Simulation of second-order wave interaction with fixed and floating structures in time domain

Abstract

The application of a time-domain second-order method in the numerical simulation of the nonlinear wave interaction with surface piercing fixed and floating circular cylinders is described. In this approach, Taylor series expansions are applied to the boundary conditions on the instantaneous free water surface and body surface, and Stokes perturbation procedure is then used to establish corresponding boundary value problems at the first and second order of wave steepness with respect to a time-independent fluid domain. A boundary element method based on a B-spline function expansion is adopted to calculate the wave field at each time step, and the time stepping scheme is implemented to predict the boundary conditions at the next time step. The combined diffraction–radiation problem is solved when the wave interaction with a floating body is considered, unlike treating them separately in the conventional frequency domain method. Additionally, a mathematical transformation is derived to remove the second-order spatial derivative appearing in the body boundary condition that may lead to the potential loss of accuracy. As an illustration, numerical results of the wave diffraction around a bottom-mounted circular cylinder, wave radiation by a circular cylinder undergoing specified motions and wave interaction with a freely and moored floating circular cylinder are presented. Comparisons of the wave forces on the fixed and floating structures with the second-order frequency domain and fully nonlinear solutions indicate that the present numerical method is accurate, efficient and stable.