This paper presents an efficient method to calculate the second-order velocity potential of finite depth water for an arbitrary three- dimensional body in a monochromatic incident wave. A boundary integral equation, including the integral of Green’s function and forcing terms of the free surface condition, is employed to obtain the second-order velocity potential with double frequency. The free surface integral is subdivided into the inner and outer regions by a circle of arbitrary small radius close to the water line of the body. A higher-order isoparametric element technique may be applied to evaluate the integral over the inner region. For the outer region, using the complete Green’s function, the integral is analytically expressed as the functions of the Fresnel Integrals and Complementary Error Function.
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