| This dissertation consists of two parts. In the first part, the desingularized Cauchy's formula is derived to solve the two-dimensional potential flow problem in an infinite domain. The Gaussian quadrature is applied to discretize the desingularized Cauchy's formula. An efficient method for implementation of Kutta condition is developed. Finally, formulations of fully nonlinear free surface flow past a two-dimensional body are also developed.; In the second part, the desingularized formulation of the problem of a ship advancing through regular waves is presented. Traditionally, ship motion problems are investigated by using either two-dimensional strip theory or three-dimensional panel method. In the desingularized formulation, the singularity involved in the Rankine source of the integral equation is removed by using the "adding and subtracting back" technique. The Gaussian quadrature is applied to distribute the, source on the body surface. In general, the body surface of a ship has no mathematical description. Therefore, the Non-Uniform Rational B-Spline (NURBS) surface is employed to model the body surface.; The influence of the desingularized formulation is demonstrated by computing hydrodynamic coefficients and wave exciting forces of several mathematically defined bodies and some ship hulls. The comparisons between the present numerical solutions and existing analytical results demonstrate the superiority of the desingularized method compared to the panel method. A series of computations are carried out and compared with the experimental results and numerical results published in the literature. |
