Algorithm for Three-dimensional Free-surface Green Function in Frequency Domain at Finite Water Depth and Its Derivatives

doi:10.19596/j.cnki.1001-246x.8187

Abstract

Abstract: Numerical evaluation of three-dimensional free-surface Green function in frequency domain and its partial derivatives is a main difficulty in hydrodynamic analyses of marine structures. We proposed two improvements in traditional algorithms of Green function and its partial derivatives. Firstly, we transformed series expressions of Green function and its partial derivatives into expressions that were applicable in numerical evaluation. The improved algorithm is able to prevent series solutions from numerical distortion. Secondly, we improved Gauss-Laguerre algorithm to make sure it is effective at high frequencies and in large water depths. Numerical results indicate that the algorithms improved effectively numerical accuracy of Green function and its partial derivatives. It is significant for heave radiation problems of floating or submerged bodies with large draft at high frequencies.

Key words: finite water depth, Green function, series method, numerical distortion at high frequency, Gauss-Laguerre quadrature

CLC Number:

O241

XU Qianlong, LI Ye. Algorithm for Three-dimensional Free-surface Green Function in Frequency Domain at Finite Water Depth and Its Derivatives[J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 2021, 38(1): 35-46.

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