Numerical Investigation on Motion Responses of a Floating Hemisphere Over a Sloping Bottom

Abstract

In the last several decades, some numerical approaches have been proposed to deal with three-dimensional wave-body interaction problems in sloping bottom environment. Most of them either adopt the finite depth Green function or add numerical damping terms into the free surface condition to treat far field radiation condition, which certainly give rise to numerical errors. The hybrid model (Belibassakis, “A Boundary Element Method for the Hydrodynamic Analysis of Floating Bodies in Variable Bathymetry Regions,” Eng. Anal. Boundary Elements 32, pp. 796–810) adopting the consistent coupled-mode system for incident wave propagation problem combining with the three-dimensional bottom-dependent Green function to treat the diffraction and radiation problem is a complete formulation, as the latter function appropriately characterize the far field radiation wave pattern over a smoothly sloping bottom. However, this model has not been validated after its publication. In this connection, comparisons with computational fluid dynamic (CFD) results are presented to verify its accuracy. Application of this hybrid model is also performed to investigate the effects on the floating hemisphere by the sloping bottom.