A green-function method for wave interaction with a submerged body

A numerical method for solving boundary-value problems related to potential flows with a free surface is presented. The method determines the hydrodynamic forces exerted on a rigid body oscillating in its six degrees of freedom under a free surface as well as the forces resulting from the wave interaction of the body held fixed. The linearized problem is first formulated for a three-dimensional body of general shape in water of finite depth. Application of Green's third identify, using the Green function that satisfies the free-surface, bottom and radiation conditions, reduces the problem to the solution of an integral equation with the unknown function being the velocity potential over the body surface. An approximate Green function which is valid for the case of a relatively deep water is also presented.