In this paper, we used numerical simulations to investigate the flow properties of soft glassy materials. These systems display a mixed fluid/solid behavior whose theoretical description remains a challenging task. The molecular dynamic simulations exhibit non-local rheological behavior, in direct line with previous experimental results. The inverse viscosity of the material at a given point, denoted as fluidity, is not a local function of the local stress, but also depends on the state of the system in the neighborhood, with a spatial correlation length typically equal to a few particles. The fluidity is furthermore related directly to the velocity fluctuations and rate of plastic events in the form of a scaling function. Correlations are the signature of a cooperative process at the origin of the flow and of the non-local effects. We compare the obtained results with a scalar fluidity model and emphasize the similarities between the two approaches.