Three-Dimensional Solution for the Diffraction Problem of a Submerged Body in Waves

The paper presents a panel method to evaluate the diffraction problem on a submerged body moving beneath the free surface in regular waves. In the process of numerical calculation, the 1/r term in the potential function is treated by the method submitted by Hess & Smith (1964) with three ways for the integration, and the pulsating source terms due to the free surface effect are solved by using four different series expansions and an integral representation submitted by Telste & Noblesse (1986). With such derivation, the numerical computing techniques become available to calculate the wave exciting force for a submerged body advancing in regular waves at constant speed. Besides, the effect of the steady potential is also considered in the paper. The replacement of the double integration by a single integral in terms of a complex exponential integral is made in the derivative of the steady potential. The source strength on panels is solved efficiently by applying the Gaussian elimination method incorporated with the partial pivoting technique. Results obtained by the present technique are compared with the other methods and good agreement is found. The effect of steady flow is generally small, but it still cannot be neglected in some cases, especially for the slender body in oblique waves. It is also found that using the present technique incorporated with a suitable body mesh distribution can lead to more satisfactory results.