## 4 Results  
### Validation of the Numerical Model  
In this section, validation studies are conducted through the numerical simulations of breaking waves past a vertical cylinder and an inclined cylinder with \(\varphi=-22.5^{\circ}\). \(\varphi\) is defined as the inclined angle parallel to the direction of wave propagation, details can be seen the set-up in [PERSON] et al. (2018). The present numerical results of the free surface elevations at the WG2 and the \(F_{T}\) are compared with the experimental data from [PERSON] et al. (2018), presented by [PERSON] et al. (2018) and other published computed results to validate the accuracy of the present model. 1.1 Comparisons of the Present Numerically Simulated Results with the Published Data for a Vertical Cylinder  
Figure 5 shows the comparison of the present predicted free surface elevations \(\eta\) at the WG2 location and published data for the vertical cylinder. The present result is in good agreement with the experimental data and the numerical results from [PERSON] et al. (2018) and [PERSON] et al. (2018) except for the slight discrepancy at around \(t/T=31.1\). This could be explained as given below. In the experiment, the wave gauges were installed near the wave tank sidewall to avoid the influence of the measurement equipment on the waves. The interactions between the wave tank sidewall and the wave gauges, as well as the interactions between different wave gauges, can affect the free surface around the measure locations. Figure 6 shows the comparison of the \(F_{T}\) on the vertical cylinder over one wave period between the present numerical simulation and the published data. The present computed result of the \(F_{T}\) agrees best with the experimental data compared with other numerical simulated results. Meanwhile, the numerical computed rise times obtained by present simulation, [PERSON] et al. (2018) and [PERSON] et al. (2018) are ahead of the experimental data at approximately \(t/T=30.4\). The reason for this is that the assumptions of incompressible flow and rigidly fixed cylinders are applied in the present numerical simulations. However, in the experiment, cylinder vibration, surface irregularities, compressibility of the flow during the impact, and water droplets on the surface of the cylinder may have an effect on the rise time ([PERSON] et al. (2018)). Figure 4: The plan view (**a**) and front view(**b**) of the medium mesh near the vertical cylinder. 1.2 Comparisons of the Present Numerically Simulated Results with the Published Data for an Inclined Cylinder  
Figures 7 and 8 show the comparisons between the numerical results and the experimental data in terms of the free surface elevations at WG2 location and the \(F_{T}\) on the cylinder with inclined angle \(\varphi=-22.5^{\circ}\), respectively. The present predicted free surface elevation agrees reasonably well with the published experimental data. A good agreement is generally observed between the present numerical results and the published experimental data for the \(F_{T}\) in Figure 8. The peak value of the \(F_{T}\) calculated by present model is slightly overestimated as compared with the experimental peak value, but smaller than the numerical result obtained by [PERSON] et al. [10].The slight discrepancy can also be seen for the rise times of wave forces at around \(t/T=30.4\) between the numerical simulations and the experimental data. Apart from the reasons mentioned in Section 4.1.1, another critical factor that cannot be ignored is the inclined angle of the cylinder. The rise time and peak value of the force are very sensitive to the inclined angle of the cylinder. In the experiment, the vibration of the cylinder caused by the large wave impact force can change the initial position of the cylinder, which may introduce the measurement inaccuracy. Figure 5: Comparison of free surface elevations at WG2 between the present result and the published data for the vertical cylinder.