A Mixed Analytical-Numerical Time Domain Approach to Second-Order Diffraction

This paper describes a mixed analytical-numerical model for solving the second-order diffraction problem on single or multiple bottom-mounted vertical cylinders. The first-order solution is given by Linton & Evans quasi-analytical frequency domain formulation [14]. We use this solution as a basis for secondorder time domain diffraction calculations with advantages both in terms of accuracy and computing effort. The better accuracy comes from the forcing terms in second-order free surface conditions being evaluated quasi-analytically. Regarding the computing effort, the advantage of the proposed scheme is two-fold. Only the second-order problem has to be solved numerically, and the free surface mesh is exclusively adapted to the second-order solution. This results in a substantial reduction of the problem size, especially if the focus is on the sum-frequency problem. Applications are presented for a single cylinder, and for a square array of four cylinders in regular and bichromatic waves. Results are shown to compare favorably both with a previously developed fully-numerical time domain solution of the second-order problem, and with frequency domain semi-analytical results. 'Introduction Second-order diffraction effects play a considerable role in the behaviour of some offshore structures, by producing exciting loads at frequencies significantly lower or higher than the dominant incident wave frequency range. As an example, tension leg platforms (TLPs) are sensible both to high frequency effects in the vertical loads which affects the fatigue life of tethers, and to low frequency horizontal excitations which will excite the horizontal drift motion of the structure. Another major influence of non linear effects is on the diffracted wave field in the vicinity of the structure, with consequences on design aspects related to the airgap estimation. It is now recognized that experimental data on the wave runup about offshore structures may be greatly underestimated by linear theory.