A time-domai.1 second-order method is developed to study the nonlinear wave radiation of a surface-piercing body of arbitrary shape in three dimensions. In this approach, Taylor series expansions are applied to the body surface boundary condition and the free surface boundary conditions, and a perturbation procedure is then used to establish corresponding boundary value problems at first and second order with time-independent boundaries. A time-integration procedure is used to satisfy the boundary conditions to second order, and the wave field at each time step is solved by an integral equation method based on Green's theorem. Numerical results are presented for the case of a truncated surface-piercing circular cylinder undergoing specified sinusoidal moti.ons and the contributions to the hydrodynamic force from the various second-order force components are examined. The method is found to be accurate, computationally efficient, and numerically very stable.
Predictions of wave forces and motions of large offshore structures generally require the solution to nonlinear potential flow problem. Due to the increasing demand of engineering applications, emphasis of hydrodynamic research over the past decade has been placed on the development of nonlinear wave diffraction-radiation theory in order to account for the extreme effects of design waves on offshore structures. In general, there are two categories of method to treat nonlinear wave-structure interactions problem. One approach is a frequency-domain second-order solution based on a Stokes perturbation procedure which is somewhat analogous to the simulation of second-order Stokes wave propagation (e.g. Eatock Taylor and Hung, 1987; Abul-Azm and Williams, 1988; and Kim and Yue, 1989). Such methods enforce a weak far-field condition and are considered to be algebraically complicated. This method involves a number of numerical complications and demands considerable computing resources.