Simplified models of macrosegregation

The macrosegregation process takes place during typical solidification of alloys. Fractions of alloy components in a liquid and solid sub-domains are time-dependent and determined by the course of border lines on the equilibrium diagram. From the mathematical point of view, the process is described by a system of partial differential equations (diffusion equations) and boundary-initial conditions. The process is coupled with the solidification one. In this paper, simplified models of macrosegregation are discussed. The volumetric solidification and the 'sharp' solid-liquid interface are considered. Examples of computations are also shown. It seems that for practical applications, the methods proposed are sufficiently exact. Additionally, they are very simple for numerical realization.