## 3 Computational Modeling
### Numerical Wave Generation and Boundary Conditions  
The numerical wave generator is positioned to the left of the wave tank, as shown in Figure 3 (highlighted in blue). The wave is generated using the methodology available in the software FLUENT(r), in which the used wave theory is defined (in the present work, it was 2 nd-order Stokes), as well as the height and wavelength using the VOF methodology defined as the open channel wave boundary condition [40]. The equation that describes the prescribed velocity boundary condition is defined by the following formulation, being divided into horizontal and vertical components [22]:  
\[u = \frac{H}{2}gk\frac{\cosh(kz+kh)}{\omega\cosh(kh)}\cos(kx-\omega t)+ \frac{3}{4}\bigg{(}\frac{H}{2}\bigg{)}^{2}\omega k\frac{\cosh 2k(h+z)}{\sinh^{4}(kh)}\cos 2( kx-\omega t) \tag{7}\] \[w = \frac{H}{2}gk\frac{\sinh(kz+kh)}{\omega\cosh(kh)}\sin(kx-\omega t)+ \frac{3}{4}\bigg{(}\frac{H}{2}\bigg{)}^{2}\omega k\frac{\sinh 2k(h+z)}{\sinh^{4}(kh)}\sin 2( kx-\omega t) \tag{8}\]  
The other boundary conditions are also shown in Figure 3. The definition is the following: an atmospheric pressure condition (outlet pressure--lines in red color) is applied on the upper left side, as well as on the upper surface of the tank and at the outlets of the turbine ducts; the condition of non-slip and impermeability (wall--lines in black color) is applied on the bottom of the tank and the walls of the devices. The right surface has a hydrostatic profile (line in yellow color) to eliminate the reflection effect of the waves.  
In addition to the boundary conditions, it is considered an initial fluid condition at rest (flat condition), with depth \(h=10\) m and \(t=0\) s in the free surface elevation equation (Equation (1)). This equation calculates the wave tank's water elevation and determines the wave height at different locations.  
A numerical beach region was inserted into the tank to decrease the wave reflection effects. A sink term (\(S\)) is added to the momentum conservation equation, given by [37,45,46]. An error is introduced with the addition of a term in the conservation equation. A more detailed study regarding its estimation with linear and quadratic terms analysis can be seen in [47].  
The mathematical formulation is presented in the following equation [45,46]:  
\[S=-\bigg{[}C_{1}\rho V+\frac{1}{2}C_{2}\rho|V|V\bigg{]}\bigg{(}1-\frac{z-z_{f} }{z_{b}-z_{f}}\bigg{)}\bigg{(}\frac{x-x_{s}}{x_{e}-x_{s}}\bigg{)}^{2} \tag{9}\]  
Figure 4: Details and characteristics of the OWC device.  
where \(C_{1}\) and \(C_{2}\) are the linear and quadratic damping coefficients, respectively, the term \(\rho\) refers to density, \(\overset{\rightarrow}{v}\) is the velocity, z is the vertical position, \(z_{\text{\tiny{$\mathrm{f}$}}}\) and \(z_{\text{\tiny{$\mathrm{b}$}}}\) are the vertical positions of the free surface and bottom, respectively, \(x\) is the horizontal position, and \(x_{\text{\tiny{$\mathrm{s}$}}}\) and \(x_{\text{\tiny{$\mathrm{e}$}}}\) are the horizontal positions of the beginning and finish of the numerical beach, respectively. According to [PERSON] et al. [48], it is recommended to assume \(C_{1}=20\) and \(C_{2}=0\).