Numerical simulation of fully nonlinear regular and focused wave diffraction around a vertical cylinder using domain decomposition

The fully nonlinear regular and focused wave propagation and diffraction around a vertical circular cylinder in a numerical wave tank are investigated. The Mixed Eulerian–Lagrangian approach is used to update the moving boundary surfaces in a Lagrangian scheme, in which a higher-order boundary element method is applied to solve the wave field based on an Eulerian description at each time step. In order to increase the efficiency of the calculation, the domain decomposition technique is implemented, with continuity conditions enforced on the interface between adjacent subdomains by an iterative procedure. In this domain decomposition method, the top layers of elements at the interfaces are semi-discontinuous to avoid problems from the singularity. In addition, mesh regridding using the Laplace smoothing technique and interpolation are applied on the free surface to deal with possible numerical instability. Numerical results are obtained for the propagation of nonlinear regular waves and focused wave groups, and for the diffraction of such waves by a vertical cylinder. These results indicate that the present method employing the domain decomposition technique is very efficient, and can provide accurate results when compared with experimental data.