The increasing global demand for energy and environmental concerns have provoked a shift from exhaustible, fossil fuel based energy to renewable energy sources. It is clear that wind energy will play an important role in satisfying our current and future energy demands. In this paper, a horizontal configuration of a Savonius and cup type wind turbines are proposed to be mounted on the upstream edge of a building, in such a way that its low performance is improved by taking advantage of the flow acceleration generated by the edge of the building. The importance of integrated simulations which include both the building and the turbine is shown and it is also demonstrated that the individual calculations of the flow around the building and the turbine individually cannot be superposed. Following the validation of the methodology with experimental data, the performance of the Savonius wind turbines placed in the vicinity of the edge of the building top was calculated. The position, blade number, and circumferential length were then investigated when the turbine is mounted on a building. The objective is to better understand wind turbine behavior for low speed urban environments. The flow fields of conventional Savonius and cup type turbines were solved using Computational Fluid Dynamics (CFD) in 3D domains. The optimal configuration shows an improvement in the power coefficient from 0.043 to 0.24, representing an improvement of 450%. The improvement also demonstrates that although cup type blades show very poor performance in free stream flow, they perform well in the right environment.