We present Athena++ grid-based, hydrodynamic simulations of accretion onto Sagittarius A* via the stellar winds of the $sim 30$ Wolf-Rayet stars within the central parsec of the galactic center. These simulations span $sim$ 4 orders of magnitude in radius, reaching all the way down to 300 gravitational radii of the black hole, $sim 32$ times further in than in previous work. We reproduce reasonably well the diffuse thermal X-ray emission observed by Chandra in the central parsec. The resulting accretion flow at small radii is a superposition of two components: 1) a moderately unbound, sub-Keplerian, thick, pressure-supported disc that is at most (but not all) times aligned with the clockwise stellar disc, and 2) a bound, low-angular momentum inflow that proceeds primarily along the southern pole of the disc. We interpret this structure as a natural consequence of a few of the innermost stellar winds dominating accretion, which produces a flow with a broad distribution of angular momentum. Including the star S2 in the simulation has a negligible effect on the flow structure. Extrapolating our results from simulations with different inner radii, we find an accretion rate of $sim$ a few $times 10^{-8} M_odot$/yr at the horizon scale, consistent with constraints based on modeling the observed emission of Sgr A*. The flow structure found here can be used as more realistic initial conditions for horizon scale simulations of Sgr A*.
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