In this study, we describe a mathematical method based on a discrete vortex method, which can be applied, in the first part, to analyze theoretically the complex flow around a Savonius rotor. In the second, we use the velocity and pressure fields, computed by this method, to deduct the mechanical and energetic performances. Calculations are performed by combining the singularity method and the discrete vortex method. The method is applied to simulate the effects of different parameters, as overlap, wind speed, number of bound vortices, and limit between two free vortices, on the flow about the rotating and stationary rotor. Early results are encouraging and are in good agreement with experimental data reported by Z. Aouachria. The study continues to understand and clarify the operation of the machine and to determine a design of the most performing rotor.