Motion responses of two ships advancing parallel in waves with hydrodynamic interactions are investigated in this paper.Within the framework of the frequency-domain potential flow theory,a semi-analytical higher-order translating-pulsating source(HOTP)method is presented to solve the problems of coupled radiation and diffraction potential.The method employs nine-node bi-quadratic curvilinear elements to discretize the boundary integral equations(BIEs)constructed over the mean wetted surface of the two ship hulls.In order to eliminate the numerical oscillation,analytical quadrature formulas are derived and adopted to evaluate the integrals related to the Froude-dependent part of the Green's function along the horizontal direction in the BIEs.Based on the method,a numerical program is originally coded.Through the calculations of hydrodynamic responses of single ships,the numerical implementation is proved successful.Then the validated program is applied in the investigations on the hydrodynamic interactions of two identical Wigley Ⅲ hulls and the underway replenishment of a frigate and a supply ship in waves with and without stagger,respectively.The comparison between the present computed results with experimental data and numerical solutions of other methods shows that the semi-analytical HOTP method is of higher accuracy than the pulsating source Green's function method with speed correction and better stability than the traditional HOTP method based on Gauss quadrature.In addition,for two ships with obviously different dimensions,the influence of hydrodynamic interactions on the smaller ship is found to be more noticeable than that on the larger ship,which leads to the differences between the motions of frigate with and without the presence of supply ship.

YANG Yun-tao;ZHU Ren-chuan;MA Chao;GAO Hui

School of Naval Architecture and Civil Engineering,Jiangsu University of Science and Technology,Zhangjiagang 215600,China;State Key Laboratory of Ocean Engineering,Collaborative Innovation Center for Advanced Ship and Deep-Sea Exploration,School of Naval Architecture,Ocean and Civil Engineering,Shanghai Jiao Tong University,Shanghai 200240,China;Key Laboratory of High Performance Ship Technology(Wuhan University of Technology),Ministry of Education,Wuhan 430063,China;School of Naval Architecture,Ocean and Energy Power Engineering,Wuhan University of Technology,Wuhan 430063,China

中国海洋工程（英文版）

[1]YANG Yun-tao;ZHU Ren-chuan;MA Chao;GAO Hui-.Numerical Study on Motion Responses of Two Parallel Ships During Un-derway Replenishment by the Semi-Analytical HOTP Method)[J].中国海洋工程（英文版）,2022(02):233-246

derway,Replenishment,HOTP,BIEs,Wigley,frigate

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