Page 470 - Practical Design Ships and Floating Structures

Practical Design of Ships and Other Floating Structures 445
You-Sheng Wu, Wei-Cheng Cui and Guo-Jun Zhou (Eds)
8 2001 Elsevier Science Ltd. All rights reserved

FULLY NONLINEAR WAVE COMPUTATIONS FOR
ARBITRARY FLOATING BODIES USING THE DELTA METHOD

Tmg-Hang Lee and Chang-Lung Chen

Department of Mechanical Engineering
Tamkang University, Taipei China

ABSTRACT

Fully nonlinear water wave problems are solved using Eulerian-Lagrangian time stepping methods in
conjunction with a desingularized approach to solve the mixed boundary value problem that arises at
each time step. In the desingularized approach, the singularities generating the flow field are outside
the fluid domain. This allows the singularity distribution to be replaced by isolated Rankine sources
with the corresponding reduction in computational complexity and computer time.
Examples of the use of the method in three-dimensions are given for the exciting forces acting on a
modified Wigley hull and Series 60 hull are presented.

KEYWORDS

Fully nonlinear, Eulerian-Lagrangian, Time stepping, Isolated Rankine sources

1 INTRODUCTION

When body motion becomes large, nonlinear waves are generated and higher-order hydrodynamic
forces appear. These phenomena can not be explained by linear theory since nonlinear effects are
essentially excluded. Therefore, time-domain calculations are necessary for fully nonlinear problems
since frequency-domain computations are only good for linear problems or a few very specific
body-exact problems.

Longuet-Higgins & Cokelet [8] first introduced the mixed Eulerian-Lagrangian time-stepping scheme
for solving two-dimensional fully nonlinear water wave problems. Faltinsen [6] used a similar scheme
to study the nonlinear transient problem of a body oscillating on a free surface.
Vinje & Breving [I21 continued the approach of Longuet-Higgins & Cokelet[8] to include finite depth
and floating bodies but retained the assumption of spatial periodicity. Baker, Dommermuth & Yue [5]
used the mixed Eulerian-Lagrangian method and postulated a far-field boundary matching algorithm
by matching the nonlinear computational solution to a general linear solution of transient outgoing
waves.