In the present paper the interaction of a wave system with a submerged or surface piercing body is studied. The wave diffraction caused by a cylinder in finite depth water and by a shoal is been computed and the results are compared with analytical solutions and experimental data. The problem is analysed numerically in the frame of irrotational incompressible flow hypothesys. Both the linearized and the fully nonlinear mathematical models are studied. The numerical solution is gained by means of a mixed panel desingularized formulation. An explicit time-marching algorithm updates the wave elevation and the potential at the free surface. In all cases, the numerical simulation mirrors the experimental data. In the case of the diffraction around a cylinder, the simulation confirms and extends the theoretical results of the second order analysis (Kriebel 1990, 1992): the linear model yields a very good estimation of the force amplitude acting on the body, while the wave profiles are poorly predicted when compared with the fully nonlinear simulation and the experimental data.
At present, there are several closed-form solutions for the diffraction problem in the case of linear interaction of waves with bodies of very simple shape, like wave-vertical circular cylinder interaction (see, for instance, Havelock (1940) for the deep water solution and MacCamy and Fuchs (1954) for the finite water depth solution). The nonlinear problem is much more difficult to be faced in analytical form. Some solutions for the interaction of a wave train with a surface piercing cylinder are sought through a perturbation expansion (see Kriebel(1990, 1992) and the bibliography cited therein), that yields separate linear boundary value problems to be solved for each term in the power series. In this case, second order analysis shows that nonlinear wave patterns differ significantly from linear theory.
