Time-domain solution for second-order wave radiation

Abstract

A time-domain second-order method developed recently to study nonlinear wave diffraction around fixed bodies is extended to account for body motions in otherwise still water. The free surface boundary conditions and the radiation condition are satisfied to second order by a numerical integration in time, and the field solution at each time step is obtained by an integral equation method based on Green's theorem. For the two-dimensional case of a semi-submerged circular cylinder undergoing oscillatory heave motions, the computed hydrodynamic forces at first and second order are compared with previous theoretical and experimental results and a favorable agreement is indicated. The performance of the present method as compared to more conventional methods is discussed and the importance of second-order effects in the evaluation of the hydrodynamic forces to second order is also highlighted.