Numerical study of the second-order wave loads on a ship with forward speed

In the 25th workshop hold in Harbin, China, we have presented a domain-decomposition based method to solve the second-order diffraction/radiation problems with a current or small forward speed [1]. The boundary value problem in the inner domain is formulated in a body-fixed coordinate system, while inertial coordinate system is applied in the outer domain. The continuity of the velocity potential and the normal velocity at the control surface act as the matching conditions of the inner- and outer-domain solutions. The highlight of the method is twofold. Firstly, no higher-order derivatives appear in the body boundary conditions and thus the m_j-terms and the derivatives of the m_j-terms are avoided. Secondly, because the body boundary condition is formulated on the instantaneous position of the body, the resulting integral equation is valid for both smooth bodies and bodies with sharp corners. What we have to pay for using this method is that the number of unknowns has been increased, since singularities with unknown strengths are distributed on the control surface. See also [2], [3] for details. In the present study, we will use body-fixed coordinate system not only near the body but also in finite distance away from the body. That means the outer domain in the previous studies disappears and no control surface is needed. Perturbation method is used so that the computational domain remains unchanged. Infinite water depth will be considered.