The nonlinear wave radiation of a surface-piercing 3D arbitrary body is investigated by a time-domain second-order method. In this approach, Taylor series expansions are applied to the body surface boundary condition and the free surface boundary conditions, and Stokes perturbation procedure is then used to establish corresponding boundary value problems at the first and the second-order of waves steepness with time-independent boundaries. A boundary element method based on a B-spline expansion is used to calculate the wave field at each time step, and numerical integration in time has been applied for predicting boundary conditions on the tiee water surface and the body surface at the next time step. An artificial damping layer is adopted on the free surface to avoid the wave reflection. Additionally, a mathematical transform is used to remove the second spatial derivative in the body surface boundary condition. Numerical results of hydrodynamic forces are presented for the case of a truncated surfacepiercing circular cylinder undergoing specified sinusoidal surge and heave motions. Comparison has been made with others' time-domain and frequency-domain approaches, and good agreement has been found between the present result and the result from a frequency-domain method.
With the development of ocean engineering, the study of nonlinear wave diftraction and radiation has become more and more important, with practical applications relating to load and response predictions for offshore structures subjected to steep waves. Generally, two approaches have been used to deal with the interactions of large fixed and floating bodies with nonlinear waves. Molin (1979), Eatock Taylor and Hung (1989), Kim and Yue (1989), Wu and Eatock Talyor (1990), Newman (1990), and Teng and Kato (1999), et al. did researches on the second-order problems, and Malenica and Molin (1995), and Teng and Dong (2001) et al. did work on the third-order problems.
