have used the integral-equation approach in their studies of fluid motion 

 in the presence of bodies. They make the restrictive assumption that the fluid 

 domain is periodic and use complex-variable techniques that cannot be extended 

 to three-dimensional problems. Greenhow et al . [9] have applied the method 

 of Vinje and Brevig to the capsizing of a body in the free surface. Baker et 

 al . [10] have developed a generalized vortex integral-equation technique that 

 has been used for a body under the free surface. It is not clear whether the 

 generalized vortex method is suitable for numerical computations when a body 

 intersects the free surface or whether it will be computationally efficient 

 when it is extended to three dimensions. Thus, even for computing nonlinear 

 two-dimensional free-surface potential flows, full generality has not been 

 attained. 



This report describes progress made in developing a tool to compute 

 large-amplitude ship motions. The method discussed Is based on an initial- 

 boundary value formulation, and it is a method that is directly extensible to 

 three dimensions. The velocity potential along the free surface and the posi- 

 tions of the moving boundaries are sought as solutions of a coupled system of 

 differential equations. An implicit finite-difference method is used to march 

 the solution of the coupled system of equations forward in time. The auxiliary 

 problem of computing the velocity potential inside the fluid region is solved 

 by a finite-difference method based on boundary-fitted coordinates. Haussling 

 [11] has presented a review of such techniques used for fluid flow problems. 



Results from calculating the potential flow about a cylinder in forced 

 heave motion are presented. The hydrodynamic force on the body has been ob- 

 tained and compared with the hydrodynamic force predicted from second-order 

 perturbation theory. 



