  This paper summarizes our recent works of studying AGN feedback in an
isolated elliptical galaxy by performing high-resolution hydrodynamical
numerical simulations. Bondi radius is resolved and the mass accretion rate of
the black hole is calculated. The most updated AGN physics, namely the
discrimination of cold and hot accretion modes and the exact descriptions of
the AGN radiation and wind for a given accretion rate are adopted and their
interaction with the gas in the host galaxy is calculated. Physical processes
such as star formation and SNe feedback are taken into account. Consistent with
observation, we find the AGN spends most of the time in the low-luminosity
regime. AGN feedback overall suppresses the star formation; but depending on
location in the galaxy and time, it can also enhance it. The light curve of
specific star formation rate is not synchronous with the AGN light curve. We
find that wind usually plays a dominant role in controlling the AGN luminosity
and star formation, but radiation also cannot be neglected.
