TIME-DOMAIN 2ND-ORDER WAVE DIFFRACTION IN 3 DIMENSIONS

A time-domain second-order method is developed to study nonlinear wave diffraction around a surface-piercing body of arbitrary shape in three dimensions. 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. The solution is separated into a known incident potential and a scattered potential to be determined. The radiation condition applied to the scattered potential is modified to incorporate a time-dependent celerity to account for transient and second-order effects. With initial conditions corresponding to a Stokes second-order wave field in the domain, the scattered potential is allowed to develop in time and space through the imposition of the body-surface boundary condition. The computed wave force and free-surface elevation components at second order are compared with previous theoretical results for the case of a surface-piercing circular cylinder and a favorable agreement is indicated.