The accuracy of a Computational Fluid Dynamics (CFD) model to capture the complex flow around a small vertical axis wind turbine (VAWT) on 2D and 3D grids is investigated. The aerodynamic complexity of the flow is mostly due to rapid variation of the angle of attack of the rotating blades. The resulting flow includes large separation flows over the blades, dynamic stall, and wake-blade interaction. These features are sensitive to the grid resolution and turbulence models. In the present research, a grid convergence study is conducted on 2D grids to examine the CFD model sensitivity to mesh resolution and to identify when grid convergence is obtained. An averaged-grid size of y^+>30 is employed along the wall to capture the near-wall region flow structures. Moreover, a parallel OpenFOAM solver is used to investigate the numerical solution of Unsteady Reynolds-Averaged Navier-Stokes (URANS) equations coupled with Spalart-Allmaras (SA) turbulence model. As a result, it is seen that the Power Coefficient (C_p), in 2D investigations, increases with the mesh size until it achieves grid convergence. For a 3D simulation, only a coarse mesh can be used due to large computational requirements. It is found that the 3D coarse mesh significantly under-predicts the Power Coefficient but is able to predict tip vortices.