Numerical simulation of wave diffraction around a fixed free surface piercing body in a 2D viscous wave tank is presented here. The fully-coupled method (Alessandrini and Delhommeau, 1995) used here to solve unsteady Navier-Stokes equations with nonlinear free surface boundary conditions is based on finite-difference schemes and moving grid technique. This method has been already successfully applied to compute wave generation and propagation (Gentaz et al., 1998). Present study is pursuit of this work by introducing a body in a wave tank in order to study wave-body interaction.


Numerical studies of wave-body interactions with computations of hydrodynamic loads is of great interest for naval hydrodynamics and ocean engineering. First methods were based on potential flow linear theory with frequency domain approach. Hydrodynamic loads and eventually motion response and drift of the body due to wave action could be calculated and gave satisfying agreement with experiments for small wave heights and body motions. Next stage has been based on a time domain approach in potential flow theory again with nonlinear free surface conditions. Longuet- Higgins and Cokelet (1976) first develop a numerical boundary elements method (BEM method) using previous assumptions. With such method boundaries of fluid domain (free surface and eventually free surface piercing or immersed bodies) are discretised with boundary elements and potential of each one is calculated by a Freedholm integral equation. Lagrangian markers allow free surface updating. That leads to simulations of numerical wave tanks with wave generation by piston or hinged wavemaker and wave absorption systems (numerical beach method or actNe absorption, see e.g. C16ment (1996) among other contributions). During these twenty last years many authors have developed such 2D or 3D models to study various hydrodynamic problems : wave propagation, absorption, wave-wave or wave-body interactions, wave breaking.....

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