## 3 CFD Modelling  
The CFD software Star-CCM+ V9.06 is used in order to simulate the two-dimensional impact of wedge sections on water. The volume of fluid (VOF) approach was used to simulate the water-air mix. Water and air were modelled as incompressible, inviscid fluids, and unsteady, while the wedge motion was modelled as a rigid body motion. Finally, the wedge motion was modelled with two approaches. In case of impact with prescribed motion, a rigid body with the rigid mesh approach was used. In the case of free fall impact, the motions were modelled with mesh morphing. The effect of gravity was taken into consideration. The VOF formulation used in the CFD includes the HRIC (High-Resolution Interface Capturing) method, the controls of this method are the lower current number Cu\({}_{\text{l}}\) that was set at 0.5, the upper current number Cu\({}_{\text{u}}\) that was set at 1.0, and the angle factor C\({}_{\text{\theta}}\) that was set at 0.05. Figure 6 shows the computational domain at 10 b wide and 4.7 b high, and the boundary conditions as: wall in the base, verticals walls, wedge boundaries, and a pressure outlet in the top boundary.  
The mesh was developed with polyhedral elements and a mesh refinement was performed in the free surface area around the wedge and wedge walls. Figure 6 shows the mesh for the computational domain after the mesh independence analysis was carried out for a free fall test with 3 DOF.  
The converge analysis was carried out according to ITTC (International Towing Tank Conference) [23], the global convergence ratio R\({}_{\text{g}}\), the global accuracy order p\({}_{\text{g}}\), the global correction factor C\({}_{\text{g}}\), and the global uncertainty U\({}_{\text{g}}\) were computed using the norm L2. We considered 425 points of the solution, the accuracy order was calculated according to [PERSON] [24], and the base size of the  
Figure 5: Forces diagram in the wedge.  
Figure 6: Computational domain.  
mesh and time step were changed. Figure 7a shows the time series for angular acceleration (\(\dot{\omega}\)) when the impact with three degrees of freedom is considered. Four different mesh sizes were evaluated, and we noticed that the results for mesh sizes \(4.3\times 10^{5}\) and \(6.0\times 10^{5}\) cells are superposed. Figure 7b shows the time series for angular acceleration when three different time steps are considered. For time steps \(\Delta t=1\times 10^{-4}\) s and \(2\times 10^{-4}\) s the curves are superposed, and a time step of \(2\times 10^{-4}\) s was selected. Table 1 shows the base size of the mesh, the number of elements, and the parameters of the study, \(0<\text{Rg}<1\). The solution is monotonic convergent, the accuracy order is 0.647, the global uncertainty is 28.1% of the maximum acceleration, the convergence ratios in the crest and hollow were computed, and they are convergent.  
Figure 8 shows the free surface during the impact in free fall of a wedge with two degrees of freedom. When the wedge touched the water is considered to be t = 0. At the beginning of the impact  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Mesh** & **h (m)** & **Cells** & **Rg** & **Pg** & **|I-Cgl** & **Ug \%** \\ \hline
3 & 1.00 & \(3.2\times 10^{4}\) & & & & \\
2 & 0.45 & \(1.4\times 10^{5}\) & 0.341 & 0.647 & 0.25 & 28.14\% \\
1 & 0.30 & \(4.4\times 10^{5}\) & & & & \\ \hline \hline \end{tabular}
\end{table}
Table 1: Mesh independence analysis.  
Figure 7: Mesh independence analysis. (**a**) Angular acceleration vs. time, and size independence. (**b**) Angular acceleration vs. time, and time independence.  
the flow is parallel to the section (Figure 8a-c), the flow separates from the both sides of the section after the jet reaches the chine (Figure 8d-f).