A numerical model is described, aiming to predict the evolution of the grain structure along a multicrystalline silicon ingot. The model is based on recent theories on the effect of rough or facetted solid liquid interface morphology and twinning on the grain boundary behavior. This physico-chemical model has been implemented in a two-dimensional numerical code, in order to check the capabilities of this approach. The structure of the code and how the evolution of the grain structure with time is tracked is described. It includes: - Time dependent heat transfer during the whole ingot casting, giving the solid liquid interface shape and velocity, as well as solid temperature gradient, versus time. - Randomly oriented nucleation on the crucible bottom. - Grain boundary by grain boundary analysis of the grain/grain/liquid triple line and its evolution with time - The intersection of grain boundaries, twinning, intersection with crucible wall and sudden changes of grain directions are considered. - Simulation results are discussed in terms of selected grain orientations and grain sizes. Perspectives toward 3D simulation are presented.