A nonlinear multi-domain method is proposed to conduct time-domain hydrodynamic analysis of ships in waves based on three-dimensional potential flow theory. The computation domain is divided into the inner domain and the outer domain by control surfaces. In the inner domain, the Rankine panel method incorporated with nonlinear boundary conditions is applied, where influence of both the steady ship wave and the incident wave on wave-body interactions are considered. In the outer domain, a fast free surface Green's function method with linear boundary conditions is used. On the control surface, the velocity potential and its derivatives are kept continuous. With marching on time step, the framework of nonlinear time-domain analysis hydrodynamic are established. Second order forces of ships in waves are then calculated with near-field integral method and components discussions are made with numerical simplification for engineering application.

Math model ship Wigley-III, container ship S175 and oil tanker 50500T are chosen for validation of motions and second order forces calculation. Effects of different components of added resistance are summarized and classified according to different working conditions, which balances the accuracy and efficiency of calculation. Based on the theoretical analysis and numerical validation, present method shows significant potential in time domain hydrodynamic analysis and second order forces calculation.


Second order forces of waves acting on ships or offshore structures in waves are related with the speed, operation rate and economic index. For ships with forward speed, the longitudinal component of the second order forces is the added wave resistance, which affects the actual performance of ships in seaways. Experimental and numerical methods are two major approaches in studying second order forces.

Experiment for the added resistance on standard ship models was conducted by several researchers such as Wigley (Journee, 1992), the S175 containership (Fujii and Takahashi, 1975) and the S60 models (Gerritsma and Beukelman, 1972). Recently, Kashiwagi et al. (2004) showed the experiment data of second order forces for 170kBC. Valanto and Hong (2015) presented the experimental results of HSVA cruise ship. Stocker (2016) measured the second order forces of KCS ship in oblique waves.

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