  We use hydrodynamic simulations with adaptive grid refinement to study the
dependence of hot gas flows in X-ray luminous giant elliptical galaxies on the
efficiency of heat supply to the gas. We consider a number of potential heating
mechanisms including Type Ia supernovae and sporadic nuclear activity of a
central supermassive black hole. As a starting point for this research we use
an equilibrium hydrostatic recycling model (Kritsuk 1996). We show that a
compact cooling inflow develops, if the heating is slightly insufficient to
counterbalance radiative cooling of the hot gas in the central few kiloparsecs.
An excessive heating in the centre, instead, drives a convectively unstable
outflow. We model the onset of the instability and a quasi-steady convective
regime in the core of the galaxy in two-dimensions assuming axial symmetry.
  Provided the power of net energy supply in the core is not too high, the
convection remains subsonic. The convective pattern is dominated by buoyancy
driven large-scale mushroom-like structures. Unlike in the case of a cooling
inflow, the X-ray surface brightness of an (on average) isentropic convective
core does not display a sharp maximum at the centre. A hybrid model, which
combines a subsonic peripheral cooling inflow with an inner convective core,
appears to be stable. We also discuss observational implications of these
results.
