The composite model, which is the combination of Boussinesq equations and the general description for three-dimensional (3-D) flow with the Volume of Fluid (VOF) method, has been developed for numerical simulation of nonlinear waves in a large domain. That is, the whole computational domain Ω is divided into two subdomains. In the near-field surrounding a structure, Ω1, the flow is governed by the 3-D Navier-Stokes equations and numerically solved with the VOF method. Whereas in the sub-domain, Ω2 (Ω2=Ω-Ω1), the flow is governed by 2-D Boussinesq-type equations and numerically solved with the predictor-corrector algorithm. The velocity and the wave surface elevation are matched on the common boundaries of the two sub-domains. Numerical verification has been conducted for the case of wave propagation and interaction with a square caisson. It is shown that the composite model is effective to the computation of nonlinear waves in a large domain taking into account the complicated flow in the near-field.
In the past two decades, with the development of high-speed computers and computational fluid dynamics, studies on nonlinear wave mechanics by use of numerical wave tanks/basins have been rapidly developed instead of model tests or field investigations. For example, various forms of Boussinesq-type equations for shallow water waves have been developed (Madsen, et al. 1991, 1992; Nwogu, 1993; Zou, 1997), which include the effect of weak dispersion and are capable of reproducing the main characters of wave phenomena in coastal and harbor engineering. Because of its depth-averaged simplification, the Boussinesq-type models turn 3-D problems into 2-D ones and are efficient for large computational domains. However, flow variations in the depth direction can not be given directly, especially near a structure where variations of vertical velocity are important.
