A time-domain method is applied to simulate nonlinear wave diffraction around a surface piercing 3-D arbitrary body. The method involves the application of Taylor series expansions and the use of perturbation procedure to estab-lish the corresponding boundary value problems with respect to a time-independent fluid domain. A boundary element method based on B-spline expansion is used to calculate the wave field at each time step, and the free surface boundary condition is satisfied to the second order of wave steepness by a numerical integration in time. An artificial damping lay-er is adopted on the free surface for the removal of wave reflection from the outer boundary. As an illustration, the meth-od is used to compute the second-order wave forces and runup on a surface-piercing circular cylinder. The present method is found to be accurate, computationally efficient, and numerically stable.

A Fast Melipole Mechod (FMM) is developed as nurnerical approach to the reduction of tile computauorai cost and requirement memory capacity for a large in solving large-scale problems. In this paper it is applied to the boundary integral equation method (BIEM) for current diffraction from arbitrary 3D bodies. The boundary integral equation is dis-crotized by higher order elements, the FMM is applied to avoid the matrix/vector product, and the resulting algebraic e-quatiun is solved by the Generalized Conjugate Residual method (GCR). Numerical examination shows that the FMM is more efficient than the direct evaluation method in computational cost and storage of computers.

Within the frame of potential theory and the assumption of weak nonlinearity of wave motion, a numerical method is developed for the third-order triple-frequency wave loads on fixed axisymmetric bodies in monochromatic incident waves. Applying the numerical code, numerical computations were carried out for surge and heave forces and pitch moments on a uniform cylinder, truncated cylinders and a hemisphere. Examinations were made of the contribution to third-order forces and moments from potentials at each wave order, and the relation of third-order forces and moments to wave number and drafts of cylinders.