A numerical method for the evaluation of hydrodynamic forces of translating bodies under a free surface

This paper presents a numerical method to evaluate the hydrodynamic forces of translating bodies under a free surface. Both steady and unsteady proble ms are considered. Analytical and numerical studies are carried out based o n the Havelock wave-source function:and the integral equation method. Two m ain problems arising inherently in the proposed solution method are overcom e in order to facilitate the numerical implementation. The first lies in ev aluating the Havelock function, which involves integrals with highly oscill atory kernels. Particular integration contours leading to non-oscillatory i ntegrands are derived a priori so that the integrals can be evaluated effic iently. The second problem lies in evaluating singular kernels in the bound ary integral equation. The corresponding non-singular formulation is derive d using some theorems of potential theory, including the Gauss flux theorem and the property related to the equipotential body. The subsequent formula tion is amenable to the solution by directly using the standard quadrature formulas without taking another special treatment. This paper also attempts to enhance the computational efficiency by presenting an interpolation met hod used to evaluate matrix elements, which are ascribed to a discretizatio n procedure. In addition to the steady case, numerical examples consist of cases involving a submerged prolate spheroid, which is originally idle and then suddenly moves with a constant speed and a constant acceleration. Also systematically studied is the variation of hydrodynamic forces acting on t he spheroid for various Froude numbers and submergence depths. Copyright (C ) 2000 John Wiley & Sons, Ltd.