Nonlinear radiation problems for a surface-piercing body.

Abstract

A Desingularized Eulerian-Lagrangian Time-domain Approach (DELTA method) is used to investigate fully nonlinear radiation problems of surface-piercing bodies. At each time step, a boundary-value problem is solved by placing fundamental singularities outside the computational domain and satisfying the boundary conditions at prescribed collocation points. This desingularization allows the use of simple isolated sources while retaining the necessary accuracy. A large outer region is investigated to postpone the free surface mean shift and wave reflection from the truncation boundary. The outer region is divided into exponential increasing panel sizes. The length, the first panel size and the panel number are found to be the crucial factors determining the effectiveness of the outer region. The effectiveness is relatively unaffected by forcing frequency and motion amplitude. Both two- and three-dimensional problems are studied. A floating body is oscillated vertically or laterally. For two-dimensional problems, results from the desingularized method agree well with experiments and other algorithms. For three-dimensional heaving motions, the results of the symmetry-plane method show good agreement with the quarter-plane and Rankine-ring source approaches. Primary convergence and stability analyses are also conducted. The convergence rate is slightly lower for swaying motions than heaving motion because the singularity at the body-free surface intersection line (points) is more crucial for swaying motions. The desingularized scheme is more stable than the conventional boundary integral method. Large-amplitude computations are also performed for an upright cylinder with a larger bottom. The results of computations demonstrate the power of the DELTA method for use in offshore applications.