A numerical scheme for solidification of an alloy

In modeling the solidification of an alloy, two central numerical problems are: 1. The calculation of thermal and species transport fields which satisfy the conservation equations and are also consistent with the underlying thermodynamics. 2. The treatment of local scale solute diffusion. In this paper, in the context of modeling inverse segregation in a uni-directionally solidified casting, a recently proposed implicit/explicit time integration scheme for coupling thermal and solutal fields is presented and possible ways of capturing the local scale solute diffusion in a macroscopic model are explored. A key element in this work is the validation of the proposed approach by comparison with a sophisticated similarity solution.