## 2 Methodology
### Grid Independence Study  
An unstructured mesh was used for both the stationary and rotating regions. In addition, mesh refinement was performed near the interface boundary and the blades. The structured mesh around the blade was constructed in such a way as to provide the coefficient values \(y^{+}=1\). Since the mesh density and quality can have a significant impact on the CFD calculation results, a mesh convergence study was conducted to determine the effect of mesh resolution on the calculation result of the torque coefficient \(\mathrm{C_{m}}\). The mesh distribution for a typical four-bladed NACA 0021 case is shown in Figure 4.  
The cell growth factor was 1.05, and the maximum cell size was less than the profile chord length. The grid structure is focused on the vertical-axis wind turbine (VAWT) region, with inflation (boundary) grid layers used around the airfoil and in the rotating region. These are necessary to improve the accuracy of the flow simulation in the boundary layer adjacent to the airfoil surface, as well as to correctly account for shear stresses and velocity gradients near the walls in the rotating region. This is especially important for an adequate description of turbulence and viscous effects. The thickness of the first layer was set to 10\({}^{-4}\) m, and the growth rate in the inflation grids was 1.1. As part of the study, grid independence was tested on one of the typical geometries, with a rotor diameter of 3 m and  
Figure 4: Topology of mesh used in numerical simulation. \begin{table}
\begin{tabular}{c c} \hline
**Parameter** & **Meaning** \\ \hline Wind speed, U & 8 m/s \\ \hline Rotation frequency, \(\upsilon\) & 100 rpm \\ \hline Air density, \(\rho\) & 1.23 kg/m\({}^{3}\) \\ \hline Molecular viscosity, \(\upsilon\) & 1.789 \(\times\) 10\({}^{-5}\) m\({}^{2}\)/s \\ \hline Empirical coefficients (model constants), \(\beta^{*}\), \(\beta\), \(\gamma\) & 0.09; 0.075; 0.5532 [32] \\ \hline Switching function, \(F_{1}\) & varies from 0 to 1 [35] \\ \hline Empirical constants of the SST model, \(\sigma_{k}\),\(\sigma_{\omega}\), \(\sigma_{\omega 2}\) & 0.85; 0.5; 0.856 [32] \\ \hline \end{tabular}
\end{table} 
Table 3: Input parameters of model. a chord length of 0.4 m. A mesh independence study was conducted to verify the accuracy of the solution using three levels of global mesh refinement: coarse, medium, and fine meshes. Both the boundary layer and external regions of the domain were proportionally refined with a maximum growth rate of 1.05 to facilitate smooth transitions between mesh sizes. The power coefficient and the torque coefficient, averaged over a single blade, served as the primary metrics for evaluating mesh sensitivity. It was determined that the discrepancy between the medium and fine meshes was less than 2%, confirming the mesh independence of the solution. Comprehensive results are presented in Table 4.  
A sensitivity test was conducted to assess the impact of the mesh transition between the boundary layer and the domain mesh. The results showed that the absence of a noticeable transition in the initial mesh did not significantly affect the computational results, with deviations remaining within 1%, as illustrated in Figure 5.  
To assess the accuracy of the numerical simulation and eliminate the influence of discretization on the calculation results, ten variants with different total numbers of elements were considered: 178566, 214127, 290642, 341081, 415934, 471592, 565187, 620011, 727322, and 809273. In all cases, the grid was densified in the rotor region, and inflation layers were used around the airfoil and in the rotating region to accurately resolve the boundary layer.