The paper presents a numerical approach to study of fluid flow characteristics and to predict performance of wind turbines. The numerical model is based on Finite-volume method (FVM) discretization of unsteady Reynolds-averaged Navier-Stokes (URANS) equations. The movement of turbine blades is modeled using moving mesh technique. The turbulence is modeled using commonly used turbulence models: Renormalization Group (RNG) k-${varepsilon}$ turbulence model and the standard k-${varepsilon}$ and k-${omega}$ turbulence models. The model is validated with the experimental data over a large range of tip-speed to wind ratio (TSR) and blade pitch angles. In order to demonstrate the use of numerical method as a tool for designing wind turbines, two dimensional (2-D) and three-dimensional (3-D) simulations are carried out to study the flow through a small scale Darrieus type H-rotor Vertical Axis Wind Turbine (VAWT). The flows predictions are used to determine the performance of the turbine. The turbine consists of 3-symmetrical NACA0022 blades. A number of simulations are performed for a range of approaching angles and wind speeds. This numerical study highlights the concerns with the self-starting capabilities of the present VAWT turbine. However results also indicate that self-starting capabilities of the turbine can be increased when the mounted angle of attack of the blades is increased. The 2-D simulations using the presented model can successfully be used at preliminary stage of turbine design to compare performance of the turbine for different design and operating parameters, whereas 3-D studies are preferred for the final design.