We present the first spectral energy distributions produced self-consistently by 2.5D general relativistic magneto-hydrodynamical ( GRMHD ) numerical simulations , where radiative cooling is included in the dynamical calculation . As a case study , we focus on the accretion flow around the supermassive black hole in the Galactic Centre , Sagittarius A* ( Sgr A* ) , which has the best constrained physical parameters . We compare the simulated spectra to the observational data of Sgr A* and explore the parameter space of our model to determine the effect of changing the initial magnetic field configuration , ion to electron temperature ratio T _ { i } / T _ { e } and the target accretion rate . We find the best description of the data for a mass accretion rate of \sim 10 ^ { -9 } M _ { \odot } /yr , and rapid spin ( 0.7 < a _ { * } < 0.9 ) . The submillimeter peak flux seems largely independent of initial conditions , while the higher energies can be very sensitive to the initial magnetic field configuration . Finally , we also discuss flaring features observed in some simulations , that may be due to artifacts of the 2D configuration .