Time‐Domain Solution for Second‐Order Wave Diffraction

Abstract

A numerical method for calculating the transient, second‐order interaction of ocean waves with large fixed offshore structures of arbitrary shape is described. The development of the flow together with the associated fluid forces is obtained by a time‐stepping procedure in which the flow at each time step is calculated by an integral‐equation method based on Green's theorem. The nonlinear free‐surface boundary conditions and Green's theorem defined on the instantaneous free surface are first expanded about the still‐water level by a Taylor series expansion and terms up to second order are retained through a perturbation procedure. The stability and numerical accuracy of the proposed solution and the treatment of the radiation condition to second order are discussed. The procedure is applied to the two‐dimensional, vertical‐plane case of a submerged circular cylinder subjected to regular incident waves. Comparisons with a previous second‐order theory and a previous experimental study are presented and indicate favorable agreement.