  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*.
