  We present general relativistic magnetohydrodynamic (GRMHD) numerical
simulations of the accretion flow around the supermassive black hole in the
Galactic centre, Sagittarius A* (Sgr A*). The simulations include for the first
time radiative cooling processes (synchrotron, bremsstrahlung, and inverse
Compton) self-consistently in the dynamics, allowing us to test the common
simplification of ignoring all cooling losses in the modeling of Sgr A*. We
confirm that for Sgr A*, neglecting the cooling losses is a reasonable
approximation if the Galactic centre is accreting below ~10^{-8} Msun/yr i.e.
Mdot < 10^{-7} Mdot_Edd. But above this limit, we show that radiative losses
should be taken into account as significant differences appear in the dynamics
and the resulting spectra when comparing simulations with and without cooling.
This limit implies that most nearby low-luminosity active galactic nuclei are
in the regime where cooling should be taken into account.
  We further make a parameter study of axisymmetric gas accretion around the
supermassive black hole at the Galactic centre. This approach allows us to
investigate the physics of gas accretion in general, while confronting our
results with the well studied and observed source, Sgr A*, as a test case. We
confirm that the nature of the accretion flow and outflow is strongly dependent
on the initial geometry of the magnetic field. For example, we find it
difficult, even with very high spins, to generate powerful outflows from discs
threaded with multiple, separate poloidal field loops.
