CONCLUSION 



A computer program to compute the fluid motion resulting from forced 

 harmonic heaving of a U-shaped body in a free surface has been produced. The 

 program computes forces in reasonable agreement with the results of previous 

 researchers who used second-order perturbation theory. The forces have been 

 computed for cases of significant nonlinear fluid motion. 



The computer program will be modified to handle a variety of body shapes 

 and motions. Unlike the complex-variable techniques of Faltinsen [5] and 

 Vinje and Brevig [6-8], the method chosen to solve the problem is extensible 

 to the problem of 3-D nonlinear ship motions. The fluid domain has not been 

 assumed periodic, as was assumed by Vinje and Brevig [6-8]. The location of 

 the intersection of the free surface and the body has not been found from 

 extrapolation, as was used by Vinje and Brevig [7]. 



Additional research needs to be performed before this method can be 

 applied to the general problem of ship motions in two or three dimensions. 

 Satisfactory results have been obtained for a heaving U-shaped cylinder, but 

 heaving wedge-shaped bodies or blunt bodies in horizontal motion in the free 

 surface are known to have more singular fluid flow behavior. Before such 

 behavior can be treated properly, a more sophisticated treatment of the flow 

 near the hull/water surface intersection will be required. Such a treatment 

 should include both the dynamic free-surface equation and the kinematic 

 condition associated with the solid boundary of the cylinder. 



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