## 3 Numerical Simulations
### Simulation Results and Analysis of the Proposed System  
In this study, the floating body is composed of a hemispherical shape (diameter = 2 m and draft = 1 m below the still water level) with the upper part as a vertical circular cylinder of diameter = 2 m, and height = 0.6 m. The mass of each float was 2147 kg. Each float  
Figure 5: Verification model description of a spherical float constrained to a hinge point. Figure 6: Pitch RAOs of a spherical float: (**a**) Linear analysis [42]; (**b**) Body-nonlinear analysis. consists of 8520 quadrilateral elements for hydrodynamic computation. Figure 7 describes the float. Before analyzing the coupled effects with the foundation structure, the pitch RAO difference between the spherical float and the present body (hemispherical float with vertical circular cylinder on top) was analyzed. The single spherical float has the same mass as the present body and consists of the same number of quadrilateral elements. The water depth was 50 m, and the applied seawater density was 1025 kg/m\({}^{3}\). Each float was fixed to a massless rigid rod, the other end of which was hinge-connected to the foundation structure. This connection allowed rotational movement with respect to the joint at the foundation structure as the center of rotation. The rotational damping proportional to the rotational velocity was applied to the hinge point to describe the PTO system, as shown in Equation (23). This PTO moment resists the rotational motion. The extraction coefficient of 100 kN\(\cdot\)m/(rad/s) was applied through a parametric study for a regular wave [19]. Figures 8 and 9 compare their pitch RAOs, showing the body-nonlinear results. The pitch RAOs of the present body were larger than those of the sphere when the wave frequency was larger than 0.5 rad/s, i.e., in practical sea states, and the present body was superior to the sphere. In this regard, the present body shape was chosen for the subsequent section. In addition, the pitch RAOs of the dual present bodies were calculated and compared. Figure 8 shows the set-up of single and dual floating bodies. The rotational displacement of the floating body was affected by the propagation direction of the incident wave. When the incident wave propagated in the x-direction parallel to the arm, the rotational displacement of the floating body became a maximum [19], which was assumed in this paper. The weather-side buoy was called the \"front\", and the lee-side buoy was called the \"rear\". In the case of dual buoys, the full hydrodynamic interactions of the two floating bodies were included. Figure 9 shows the pitch RAOs of various cases. The pitch RAOs of the front and rear tend to be similar, but the rear becomes slightly larger when the wave frequency is larger than 0.7 rad/s. The differences between the single and dual were small, suggesting that the two-body interaction effects were insignificant in this example. For multiple WECs, more detailed research on the optimal arrangement needs to be investigated for maximum energy extraction efficiency [43]. In the remainder of this study, the fully coupled dynamic analysis of a bottom-fixed elastic foundation platform with WECs attached was performed. For the real sea conditions, Buan, one of the nearshore regions of Korea, was selected by referring to previous studies [19,25]. Figure 10 shows the location of the wave buoy installed in the Buan site for wave data measurement. The five-year average winter wave data were collected by the Korea Meteorological Administration (KMA) from November to February, from 2017 to 2021 [44]. Figure 7: Description of a hemispherical floating body with a vertical circular cylinder on top: (**a**) Numerical model; (**b**) Panel distribution.