Straightforward integration for free surface Green function and body wave motions

An alternative manner is provided for solving the classical linearised problem of the radiation and diffraction of regular water waves caused by oscillation of a floating body in deep water. It is shown that the singular wave integrals of the three-dimensional free surface Green function $G$ and its gradient $\nabla G$ can be regarded as regular wave integrals and are integrated directly. The method is validated by comparing with benchmark data for a floating or submerged body undergoing oscillatory wave motions. The comparison shows that the evaluation is sufficiently accurate for practical purposes. As the significance of the method, the numerical approximation stability for the gradient $\nabla G$ is shown to be the same with that for $G$.