Numerical Simulation of Stefan Problem Coupled with Mass Transport in a Binary System Through XFEM/Level Set Method

Abstract

This paper deals with the application of the extended finite element method to simulate the phase change phenomenon in a binary system while considering the interaction with the mass transport of chemical species. To this end, the thermal conduction equation with the Stefan condition and the mass diffusion equation are solved to depict the temperature and solute concentration distributions, respectively. In dealing with the heat transfer problem with phase change, the temperature field is weakly enriched using the corrected abs-enrichment scheme to avoid the blending element problem. The melting temperature imposed by the penalty method at the solid–liquid interface is solute concentration dependent. On the other hand in dealing with the mass transport problem, due to the strong discontinuity in the concentration field at the interface, the sign-enrichment scheme is used. A constant separating out concentration is enforced on the solid side of the interface also by the penalty method, while a mass flux is naturally applied on the liquid side. The phase interface is captured implicitly by the level set method, which is applied on the same fixed finite element mesh. The robustness and the accuracy of the model are demonstrated through numerical case studies.