杨鹏, 叶梦熊, 李金成, 何景异, 杜兆伟. 对称格林函数简化计算的数学推导[J]. 中国舰船研究, 2018, 13(S1): 22-28. DOI: 10.19693/j.issn.1673-3185.01345
引用本文: 杨鹏, 叶梦熊, 李金成, 何景异, 杜兆伟. 对称格林函数简化计算的数学推导[J]. 中国舰船研究, 2018, 13(S1): 22-28. DOI: 10.19693/j.issn.1673-3185.01345
YANG Peng, YE Mengxiong, LI Jincheng, HE Jingyi, DU Zhaowei. Mathematical derivation of simplified calculation of symmetrical Green function[J]. Chinese Journal of Ship Research, 2018, 13(S1): 22-28. DOI: 10.19693/j.issn.1673-3185.01345
Citation: YANG Peng, YE Mengxiong, LI Jincheng, HE Jingyi, DU Zhaowei. Mathematical derivation of simplified calculation of symmetrical Green function[J]. Chinese Journal of Ship Research, 2018, 13(S1): 22-28. DOI: 10.19693/j.issn.1673-3185.01345

对称格林函数简化计算的数学推导

Mathematical derivation of simplified calculation of symmetrical Green function

  • 摘要:
      目的  为了减少利用边界元法计算大型浮体运动的水动力系数时的面元数量,并提高计算速度,
      方法  针对具有对称面的浮体,利用其在求解奇点源强时系数矩阵可以看成循环矩阵的特性,提出对称格林函数的简化计算方法。
      结果  利用该方法可以显著地加快对称浮体在波浪中运动的水动力系数求解过程:对于具有1个对称面的浮体,源强系数矩阵只需求解1/2的元素,同时线性方程组的求解时间降为原来的1/4;对于具有2个对称面的浮体,源强系数矩阵只需求解1/4的元素,同时线性方程组的求解时间缩短为原来的1/16。
      结论  数值计算结果表明给出的对称性简化方法是有效的,能够极大地提高计算效率。

     

    Abstract:
      Objectives  This paper studies the way to reduce the elements used for calculating the hydrodynamic coefficient for movement of a large floating body with boundary element method and to quicken the calculation.
      Methods  Based on the characteristic of the symmetrical floating body that the coefficient matrix can be considered as a circulant matrix during solvement of source intensity of singular point, a simplified calculation method of symmetrical Green function is proposed. Besides, detailed mathematical derivation is carried out and the physical meanings are explained.
      Results  It is found that, through this method, the process of solving the hydrodynamic coefficient for wave movement of symmetrical floating body can be quickened significantly. For the floating body with one symmetrical plane, it only needs to solve half of the elements of the coefficient matrix of source intensity; meanwhile the time of solving linear equations is reduced by one quarter. And for the floating body with two symmetrical planes, it only needs to solve a quarter of elements of the coefficient matrix of source intensity; meanwhile the time of solving linear equations is reduced by one sixteenth.
      Conclusions  The numerical results show that the proposed symmetrical simplification method is effective, and can greatly improve the calculation efficiency.

     

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