Non-linear Wave Interaction With Arbitary 3-d Bodies

In this paper, the non-linear wave interaction with a surface-piercing body of arbitrary shape in three dimensions is investigated by a time-domain second-order method. On the basis of Laplase equation, second-order wave diffraction and radiation problems are computed.Since the time-domain theory requires more memory and computation, an efficient B spline based boundary element method is developed firstly. Numerical examinations on first-order wave forces, first-order body responses, fluid velocities and second-order mean drift forces in the frequency-domain theory show that the B spline based BEM is more accuracy and more computational efficient than conventional BEM.In this paper, the fully non-linear problem is transformed to corresponding boundary value problems to first and second order in wave steepness with respect to a time invariant computational domain by the applications of Taylor series expansions to the boundary conditions and the Stokes perturbation procedure. The free surface boundary condition is satisfied to the second order in wave steepness by a numerical integration in time, and the B spline based BEM is used to calculate the wave field at each time step. An artificial damping layer is adopted as the far field radiation condition on the free surface to avoid the wave reflection from the outer boundary, and the present method is found to be numerically stable for various incident frequencies. Additionally, a mathematical manipulation is adopted to remove the second-order spacial derivatives in the body surface boundary condition, and the body response can be obtained by solving the motion equations with the standard Runge-Kutta method.After simulating the linear wave interaction with arbitrary 3-D bodies in time-domain, the tune-domain second-order method is applied to study the wave diffraction around fixed bodies in this paper. The wave forces and free-surface elevations at first and second order in wave steepness are presented. Forfloating bodies, the combined non-linear diffraction-radiation problem is solved. Numerical examples presented relate to the forced oscillation, transient motion and free motion of floating bodies. Furthermore, the time-domain method is also applied to simulate the numerical wave tank preliminarily. As indicated above, all of the numerical results in this paper agree very well with the frequency-domain results and others' time-domain results.