Multi-scale homogenization of moving interface problems with flux jumps: application to solidification

In this paper, a multi-scale analysis scheme for solidification based on two-scale computational homogenization is discussed. Solidification problems involve evolution of surfaces coupled with flux jump boundary conditions across interfaces. We provide consistent macro-micro transition and averaging rules based on Hill’s macrohomogeneity condition. The overall macro-scale behavior is analyzed with solidification at the micro-scale modeled using an enthalpy formulation. The method is versatile in the sense that two different models can be employed at the macroand micro-scales. The micro-scale model can incorporate all the physics associated with solidification including moving interfaces and flux discontinuities, while the macro-scale model needs to only model thermal conduction using continuous (homogenized) fields. The convergence behavior of the tightly coupled macro-micro finite element scheme with respect to decreasing element size is analyzed by comparing with a known analytical solution of the Stefan problem.