Solving water wave diffraction by an elliptic cylinder using scaled boundary finite element method

The scaled boundary finite element method (SBFEM), a novel semi-analytical mathematical method, is modified to solve the water wave interaction with an elliptic cylinder. By introducing a virtual circular cylinder surrounding the elliptic cylinder, the whole fluid domain is divided into one unbounded subdomain and several bounded subdomains. The corresponding boundary value problems in bounded and unbounded domains are solved by the SBFEM semi-analytically. Comparisons to the previous numerical solutions demonstrate excellent computational accuracy and efficiency of the present SBFEM approach, as well as the benefit of not suffering from the difficulties of irregular frequency, which are often encountered by the boundary element method. The method can be extended to solve more complex wave structure interaction problems resulting in direct engineering applications. References Mei, C. C., The applied dynamics of ocean surface waves, World Scientific, Singapore, 1989. Tao, L., Song, H. and Chakrabarti, S., Scaled boundary fem solution of short-crested wave diffraction by a vertical cylinder, Comput. Method Appl. M., 197, 2007, 232--242. doi:10.1016/j.cma.2007.07.025. Williams, A. N., Wave forces on an elliptic cylinder, J. Waterw. Port. C. ASCE, 111, 1985, 433--449. http://cedb.asce.org/cgi/WWWdisplay.cgi?8500462. Wolf, J. P., The scaled boundary finite element method, John Wiley and Sons Ltd, Chichester, England, 2003. Zhu, S. and Moule G., Numerical calculation of forces induced by short-crested waves on a vertical cylinder of arbitrary cross-section, Ocean Eng., 21, 1994, 645--662. Au, M. C. and Brebbia, C. A., Diffraction of water waves for vertical cylinders using boundary elements, Appl. Math. Model., 7, 1983, 106--114. doi:10.1016/0307-904X(83)90120-8. Bettess, J. A. and Bettess, P., A new mapped infinite wave element for genearal wave diffraction problems and its validation on the ellipse diffraction problem, Comput. Method Appl. M., 164, 1998, 17--48. doi:10.1016/S0045-7825(98)00045-0. Chen, H. S. and Mei, C. C., Wave forces on a stationary platform of elliptical shape, J. Ship Res., 17, 1973, 61--71. Li, B., Cheng, L., Deeks, A. J. and Zhao, M., A semi-analytical solution method for two-dimensional Helmholtz equation, Appl. Ocean Res., 28, 2006, 193--207. doi:10.1016/j.apor.2006.06.003