Froude-Krylov forces from exact pressure integrations on adaptive panel meshes in a time domain partially nonlinear model for ship motions

Abstract

A partially nonlinear time domain model for predicting ship motions is presented with Froude-Krylov forces being calculated on the exact instantaneous wet part of the floating body. An adaptive mesh technique following a quad-tree subdivision and cutting scheme is applied, in order to track the free-surface of the undisturbed wave, and its intersection with the hull, to generate instantaneous wet meshes. Analytical exact pressure integration expressions are evaluated on the, thus formed, wet panel mesh, regarding the undisturbed wave and hydrostatic pressures, which allow for considerably coarse meshes without any loss of accuracy. Diffraction and radiation forces are kept linear with the latter being introduced using linear unit impulse response functions. The body is impeded from drifting by artificial kinematic restrains in non-restoring modes.Roll decay motions of a military vessel's hull, and under head, beam and quartering waves are numerically predicted and compared with published experimental ones, for zero advance speed. The capabilities and limitations of the proposed method, taking into account the specific simulation setup applied, are addressed. An overall agreement with the experiments is witnessed, with the method showing a considerable improvement of numerical predictions of the ship motions in beam and quartering waves in comparison with those by a linear method.