Proceedings of OMAE 2009 28th International Conference on Offshore Mechanics and Artic Engineering 31 May - 5 June, 2009, Honolulu, USA OMAE2009-79517 WAVE KINEMATICS AND SEAKEEPING CALCULATION WITH VARYING BATHYMETRY Guillaume de Hauteclocque Research Department Bureau Veritas (France) Fl´ avia Rezende Research Department Bureau Veritas (France) Yann Giorgiutti Research Department Bureau Veritas (France) Xiao-Bo Chen Research Department Bureau Veritas (France) Professorship, HEU (China) ABSTRACT Diffraction/Radiation theory is used to calculate the wave kinematics and the motions of a floating body in area of vary- ing bathymetry. The bathymetry is modeled as a second body, which, without special measures, leads to spurious reflection at the edge of the mesh. A modified formulation of the Bound- ary Element Method is introduced to model partially transparent panels. Those panels, when properly used to smoothly extend the actual (opaque) bathymetry, allow much more accurate compu- tation. The efficiency of the method is tested with regards of sev- eral parameters concerning the bathymetry size and the way to smooth the truncation. Numerical results are satisfactorily com- pared with a 3D shallow water code based on Green-Naghdi the- ory. The sensitivity to the slope on the ship response is then in- vestigated (motion, added mass, radiation damping and second order loads). The differences with the constant depth calculations are significant, due to the modified incident wave field, but also due to modified added mass and radiation damping terms. The method presented here could be useful in the context of LNG terminals where the depth is quite shallow and the bathymetric variations significant. INTRODUCTION The recent development of LNG terminals has shown the need to extend the capability of seakeeping computations to rel- atively shallow water area. Among the different issues associ- ated with the shallow water, there is the influence of a varying bathymetry which might induce significant changes on kinemat- ics of waves and on the behavior of the ship. A classical way to take into account varying bathymetry in diffraction/radiation seakeeping code is to model the bottom as a fixed second body. However, it has been shown that this method presents difficulties when the bottom has to be truncated at dif- ferent water depths (Buchner 2006). Indeed, the abrupt trunca- tion of the bathymetry induces unwanted and strong reflections. A smoothly sloped extension of the boundary does reduce these reflections but not as much as expected (Buchner 2006). This pa- per presents a new way to smooth more efficiently the truncation by introducing a partially transparent extension. The theoretical formulation of the transparency is explained in a first part; next the efficiency of the method is tested and discussed on different configurations. 1 Copyright c  2009 by ASME Proceedings of the ASME 2009 28th International Conference on Ocean, Offshore and Arctic Engineering OMAE2009 May 31 - June 5, 2009, Honolulu, Hawaii, USA OMAE2009-79517