ABSTRACT

In this paper, the fully nonlinear computations are done in the time-domain, using an Euler-Lagrange method. At each time step, the resulting mixed boundary value problem is solved using desingularized isolated sources. On the free-surface, the kinematic condition is used to time step the free surface elevation and the dynamic condition is used to march the potential. The waves generated by a source-sink pair and a ellipsoid moving below a free surface are considered.

INTRODUCTION

At the present time, most computations for ship seakeeping or for the diffraction-radiation motions of platforms are done in the frequency domain. To date, the majority of research has assumed that the water can be considered as incompressible and inviscid and that the flow around the body remains irrotational. In this case, the Laplace equation is valid everywhere in the fluid domain and the hydrodynamic forces acting on the body are determined as the solution to a boundary value problem. This problems can be solved by panel methods using either Rankine singularities (aerodynamic) or Kelvin ones satisfying a linearized free-surface boundary condition with use of Green's function. In the first case, unknown singularities have to be distributed on the body and also on a part of the free surface to be determined; furthermore the radiation condition is difficult to satisfy and computational difficulties can be observed at the truncated boundary of the free-surface. In the second case, if problems due to the radiation condition and to the boundary reflections are suppressed, high computational times are required due to the complicated form of the Green's function (Inglis and Price, 1981; Guevel and Bougis, 1982; Wu and Eatock Taylor, 1987; Squire and Wilson, 1992 and Iwashita and Okhusu, 1992 or more recently Ba and Guilbaud, 1995).

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