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首页> 外文期刊>Ocean Engineering >An efficient algorithm with new residual functions for the transient free-surface green function in infinite depth
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An efficient algorithm with new residual functions for the transient free-surface green function in infinite depth

机译：无限深度下的瞬态自由表面绿色函数的具有新残函数的高效算法

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摘要

Efficient evaluation of the transient free-surface Green function with sufficient accuracy is the key to employ time-domain panel method in solving hydrodynamic problems. In this paper, series and asymptotic expansions for the Green function and its two spatial derivatives are deduced in detail for the evaluation. New residual functions are derived straightforwardly from the resulted asymptotic formulas and it is concluded that the present residual functions decay rapidly than existing choices. The ultimate algorithm is the combination of Chebyshev approximations and asymptotic expressions, along with a special partitioning line introduced to speed up the evaluation. After comprehensive numerical validation, it is pointed out that the present algorithm owns at least 6 digits of accuracy and sufficient efficiency for practical application. Any efficient method for evaluating the Green function will use the asymptotic expansions. Furthermore, it should be pointed out that the present residual functions can also be conveniently applied to the scheme of interpolation in a precomputed table.
机译：有效地评估瞬态自由表面格林函数具有足够的精度，是采用时域面板方法解决流体动力学问题的关键。在本文中，详细推导了Green函数及其两个空间导数的级数和渐近展开以进行评估。新的残差函数可以直接从所得的渐近公式中得出，并且可以得出结论，当前的残差函数比现有的残差函数衰减更快。最终的算法是将切比雪夫（Chebyshev）逼近和渐近表达式结合在一起，并引入了一条特殊的分割线以加快评估速度。经过全面的数值验证，指出本算法具有至少6位的精度和足够的实际应用效率。评估Green函数的任何有效方法都将使用渐近展开式。此外，应该指出，当前的残差函数也可以方便地应用于预计算表中的插值方案。

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  • 来源
    《Ocean Engineering》 |2019年第15期|435-441|共7页
  • 作者

    Shan Penghao; Wang Yuhan; Wang Fuhua; Wu Jiameng; Zhu Renchuan;

  • 作者单位

    Marine Design & Res Inst China, Shanghai, Peoples R China|Shanghai Jiao Tong Univ, Sch Naval Architecture Ocean & Civil Engn, Shanghai, Peoples R China;

    Shanghai Waigaoqiao Shipbldg Co Ltd, Shanghai, Peoples R China;

    Shanghai Jiao Tong Univ, Sch Naval Architecture Ocean & Civil Engn, Shanghai, Peoples R China;

    Marine Design & Res Inst China, Shanghai, Peoples R China|Shanghai Jiao Tong Univ, Sch Naval Architecture Ocean & Civil Engn, Shanghai, Peoples R China;

    Shanghai Jiao Tong Univ, Sch Naval Architecture Ocean & Civil Engn, Shanghai, Peoples R China;

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  • 正文语种 eng
  • 中图分类
  • 关键词

    The transient green function; New residual functions; Asymptotic expansions; Chebyshev approximations; Marine hydrodynamic;

    机译：瞬态格林函数;新的残差函数;渐近展开;切比雪夫逼近;海洋流体动力学;

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