THE APPROXIMATION OF FREE-SURFACE GREEN FUNCTIONS
THE APPROXIMATION OF FREE-SURFACE GREEN FUNCTIONS
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2012
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讨论了三维自由表面格林函数的评估，重点是多元经济多项式近似的使用。当适用时，这些提供了具有受控精度的快速算法，相对于基于数值积分的直接评估，大大提高了计算的效率和鲁棒性。描述了一般方法，并将其应用于涉及朗肯源的周期性阵列的相对简单的示例中。在频域和时域中描述了自由表面格林函数的更复杂的算法，其近似形式由渐近展开引导。特别关注有限深度脉冲格林函数的大时间渐近，其中前进波前与艾里积分的平方相关。
The evaluation of three-dimensional free-surface Green functions is discussed, with emphasis on the use of multivariate economized polynomial approximations. When applicable these provide fast algorithms with controlled accuracy, greatly improving the efficiency and robustness of the computations relative to direct evaluations based on numerical integration. The general method is described, and applied in a relatively simple example involving a periodic array of Rankine sources. More complicated algorithms are described for the free-surface Green function in both the frequencyand time-domains, with the form of the approximations guided by asymptotic expansions. Special attention is given to the large-time asymptotics of the finite-depth impulsive Green function, where the advancing wave front is related to the square of the Airy integral.