  We simulate shells created by supernovae expanding into the interstellar
medium (ISM) of the nuclear region of a galaxy, and analyze how the shell
evolution is influenced by the supernova (SN) position relative to the galactic
center, by the interstellar matter (ISM) density, and by the combined
gravitational pull of the nuclear star cluster (NSC) and supermassive black
hole (SMBH).We adopted simplified hydrodynamical simulations using the
infinitesimally thin layer approximation in 3D (code RING) and determined
whether and where the shell expansion may bring new gas into the inner parsec
around the SMBH. The simulations show that supernovae occurring within a
conical region around the rotational axis of the galaxy can feed the central
accretion disk surrounding the SMBH. For ambient densities between 10$^3$ and
10$^5$ cm$^{-3}$, the average mass deposited into the central parsec by
individual supernovae varies between 10 to 1000 solar masses depending on the
ambient density and the spatial distribution of supernova events. Supernova
occurring in the aftermath of a starburst event near a galactic center can
supply two to three orders of magnitude more mass into the central parsec,
depending on the magnitude of the starburst. The deposited mass typically
encounters and joins an accretion disk. The fate of that mass is then divided
between the growth of the SMBH and an energetically driven outflow from the
disk.
