Abstract
A two-dimensional boundary element method is used to study the hydrodynamics of a single barge with prescribed motions of large amplitudes and high frequencies. The wave radiation problem is solved in the time domain based on the fully nonlinear potential flow theory. For numerical simulations, special treatments like plunging wave cutting and remeshing approaches are presented in detail. The numerical schemes are verified through comparing with analytical results. Both the generated outgoing wave amplitudes and hydrodynamic coefficients can be calculated with sufficient accuracy. Then, we focus on large heave, sway and roll motions to investigate the nonlinear effects on hydrodynamic forces, respectively. In particular, the heave motion with two frequencies is also simulated to study the interactions between results at different frequencies. It is interesting to see the sum and difference frequency components and the envelopes in time histories as a result. For forces caused by forced sway or roll motions, there are only even-order harmonics for vertical forces and only odd-order harmonics for horizontal forces. Finally, a single body with combined sway, heave and roll motion is studied to examine the interactions between motion modes.
Highlights
The wave–body interaction problem has long been one of the focuses of hydrodynamics
The oscillating fluid pressure resulting from the fluid motions and radiated waves is the source of hydrodynamic forces
In terms of the hydrodynamic loads, nonlinearity is manifested in the occurrence of the higher order harmonic forces
Summary
The wave–body interaction problem has long been one of the focuses of hydrodynamics. The study starts from wave interactions with one single body. The wave radiation problem is related to a rigid body in forced motions in otherwise calm water, which can generate outgoing waves. The study of wave radiation problem dates at least back to Ursell [1]. He studied the harmonic heave motion of a horizontal circular cylinder in infinite water depth. Black et al [3] calculated the radiation problem including heave, sway and roll of a rectangular section (2D) and a vertical circular cylinder (3D) by employing Schwinger’s variational formulation. An analytical solution to the heave radiation of a rectangular body was presented by Lee [4], who divided the whole fluid region into three sub-regions and solved the nonhomogeneous boundary value problem separately. Li et al [5] considered the radiation problem of a circular cylinder submerged below an ice sheet with a crack
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