On the development of a higher order time-domain Rankine panel method for linear and weakly non-linear seakeeping computations

Abstract

The development of a numerical method for the computation of the linear and weakly non-linear wave effects on floating bodies is presented. The method is formulated in terms of a higher order time-domain boundary elements method based on the Rankine sources. The higher order approach is assumed for both body geometry (using NURBS) and computed function (using B-splines), the former in a standard CAD geometry format to provide more flexibility. In this paper, the procedures adopted for the numerical solution of the main mathematical problems involved are thoroughly described and discussed, with the purpose of documenting important aspects of these methods that are often absent in the literature. Several verification cases are presented, including first-order quantities (motion RAOs, velocity field, and free-surface elevation) and second-order loads (mean drift, sum, and difference components). Regarding the latter, at the present stage of the development, the numerical method is able to compute the so-called quadratic components of forces and moments. For these loads, steady-state solutions in both monochromatic and bichromatic waves are compared to the results obtained with a well-known frequency-domain code. Keywords Higher order boundary element method Á Time-domain Á Rankine sources Á Seakeeping Á Quadratic second-order loads.

Prediction of non-linear wave loads on large floating structures using a 3D numerical wave tank approach

“…The other important difference is in the modeling of the non-linearities. In Ruggeri et al [33], the 2nd order loads are theoretically consistent up to second-order arising 1 3…”

“…This is subsequently extended by considering multiple bodies that may undergo large relative displacement and thus necessitates re-gridding the domain [39]. Next the authors extend their approach to compute quadratic component of forces and moments [33] and results presented in this last development include second-order forces on floating spheres. Except in Watai et al [39], in all the developments the fluid boundary domain remains the mean domain which means that the surface mesh remains invariant with time enabling the so-called influence coefficients to be determined only once.…”

“…As regards differences, we use a low-order BEM compared to a Non-Uniform Rational Basis Spline (NURBS)based BEM in Ruggeri et al [33], which is an aspect primarily concerned with the accuracy achievable from a given mesh size. The other important difference is in the modeling of the non-linearities.…”