## 2 Numerical Model of the Semi-Submerged FOWT  
The semi-submerged FOWT is composed of an NREL 5-MW reference wind turbine [36], a concrete semi-submerged (CSS) platform, and a catenary mooring system. The CSS platform is conceptually designed by the authors and meets the requirements of the Det Norske Veritas Germanischer Lloyd (DNV GL) standard [37]. The platform is designed with three side columns and a central column, and each side column features a cylinder-shaped heave plate with a larger diameter. These columns are interconnected by the pontoon structure. The mooring system is formed by three catenary cables. In the mooring system, cable 1 is along the positive X axis and the angle between two adjacent cables is 120\({}^{\circ}\). The physical parameters and dimensions of the CSS platform and mooring system are summarized in Tables 1 and 2. The natural period of heave and pitch motion of the CSS FOWT is 20 s and 17 s, respectively. The schematic diagram of the CSS FOWT with three mooring cables is shown in Figure 1.  
\begin{table}
\begin{tabular}{c c} \hline
**Parameters** & **Values** \\ \hline Draft & 25 m \\ Platform mass & 11,778,000 kg \\ Radius of gyration about X axis & 33.43 m \\ Radius of gyration about Y axis & 33.70 m \\ Radius of gyration about Z axis & 40.14 m \\ Side column diameter & 13.5 m \\ Side column height & 28 m \\ Center column diameter & 8 m \\ Center column height & 28 m \\ Central distance between center and side column & 55 m \\ Bottom column height & 7 m \\ Bottom column diameter & 18 m \\ Bottom pontoon height & 7 m \\ \hline \end{tabular}
\end{table}
Table 1: Characteristics of the concrete semi-submerged platform.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Values** \\ \hline Type & R4 stuldess steel chain \\ Depth to anchors below MSWL & 100 m \\ Depth to fairlead below MSWL & 18 m \\ Diameter of mooring lines & 70 mm \\ Radius to anchors & 800m \\ Unit mass of mooring cables & 107.39 kg/m \\ Breaking strength & 5156 kN \\ Axial stiffness & 41,486 kN \\ \hline \hline \end{tabular}
\end{table}
Table 2: The detailed information of the mooring system.  
Figure 1: The schematic diagram of the CSS FOWT with three mooring cables.  
The entire numerical model of the CSS FOWT with a catenary mooring system is built by using an advanced FAST-to-AQWA (F2A) coding program, which is a fully coupled aerohydro-servo-elastic modeling tool developed in the AQWA software (v.2019R2), combining AQWA with the FAST platform. The F2A coding program is implemented by using a built-in dynamic link library (DLL) of AQWA interacting with external results from FAST [38; 39; 40]. It means the model of the CSS and the mooring system is constructed in AQWA, while the model of the superstructures (tower, turbine, blades) is formed in FAST. Waves and currents are defined in AQWA as hydrodynamic analysis carried out within it. Turbulent wind is generated by the Kaimal wind spectrum in FAST. Therefore, the dynamic motions of the floating platform and mooring tension are calculated in AQWA by using potential flow theory to solve the velocity and pressure fields. In the solving process, the floating platform is regarded as a rigid body with six motion degrees, and the mooring tension of the cables is obtained by employing the finite element method. The aerodynamics of the turbine and the forces of the superstructures are directly worked out in FAST and then loaded as external input to AQWA by using DLL. Here, the blade element method and multi-body dynamics method are utilized to calculate the aerodynamic and tower base forces, respectively. The work flow, in detail, of F2A code can be seen in reference [38]. The flowchart of the entire simulation process in F2A is shown in Figure 2. Wind is along the positive X direction in all cases, and the waves and currents are along the X or Y direction based on different cases.