We present a numerical three-dimensional time-domain method which is used to study the nonlinear wave diffraction by a vertical bottom-mounted cylinder. The flow evolution is computed using a fourth-order Runge-Kutta scheme. Laplace's equation for the velocity potential is solved by a boundary element method. The free-surface conditions are applied on the actual water surface, the pressure on the cylinder is integrated over its actual wetted surface. We compute the nonlinear diffraction of steady periodic waves by a fixed surface-piercing circular cylinder. The prediction of the horizontal force acting on the cylinder is in good agreement with experimental observations and other numerical results.
An accurate prediction of the wave load on vertical cylinders is crucial in the design process of offshore structures. A linear diffraction theory for calculating the wave forces on a bottom-mounted cylinder was first developed by MacCamy and Fuchs (1954). Despite the usefulness of their method, linear diffraction theory has been found to have a rather limited range of validity since water waves generally behave in a nonlinear (and unsteady) fashion. Time domain boundary element methods (BEM) have also been used to tackle the nonlinear diffraction problem. First introduced by Longuet-Higgins and Cokelet (1976) in the computation of spatially periodic gravity waves, this method was further developed by Faltinsen (1977), Vinje and Brevig (1981), Lin, Newman and Yue (1984) and many others. Isaacson (1982) was the first to use this technique in the three-dimensional problem of nonlinear wave diffraction by a circular cylinder; however, his numerical simulations ended as soon as the diffracted waves reached the outer boundaries. In principle this method is suitable even for highly nonlinear waves. The main diffi- culties arise from the radiating boundaries and the intersection of the free surface and the fixed or floating body.
