The Greenland ice sheet represents a potential sea level rise contribution of 7.3 meters. When drastic changes are recently observed, multi-centennal futur projections are urgently needed. 3D numerical modelling is one of the tools to realize these projections. This work intensively incorporates the use of Greenland deep ice core drillings, which represent an important amount of information of past states of the ice sheet. The validity of the reconstructions are thus assured by constant back and forth between observations and simulations. Robustness of these reconstructions and of future projections are largely questionned through wide sensitivity experiments. The ice sheet model calibration is performed during the last deglaciation considering the numerous constraints during this period. Given that, scenarios of ice sheet states during the whole last climatic cycle, in particular during the last interglacial, the Eemian, potential analogue for a future climate.