# A Numerical Study of the Performance of Point Absorber Wave Energy Converters
## 1 Introduction  
Wave energy converters (WECs) can capture and convert energy from ocean waves into electrical energy. Different types of WECs exist, including oscillating water columns, point absorbers, and overtopping systems. The design investigated here is a point absorber for offshore applications [1; 2; 3]. This system consists of a buoy interacting with ocean waves and different mechanical units, which convert the buoy's movement into electricity. It harnesses the energy from the sea in all directions and is small in shape, with the buoy generally floating on the water surface. Frequent changes in wave conditions, harsh weather, and storms can make a buoy's operation unpredictable. To avoid these problems, submerged wave energy converter (SWEC) devices are designed. They are typically attached to a static platform [2; 4; 5], are well suited for offshore applications, and can be deployed in large arrays to generate significant amounts of electricity. SWECs should withstand extreme wave loads and corrosion from seawater. Although submergence increases their survivability in harsh conditions, as negative effects due to strong wind and rain are limited, their hydrodynamic properties are affected, for instance, the maximum absorbed power [6]. A cylindrical submerged wave energy converter was investigated in [7; 8], and the authors demonstrated that the linear theory fails to predict its performance for steep waves. The effects of the phase shift, cylinder radius, wave height, and wave period on the efficiency of a similar system were considered in [9]. The authors used the potential flow theory for their simulation work and found that the elliptical motion of the WEC was more efficient than the horizontal and vertical ones. The performance of different point absorber converters was studied in terms of energy extraction, bandwidth, and optimal size for a particular wave condition in [6]. A sphere, a vertical cylinder, an ellipsoid, and a chamfered cylinder were simulated at different submergence depths (0, 3.75, and 6.5 m) using the Boundary Element Method (BEM) under regular and irregular waves. The authors showed that the sphere and the vertical cylinder displayed lower energy conversion than the other two systems. The impact of pitch on the power extraction capabilities of a submerged cylindrical WEC with a radius of 12.5 m and a height of 5 m using a weak-scatterer model was studied in [10]. The authors considered linear and nonlinear potential theories for water and submergence depths of 6.5 and 30 m. The results show that using the nonlinear theory improves the WEC performance due to more stable pitch adjustments, resulting in better power absorption. The importance of the controller and geometric design aspects in the development of multi-mode WECs is highlighted, as these factors significantly affect the system's dynamics. The authors also investigated the design of a planar three-tethered WEC, focusing on optimizing the surge, heave, and pitch hydrodynamic modes to maximize power absorption. Most studies of submerged point absorbers are based on the BEM [11]. This approach shows drawbacks due to limiting assumptions, the flow being considered linear and irrotational, and viscosity effects being neglected. The nonlinear effects of point absorber wave energy converters can, however, be modeled through Computational Fluid Dynamics (CFD). There are two approaches: conventional mesh-based methods (typically Eulerian) and mesh-free methods, such as Smooth Particle Hydrodynamics (SPH), which is a Lagrangian approach. For the first approach, the Finite Volume Method (FVM) is generally used to track the nonlinear interaction between a floating object and water waves, with the coupling of the fluid and the rigid body. For the SPH method, the fluid is modeled as a collection of particles, and the solid body is modeled through a boundary representation.