The Earthquake Engineering Online Archive

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

Kioka, Wataru

UCB/EERC-80/11, Earthquake Engineering Research Center, University of California, Berkeley, 1980-04, 142 pages (555.1/K56/1980)

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 identity, 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. The integral equation is solved numerically by means of a finite element technique consisting of triangular elements. An approximate Green function, which is valid for the case of a relatively deep water, is also presented. The numerical procedure is outlined in detail for the bodies fully submerged under the free surface. Test computations were carried out for a sphere, an ellipsoid, and a circular cylinder. Agreement with results obtained by others is generally very good. The approximate Green function produces accurate results for many practical situations with less computer time required for numerical evaluations.

Available online: http://nisee.berkeley.edu/documents/EERC/EERC-80-11.pdf (3 MB)