Second-order wave interaction with two-dimensional floating bodies by a time-domain method

Abstract

In this paper a time-domain method is used to simulate second-order wave interactions with a large floating body in two dimensions. In the numerical scheme adopted, a boundary integral equation method based on Green's theorem is used to calculate the velocity potential of the resulting flow field at each time step, and the second-order free-surface boundary conditions and the radiation condition of the corresponding initial-boundary value problem are treated by a time-integration scheme to obtain the development of the flow. The equations of motion of the body are solved numerically by the fourth-order Runge—Kutta algorithm. The method is applied to the case of a semi-submerged circular cylinder. Numerical calculations presented include the transient motion of a freely-floating cylinder with a specified initial displacement, and the diffraction—radiation of Stokes second-order waves by a moored floating cylinder. Important second-order wave effects associated with the hydrodynamic forces and motions of the floating structures in regular waves are highlighted. It is found that the present approach is both computationally efficient and stable.