A boundary element method for the hydrodynamic analysis of floating bodies in variable bathymetry regions

In this work, a hybrid technique is presented for the hydrodynamic analysis of floating bodies in variable bathymetry regions. Our method is based on the coupled-mode theory for the propagation of water waves in general bottom topography, developed by Athanassoulis and Belibassakis [Athanassoulis GA, Belibassakis KA. A consistent coupled-mode theory for the propagation of small-amplitude water waves over variable bathymetry regions. J Fluid Mech 1999;389:275–301.] and extended to 3D by Belibassakis et al. [Belibassakis KA, Athanassoulis GA, Gerostathis TP. A coupled-mode model for the refraction–diffraction of linear waves over steep three-dimensional bathymetry. Appl Ocean Res 2001;23:319–336.], which is free of any mild-slope assumption, in conjunction with a boundary integral representation of the near field in the vicinity of the floating body. Both 2D and 3D problems have been considered. In all cases the near field is represented by boundary integral representation involving simple (Rankine) sources. In the 2D case, the far-field is modelled by complete (normal-mode) series expansions derived by separation of variables in the constant-depth half-strips. In the 3D case, the far-field is modelled by an integral representation involving the appropriate Green's function for harmonic water waves over a bottom with different depths at infinity, developed by Belibassakis and Athanassoulis [Belibassakis KA, Athanassoulis GA. Three-dimensional Green's function for harmonic water waves over a bottom with different depths at infinity. J Fluid Mech 2004;510:267–302.]. The numerical solution is obtained by means of a low-order panel method materialising the hybrid technique. Numerical results are presented concerning floating bodies of simple geometry, lying over sloping and undulating seabeds. With the aid of systematic comparisons with benchmark solutions the convergence and accuracy of the present method in 3D has been studied, and the effects of bottom slope and curvature on the hydrodynamic characteristics (hydrodynamic coefficients and responses) of the floating bodies are illustrated and discussed.