Chebyshev polynomial-based accurate evaluation of three-dimensional free-surface Green's function integrals for large-amplitude floating body motion

• Published in: Physics of fluids (1994) Vol. 37; no. 8
• Main Authors: Liu, Yanshuo, Li, Hongxia, Liu, Gang, Huang, Yi, Jiang, Zhongyu
• Format: Journal Article
• Language: English
• Published: Melville American Institute of Physics 01.08.2025
• Subjects: Amplitudes; Chebyshev approximation; Derivatives; Floating bodies; Free surfaces; Green's functions; Polynomials; Submerged bodies; Time domain analysis
• ISSN: 1070-6631; 1089-7666
• DOI: 10.1063/5.0281970

An accurate and efficient solution method is proposed for applying the time-domain free surface Green's function. This method addresses the equations governing the large-amplitude motion of floating or submerged bodies. The proposed approach introduces an improved integration technique that evaluates the integral of the time-domain Green's function. It leverages Chebyshev polynomials to compute the Green's function and its partial derivatives rapidly. This method not only significantly enhances numerical accuracy but also improves computational efficiency. Furthermore, an analytical expression for the time-domain integral is derived, enabling precise evaluation of the Green's function and its partial derivatives. The accuracy and efficiency of the proposed method are rigorously validated for inclined cells near the water surface and for underwater vertical and horizontal cells, demonstrating its robustness and reliability.