  We study how jets driven by active galactic nuclei influence the cooling flow
in Perseus-like galaxy cluster cores with idealised, non-relativistic,
hydrodynamical simulations performed with the Eulerian code ATHENA using
high-resolution Godunov methods with low numerical diffusion. We use novel
analysis methods to measure the cooling rate, the heating rate associated to
multiple mechanisms, and the power associated with adiabatic
compression/expansion. A significant reduction of the cooling rate and cooling
flow within 20 kpc from the centre can be achieved with kinetic jets. However,
at larger scales and away from the jet axis, the system relaxes to a cooling
flow configuration. Jet feedback is anisotropic and is mostly distributed along
the jet axis, where the cooling rate is reduced and a significant fraction of
the jet power is converted into kinetic power of heated outflowing gas. Away
from the jet axis weak shock heating represents the dominant heating source.
Turbulent heating is significant only near the cluster centre, but it becomes
inefficient at 50 kpc scales where it only represents a few percent of the
total heating rate. Several details of the simulations depend on the choice
made for the hydro solver, a consequence of the difficulty of achieving proper
numerical convergence for this problem: current physics implementations and
resolutions do not properly capture multi-phase gas that develops as a
consequence of thermal instability. These processes happen at the grid scale
and leave numerical solutions sensitive to the properties of the chosen hydro
solver.
