A general enthalpy method for modeling solidification phenomena

The development of fast, accurate, and robust computation methods is crucial to the modeling of fluid How and solidification in continuous casting. A basic solidification modeling approach, nearing 60 years of use, is the enthalpy formulation; an approach that is able to provide numerical solutions on fixed grids. Enthalpy methods work well when the solid/liquid interface is at a constant phase-change temperature. In a general solidification system, however, the phase change temperature may be a function of (i) the curvature of the interface, (ii) the speed of the interface, and (iii) the redistribution of solute phases. In this paper it is first shown that the modest enthalpy method can be easily and straightforwardly modified to model all three of these situations. This modified approach is verified by comparison with available analytical solutions and alternative, more sophisticated front tracking approaches.