Many characteristics of galactic nuclei may be associated with the accretion of ambient gas by a central concentration of mass. Using a 3D hydrodynamical code, we have been simulating this accretion process for Sgr A∗, the compact nonthermal source at the center of the Milky Way, in order to realistically model the gaseous flows in the inner parsec of our Galaxy. In the most recent simulations, we have taken into account the multi-point-like distribution of wind sources and we find that the structure of the flow can be significantly different from that due to a uniform medium. We here present our results concerning the mass and angular momentum accretion rates and discuss how these may be used to set constraints on our Galaxy's central engine.