects in wave force calculation for offshore structures, at the same time it is also one of the most challenging tasks due to the singularity in the Cauchy principal value integral and the oscillation behavior of the Bessel function. In this paper, a new integral equation is proposed in which the singular term is deducted from the Green function. Furthermore, the GaussLaguerre integral equation proposed by other researcher has been improved to obtain a new form of the equation. Using these two proposed methods, numerical calculations are performed for the pulsating source Green function and its derivatives for finite water depth. The results show that very good agreements are achieved between the present results and other published data. The precision and efficiency of the present methods are also investigated and compared with the series solution and traditional Gauss-Laguerre integral method. It shows that both of the new methods have better precision than the traditional Gauss-Laguerre integral, but less efficient than the series solution. On the other side, the series solution would lose precision in the near-fields approaching zero, but the new Gauss-Laguerre integral equation could obtain right results. Furthermore the series solution has poor precision in large wave frequency and water depth in which case both of the new methods could obtain right results. Finally, one strategy was proposed which could properly obtain the value of green function and its derivatives.

关 键 词：有限水深 格林函数 三维 柯西主值 

分 类 号：O35[理学—流体力学]