A numerical model is presented in this paper to solve the diffraction problem of the nonlinear long wave acting on the vertical offshore structure with arbitrary in shallow water. Based on Boussinesq equations combining with the open boundary condition proprosed by Lu (1989), using the finite difference scheme defined at node of triangular element, this method has several advantages such as dealing easily with any vertical cylinder with arbitrary shaped-section, reducing extensively the requirement both on storage and CPU time. The numerical results demonstrate that the present method is capable of simulating efficiently the diffraction problem of nonlinear long wave interacting with a vertical cylinder in shallow water.
Correct prediction of wave force on an offshore structure has been a major concern in offshore engineering. The linear wave diffraction theory is more frequently adopted to evaluate the wave force on large offshore structures. In which the integral equation method and finite clement method arc dominately the two classes of numerical solution techniques for such a problem. Mei (1978) and Zicnkiewicz ct al (1978) had reviewed different approaches adopted in the numerical method solving the linear wave diffraction and radiation problems. The transient wave flow is constrained by an unknown free surface, on which the boundary condition is of a mixed, parabolic type and it contains highly nonlinear terms. In addition, the proper description of the radiation boundary condition is of necessity since the diffraction or radiation wave, once generated, propagates upstream and downstream. Lu (1989) had reviewed the difficulties encountered in the approaches developed for the solution of nonlinear wave diffraction problem. As for the wave diffraction in shallow water, theoretical model is based on Boussinesq equation, which is derived in terms of vertically integrated variables, and the equation itself is nonlinear.