Time‐Domain Second‐Order Wave Diffraction in Three 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.