Within the general context of solid-state sintering process, this work presents a numerical modelling approach, at the grain scale, of ceramic grain packing consolidation. Typically, the sintering process triggers several matter diffusion routes that are thermally activated: surface, grain boundary and volume diffusions. Including this physics into a high-performance computing framework would permit to investigate and to track the changes occurring into a granular packing during sintering. In performing this kind of simulations, one will face several challenges: the strong topological changes appear during sintering simulation at the grains scale, the evolution of the structure is mainly driven by the surface tension phenomena through the Laplace's law, and the mechanical properties of the grains could, possibly, be different. The proposed numerical simulations are carried out within an Eulerian Finite Element framework and the Level-Set method is used to cope with changes in the microstructure. The results obtained with this numerical strategy are compared with success to the usual geometrical models.