We present kinematic simulations of a galactic dynamo model based on the large scale differential rotation and the small scale helical fluctuations due to supernova explosions. We report for the first time direct numerical simulations of the full galactic dynamo using an unparameterized global approach. We argue that the scale of helicity injection is large enough to be directly resolved rather than parameterized. While the actual superbubble characteristics can only be approached, we show that numerical simulations yield magnetic structures which are close both to the observations and to the previous parameterized mean field models. In particular, the quadrupolar symmetry and the spiraling properties of the field are reproduced. Moreover, our simulations show that the presence of a vertical inflow plays an essential role to increase the magnetic growth rate. This observation could indicate an important role of the downward flow (possibly linked with galactic fountains) in sustaining galactic magnetic fields.