Numerical Simulation of Focused Wave Based on Fourth Order Compact Finite Volume Scheme

Freak wave is an unexpectedly large wave in ocean with extreme height and abnormal shape. The viscous effect is important in prediction of the flow patterns of the freak wave due to its strong nonlinearity. Thus, compared with the potential theory, more accurate information of flow field of the freak wave can be obtained by using the computational fluid dynamics (CFD) method. In laboratory test and numerical study, the focused wave is often adopted to substitute the freak wave in real sea. In this paper, we present a high accurate numerical model for large eddy simulation of the focused wave. In this model, the space filtered Navier-Stokes equations are solved on non-staggered grids by the finite volume. The fourth order compact scheme is adopted for discretization of both convection and diffusion terms of the governing equations. The standard fourth-order Runge-Kutta method is used for time advancement. The velocity-pressure coupling is ensured at each stage and the discretized equations are solved by strongly implicit procedure (SIP) method. The turbulence is simulated by the Smagorinsky model while the free surface is captured by using of the volume of fluid (VOF) method. The model is firstly validated by simulation of the cavity flow and linear wave. The simulation results are compared with theoretical values and published results, respectively. Finally, large eddy simulation of focused wave is presented. The comparison of the numerical results and measured data reveals that the proposed model is capable of reproducing the propagation and evolution of the focused wave.