The application of a fully non-linear boundary element method to the simulation of wave-body-current interactions in the time domain is presented. Stream function theory is used to model the incoming flow composed of non linear regular waves combined with a uniform current. A time dependent boundary value problem for the nonlinear diffraction flow is formulated and solved using a boundary element method based on triangular isoparametric elements. A fourth order Runge-Kutta method is applied for the time marching. New and original results on the non-linear influence of wave steepness and current velocity on the wave runup about a bottom-mounted vertical cylinder are presented and discussed. Results include time series as well as harmonic components of the runup.
Most recently published numerical methods for the solution of the wave-body-current interaction problem were developed within the frame of frequency-domain analysis, with significant contributions including Nossen·et al (1991), Emmerhof & Sclavounos (1992), Teng & Eatock-Taylor (1995), Malenica et al (1995), among others. The advantage of this first approach is to provide results of interest such as wave forces and runups on the structures in a relatively straightforward manner. On the other, hand, the mathematical formulation is significantly more complicated than with zero current speed, with specific problems such as secularity. There are also a number of practical limitations, such as regular incoming waves and uniform bottom topography only. At last, the perturbation expansion of boundary conditions with respect to wave steepness and current speed limits the analysis to linear or weakly nonlinear phenomena, and up to the author's knowledge, only linearized formulations have been published to date. In these conditions, as for a number of other problems (Ferrant 1996b), time domain analysis represents a very attractive alternative.
