A frequency domain hybrid Green function method for seakeeping and added resistance performance of ships advancing in waves

A three-dimensional hybrid Green function method is proposed to investigate the seakeeping and added resistance performance of ships advancing in waves. As for the method, the whole fluid domain is divided into two subdomains by introducing a regular virtual control surface. In the inner domain, the first order Taylor Expansion Boundary Element Method (TEBEM) based on simple Green function (Rankine source) is applied. Meanwhile, three-dimensional panel method based on the translating-pulsating panel source (3DTP-PS) Green function is adopted in the outer domain, to overcome the difficulty in proposing a proper boundary condition of the control surface for the Rankine source panel method. With respect to the coupled solutions in the two subdomains, the continuous conditions of velocity potential and its normal derivative are imposed on the virtual control surface. Different treatments of linearization of the free surface and the corresponding ship hull conditions in the inner domain are discussed. Furthermore, six ship models are selected to investigate: the Wigley III, Slender Wigley, Blunt Wigley, S-60, SCb-84 and RIOS ship models (which include different ship types, such as slender, blunt, with bulbous bow, and without bulbous bow). Firstly, through the calculations of radiation and diffraction forces on two modified Wigley hulls and S-60 with block coefficient equals to 0.7, the present method is proved to have good mesh convergence, and satisfactory results can be obtained. Then, the present numerical method is applied to evaluate the hydrodynamic responses of ships sailing in head and oblique waves. Finally, the ship motions and the wave‑induced mean second order wave forces are calculated, including multiple wave directions. Good agreement between the experimental measurements and the numerical results is obtained in all cases, indicating that the present hybrid Green function method is useful and applicable. For present hybrid Green function method, TEBEM is used instead of the traditional constant panel method, which has the advantages of accuracy, and provides a new way for ship hydrodynamic calculation.