| Abstract | This paper presents the recent development of a second generation of numerical methods for the modelling of hydrodynamic forces and large motions induced on partly submerged floating bodies by steep water waves. The methods are based om the potential flow hypothesis and include a direct numerical solution of the resulting non-linear boundary value problem in the time domain for the unknown fluid velocity potential. The equation is solved in a fluid domain bounded by the free surface of the fluid in its instantaneous configuration, the instantaneous wetted surface of the floating body, and a bottom. The boundary value problem is solved numerically using boundary element techniques. In the examples presented in the paper both zero order (constant source density) and first order (linearly varying source density) Rankine source boundary elements are applied. The evolution of the free surface is formulated in both Eulerian and Lagrangian schemes. The numerical models are applied to simulate two-dimensional propagation of linear and non-linear waves through the control fluid domain, and the interaction of such waves with fixed bodies. The accuracy, stability and convergence of the solutions are throughly investigated, including the satisfaction of mass and energy conservation principles. |
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