时域格林函数卷积的新算法

New convolution algorithm of time-domain Green function

应用三维时域格林函数求解水动力问题需要计算复杂且耗时的卷积积分。该文运用卷积定理,将时域格林函数与速度势的卷积转化为对应傅立叶变换的乘积形式。利用时域格林函数与频域格林函数的傅立叶变换关系,提出了一个卷积计算的递推公式。该方法降低了格林函数的计算难度,卷积的计算量和存储量不随时间增长,对于格林函数计算复杂的有限水深问题和长时间的数值模拟具有优势。文中计算了漂浮半球和Wigley船的波浪力及运动响应,并与现有文献结果进行了对比。

Hydrodynamic computations using a three dimensional time-domain Green function are extremely complex and time-consuming due to the convolution integrals. Based on convolution theorem, the convolutions of time-domain Green function and velocity potential was replaced by the product of their Fourier transformations. Using the Fourier transform relationship between time-domain Green function and frequency-domain Green function, a recursive algorithm for convolution was proposed. This provides an efficient way to perform it in a finite-depth or a long-time simulation since the computational cost keeps constant at any time. Finally computed wave forces and motion responses of a hemisphere and a Wigley hull are compared with published results .