The problem of monochromatic water wave diffraction by arbitrary shaped bodies is solved in the time domain. A model exact to second order in the wave steepness is implemented and compared to second order frequency domain semi-analytical results in the case of single and multiple vertical cylinders, representing typical geometries in offshore engineering. The model combines a 3D BEM with a time marching procedure for the free surface based on a 4th order Runge-Kutta scheme. As a compromise between accuracy and versatility, the BEM is implemented with continuous linear basis functions applied on triangular elements with collocation at panel vertices. A multiple node technique is applied at intersections between elementary boundary surfaces. The incident wave is explicitly described as a second order Stokes wave. The boundary value problem is therefore formulated for the diffracted wave field. For applications on arbitrary free surface configurations, local higher order interpolation schemes based on special spline patches are used for the computation of space derivatives at the free surface. Results are presented for the interaction of regular waves both with a single vertical cylinder and with a square array of fourbottom-mounted cylinders, and are shown to compare very accurately with benchmark frequency domain results.
Beyond linear diffraction theory, the usual practice for estimating loads and free surface motions is to rely on frequency domain second order theory. For simple shapes such as vertical cylinders, semi-analytical formulations have been derived [e.g. Eatock-Taylor & Huang (1997)]. However, for realistic offshore structures, the computation of the full quadratic transfer function (QTF) matrix remains a difficult task, relying on the computation of slowly convergent integrals on the free surface. An interesting alternative is to solve the second order diffraction problem in the time domain. This solution presents a number of advantageous features.
