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

This 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 timedomain 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.