有限水深三维脉动源格林函数数值算法研究

发布时间：2017-12-28 02:37

本文关键词：有限水深三维脉动源格林函数数值算法研究　出处：《船舶力学》2016年Z1期 　论文类型：期刊论文

【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。
[Abstract]:Because of the oscillation of the Cauchy principal value integral and the singularity of the Bessel function, the exact numerical solution of complex Green function and its derivatives in finite water depth is always difficult to calculate the wave hydrodynamics in shallow water, therefore find the accurate numerical solution of the Green function is very important. By deriving the deformation of the singular term of Green's function, a new integral form is given out of the singular point. In addition, by improving the Gauss-Laguerre integral method derived by predecessors, an improved new Gauss-Laguerre integral method is given. The numerical results of Green's function and its derivative show that the two new methods given in this paper can effectively calculate the complex Green function and its derivative. Finally, the accuracy and efficiency of the two methods, the series solution and the traditional Gauss-Laguerre integral method were studied and compared. The results show the accuracy of the two methods are given to the Gauss-Laguerre is higher than that of the traditional integral method, but its computational efficiency is lower than the series solution. But the series solution near the near field near 0 is distorted, and the improved new Gauss-Laguerre integral method proposed in this paper can get the correct results. At the same time, the series solution is distorted when the frequency and the depth of water are large, and the method proposed in this paper can also get the correct results. Finally, in view of the advantages and disadvantages of these methods, the proposed strategy is proposed to calculate the finite water depth Green function.
【作者单位】：中国船舶科学研究中心;
【基金】：国家973计划项目基金资助(2013CB036100)
【分类号】：U661
【正文快照】： 0引言近岸和近岛礁附近的水深一般较浅,位于浅水中的浮体水动力运动和载荷响应与深水中的存在较大差别,因此需要研究浅水中浮体在波浪中的运动和载荷响应。其中浅水中浮体运动与深水中的最大差别和难点在于有限水深格林函数的准确求解。只有有限水深格林函数及其偏导数的准确

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