Time-domain solution of freely floating cylinders in a viscous fluid

To realistically simulate motions of a floating cylinder in waves, a fully nonlinear model that includes the effects of viscosity is developed. The equations of rigid-body motions are coupled with the Navier-Stokes equations, which are solved by the Free-Surface Random-Vortex Method (Yeung & Vaidhyanathan, 1994). Inviscid results that are of interest for comparison or validation purposes can be recovered by "shutting-off" viscosity in this formulation. This nonlinear model is first applied to study the transient response of a body with initial displacements for pure heave or roll motion, for comparison with some existing inviscid results. Frequency-domain response in waves is obtained by simulating heave motions in the time domain over a range of frequency. For a freely-floating body in waves, the roll amplitude near resonance is observed to be reduced by viscosity by as much as 50%. The fully nonlinear model is validated by comparing the numerical results with those from the measured values of Sen (1993), revealing considerable improvement over existing predictions based on inviscid fluid.