| In this paper, the non-linear wave interaction with a surface-piercing body in three dimensions is investigated by a time-domain second-order method. On the basis of Laplase equation, second-order wave radiation and diffraction problems are computed.In this paper, the fully non-linear problem is transformed to corresponding boundary value problem of first and second order in wave steepness, with respect to a time invariant computational domain by the application of Taylor series expansions to the boundary conditions and the Stokes perturbation procedure.A simulation method of radiation condition------MTF(multi-transmittingformula), which is widely used in many fields such as seismology is investigated in this paper. An attempt has been made to apply the ABC (artificial-boundary condition), into hydrodynamics field, which is based on the MTF, to solve second-order wave radiation and diffraction problems. Some techniques of choosing parameters are summarized to implement the ABC. The computed numerical results have been compared with those calculated by the previous theoretical method.Numerical models, based on the boundary element method have been created to solve the second-order wave radiation and diffraction problems around three-dimensional bodies. One numerical model is used to solve the problem of wave radiation around a neutrally buoyant cylinder. Another numerical model is created to solve the problem of regular wave diffraction around a 3D vertical column fixed at sea bed. Some parameters such as time step, panel size, artificial-velocity of waves, the distance and shape of the far fluid surface etc, are investigated to get the steady results. The potentials on the free surface, the time histories of wave elevations and wave forces on the body are calculated. All these parameters prove that this method can simulate the far field radiation condition well. This new method may help to solve the non-linear wave interaction with a...
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