Diffraction/Radiation theory is used to calculate the wave kinematics and the motions of a floating body in area of varying 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 Boundary 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 computation. The efficiency of the method is tested with regards of several parameters concerning the bathymetry size and the way to smooth the truncation. Numerical results are satisfactorily compared with a 3D shallow water code based on Green-Naghdi theory. The sensitivity to the slope on the ship response is then investigated (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.

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