Computation Of Wave Diffraction By 2D Obstacles Using A Scaled Boundary Finite-Element Method

The Scaled Boundary Finite-Element Method (SBFEM) is a novel semi-analytical technique. The method discretizes the governing equation only on the boundary of the computational domain. Compared to the FEM, the method reduce one dimension to be discretized, the analytical procedure are applied at the reduced direction instead. Compared the BEM, the SBFEM need not the fundamental solution. So the SBFEM combines the advantages of the FEM and BEM.A numerical model for diffraction problem of wave action on 2D-fixed boxes is based on Laplace equation in this paper. The derivations and solution of SBFEM equation is expressed in detail. Analytical solution of diffraction problem of water waves by two rigid bodies based on eigenfunction expansions method is established and the results from this analytical method compared with others are in good agreement.The benchmark problem of wave diffraction by a rectangular buoy is computed and numerical results are compared to the analytical ones and those from BEM. The comparisons prove that the present method can well simulate the flow field, and its accuracy is high.The entire computational domain is divided into several sub-domains, and the problem of wave action with twin caissons in a water of finite depth is computed and compared with BEM and other numerical methods. Another problem of wave action with three 2D identical boxes in a fixed mean position in a finite water depth is computed and compared with result obtained by BEM. Sharp peak responses for both horizontal and vertical wave forces on each block are found around two closely special resonance frequencies. While horizontal wave force and vertical wave force on the middle box resonant only around alternative special resonance frequencies, which is different form the other boxes. The distribution of potential and its phase on boxes at two special resonance frequencies is plotted to analyze that the wave force on the middle box respond only one frequency. Numerical experiments are carried out for different 2 or 3 identical caissons with various drafts and gap widths to study the resonance phenomena on the hydrodynamic interaction between modules due to the influence of gaps between blocks. With the decrease of gap width and box draft, the position of the resonant wave number increases. The band width of the resonant wave number depends on gap width closely. With the increase of gap width, the band width increase. Finally, a new floating-bodynamed "rectangular boat" is designed, and the comparisons of wave forces on box and "rectangular boat" are maded.This paper proves that the present method can well simulate the wave diffraction problem, it has a potential to analyse the super large floating structures take the gap into consideration without numerical difficulties. The present results are of practical significance to design of links of modules for very large floating structures.