| A pseudo-spectral method for nonlinear wave-body interaction problems is developed. The method decomposes the velocity potential into two separate potentials, one due to the presence of the free surface, and the other due to the presence of the body. This decomposition transforms the wave-body interaction problem into a pair of coupled problems for the free surface and the body, each of which can be solved efficiently. The coupling occurs through modifications to the body boundary condition and the free-surface evolution equations. The modified body problem is solved in an infinite domain using a boundary-integral method, while the coupled free-surface evolution problem is described by a pair of fully nonlinear, closed, explicit, evolution equations which can be solved pseudo-spectrally.; This approach is more efficient than previous High-Order Spectral (HOS) methods because instead of solving the Laplace equation for each order using a spectral approach, as is done in HOS methods, the approach presented here uses explicit equations to describe the free-surface evolution and solves a modified body-problem in an unbounded domain with a greatly reduced number of points.; Numerical experiments are carried out using a pseudo spectral method to solve the third-order form of the evolution equations for the free-surface, and a desingularized boundary-integral approach to solve the body problem. The results obtained show good agreement with previous theoretical and experimental results for various problems, including free-waves and pressure-forced waves in two and three dimensions, and wave-body interaction problems in two dimensions with the body submerged or piercing the free surface. |
