A central problem in the numerical treatment of the solidification of alloys is the coupling between the temperature and concentration fields. In this paper, governing equations and relationships that describe the temperature-solute coupling in a multicomponent alloy are presented. An overview of previous numerical coupling schemes is outlined. Following the presentation of a mixed explicit/implicit discretization of the governing equations a new numerical temperature-solute coupling scheme is developed. This new scheme can model the solidification of multicomponent alloys for a wide range of local scale behaviors. The performance of the scheme is tested on comparing numerical predictions for a ternary eutectic alloy with results obtained from a similarity solution.