## 4 Results and Discussion  
### Analysis of Hydrodynamic Coefficients  
The surface of the DeepCwind semi-submersible FOWT is divided into several meshes, which are composed of non-diffracting and diffracting elements. For obtaining the hydrodynamic coefficients, the semi-submersible is under 0-degree waves, and the radiation force on diffracting elements is precisely calculated. With Equation (5), the hydrodynamic coefficients in six modes are thus obtained. The interaction between waves and the semi-submersible FOWT is illustrated in Figure 7.  
The added-mass and damping coefficients with five panel numbers was compared to the WAMIT data obtained from University of Ulsan (UOU) [16] in the surge, heave and pitch modes, as illustrated in Figures 8 and 9. In the UOU in-house code, the hydrodynamic coefficients, including added mass, radiation damping and wave exciting forces, of the DeepCwind semi-submersible FOWT were calculated by using a diffraction/radiation solver in the frequency domain. It is noted that the surge-surge elements of the added-mass and damping coefficients, \(\mu_{11}\) and \(\
u_{11}\), are identical to the  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Mooring Line Properties** & **Value** & **Unit** \\ \hline Number of mooring lines & 3 & N/A \\ Angle between adjacent lines \(\theta_{M}\) & 120 & degree \\ Depth to anchors below SWL & 200 & m \\ Depth to fairleads below SWL & 14 & m \\ Radius to anchors from platform centerline \(R_{A}\) & 837.6 & m \\ Radius to fairleads from platform centerline \(R_{F}\) & 40.868 & m \\ Unstretched mooring line length \(S\) & 835.5 & m \\ Mooring line diameter \(D_{e}\) & 0.0766 & m \\ Equivalent mooring line mass density \(\rho\) & 113.35 & kg/m \\ Equivalent mooring line extensional stiffness \(K\) & 753.6 & MN \\ \hline \hline \end{tabular}
\end{table}
Table 2: Mooring line properties [11].  
Figure 6: The mooring layout in \(\theta=0^{o}\), \(30^{o}\), \(60^{o}\), and \(90^{o}\) wave heading angles.  
sway-sway elements, \(\mu_{22}\) and \(\
u_{22}\) due to the symmetry of the DeepCwind semi-submersible FOWT. Furthermore, the roll-roll elements, \(\mu_{44}\) and \(\
u_{44}\), are also identical to the pitch-pitch elements, \(\mu_{55}\) and \(\
u_{55}\). Thus, identical results were assembled in the same plots.  
According to the grid-independence test, the difference ratios of 9117 panels and 20,545 panels are less than 1%. Therefore, 9117 panels is enough for the simulation. Additionally, it is obvious in Figures 8 and 9 that the numerical results in both surge and heave modes are close to the WAMIT data, and the peak frequency of these two hydrodynamic coefficients are perfectly met. However, the peak frequencies in the pitch mode slightly deviate from the WAMIT data, which is similar to the findings [17]. The discrepancies between the WAMIT data [16] and our simulation results may be due to the geometric description methods. For WAMIT analysis, a higher-order representation geometric description file, in which the velocity potential on the body surface was represented using B-splines, for the DeepCwind semisubmersible FOWT was created. For our simulation, the un-structured panel grids on most parts of the wetted hull were generated, whereas the structured grids were only distributed on the columns. Even though there are some differences between the numerical results and the WAMIT data, the trends of the hydrodynamic coefficients are similar. The comparison demonstrates that the current 3D panel method is an acceptable calculation for generating the hydrodynamic coefficients required by subsequent time-domain analysis.  
Figure 8: The comparison of added-mass coefficients between different mesh numbers and the UOU data in (**a**) surge and sway, (**b**) heave, (**c**) roll and pitch, and (**d**) yaw modes.  
Figure 9: Cont.