Numerical Simulation of Focused Wave and Its Uncertainty Analysis

On the basis of the transient water wave (TWW) theory, focused wave is generated in the circulating water channel. Numerical simulation of the focused wave is carried out by solving the Reynolds averaged Navier-Stokes (RANS) equations. The dynamic grid technique is adopted to simulate the motion of the wave maker, and the volume of fluid (VOF) method is used to capture the free surface of the wave. The simulation results are compared with the measured data, and good agreement is obtained. For quantitative estimation of the numerical simulation error and uncertainty, the uncertainty analysis method recommended by the International Towing Tank Conference (ITTC) procedure is performed for the simulation results of the surface elevations at different positions. Both grid-convergence and time-step-size convergence studies are conducted using three types of grids and time step sizes. The simulation results are all monotonously convergent in the verification procedure, and the validations of the simulated surface elevations with the positions at 3.5, 4.0 and 4.5m are all achieved by comparing with the validation uncertainty. It is found that the numerical simulation errors caused by the grid and time-step-size in the convergence studies have the same order of magnitude. In addition, the numerical errors and uncertainties for the surface elevations at different positions are compared and discussed in detail. This paper presents the first attempt to carry out the uncertainty analysis of the simulation of focused wave, and the effectiveness of the proposed verification and validation procedures in the uncertainty analysis is demonstrated.