The processes of solidification and macro-segregation involve intricate interactions across multiple physical, phase, and compositional fields, including mass, momentum, energy, and material transfer. Accurate prediction of phase transitions, chemical heterogeneities, and compositional flows is crucial in fields such as materials science, energy science, and planetary science. Numerical benchmark studies provide an effective means to explore these phenomena. This paper presents an iterative scheme based on operator splitting and evaluates its accuracy, stability, and implementation through a relevant benchmark problem. The results demonstrate strong performance of the scheme, particularly in capturing key physical phenomena such as channel segregation, freckle formation, and edge effects.