Non‐linear time‐domain models for irregular wave diffraction about offshore structures

Abstract

AbstractThis paper is devoted to the numerical simulation of non‐linear wave diffraction by three‐dimensional (3D) surface‐piercing structures in the time domain. Two different methods are presented. First a second‐order diffraction model is described, in which a boundary‐element method combined with a time‐stepping procedure are used to solve the first‐ and second‐order diffraction problems in the time domain. The Stokes expansion approach of the free surface non‐linearities results in relatively moderate simulation times, so that long simulations in irregular incident waves become feasible. The model has previously been systematically validated by comparison with available semi‐analytical frequency domain results on regular wave diffraction about simplified geometries. In the present paper, the flexibility and stability of the time‐domain approach to second‐order wave diffraction are further demonstrated by the simulation of bichromatic wave diffraction over a large number of incident wave periods. The second part of the paper addresses the problem of fully non‐linear wave diffraction. Again, the solution procedure is based on a boundary element method (BEM) solution of the boundary‐value problem in the time domain, but the non‐linear boundary conditions are accounted for without any approximation this time. In this fully non‐linear diffraction model, an explicit description of the incident wave is exploited to solve the problem for the diffracted flow only. This approach has a number of practical advantages in terms of accuracy and computational efficiency. In previous publications related to this approach stream‐function theory was utilized to model non‐linear regular incident waves. In this paper, irregular two‐dimensional (2D) incident waves are modelled by means of a recently developed fully non‐linear time‐domain pseudospectral formulation. An original coupling of this 2D pseudospectral model with the 3D non‐linear BEM model is proposed, and its effectiveness is shown on the case of 2D wave packets interacting with a vertical bottom‐mounted cylinder. Copyright © 2003 John Wiley & Sons, Ltd.