[en] In solidification processes of large industrial castings and ingots, the transport of solid in the liquid has an important effect on the final grain structure and macrosegregation. Modeling is still challenging as complex interactions between heat and mass transfers at microscopic and macroscopic scales are highly coupled. This paper first presents a multi-scale numerical solidification model coupling nucleation, grain growth and solute diffusion at microscopic scales with heat and mass transfer, including transport of liquid and solid phases at macroscopic scales. The resolution consists of a splitting method, which considers the evolution and interaction of quantities during the process with a transport stage and a growth stage. This splitting reduces the nonlinear complexity of the set of considered equations and provides an efficient numerical implementation. It is inspired by the work of Založnik et al. [1,2], which used a finite volume method (FVM). The present work develops the solution based on the finite element method (FEM). Numerical results obtained with this model are presented and simulations without and with grain transport are compared to study the impact of solid-phase transport on the solidification process and on the formation of macrosegregation. (paper)