Savonius wind turbines are special class of vertical axis wind turbines (VAWTs). These are low-cost drag-driven turbines and are known to be inefficient. It is proposed in this study that a simple modification to the turbine blade design can yield a significant improvement in power efficiency. The performance of the new design is extensively studied on OPENFOAMv1812, a popular open source computational fluid dynamics (CFD) library. The flow equations coupled with equations of rotation of the turbine are solved on an overset mesh framework. This study also serves as a validation of recently released overset support in OPENFOAM. The turbulence is incorporated by coupling Reynolds-averaged Navier-Stokes (RANS) with shear stress transport (SST) κ-ω eddy viscosity turbulence model. The turbulence parameters are set to produce a flow with the Reynolds number, Re=4.8 × 105. To have better confidence in simulations, this study also presents a comparison of numerical flow over conventional Savonius turbine designs with the published data. It is observed that a majority of CFD analysis on wind turbine designs are performed for the fixed tip speed ratio on a traditional static mesh structure. But, in this CFD study, a winddriven rotation of Savonius turbine is simulated on an overset dynamics approach. The results of the study are compared and discussed based on the predicted moment and power coefficients, pressure variation on the blades, flow velocity field, and wake analysis. The study indicates that the blade design presented here has a potential to increase the power efficiency of a Savonius wind turbine by 10-28\%. © 2020 American Society of Mechanical Engineers (ASME). All rights reserved.