Multiscale Modeling for Material Phase Change Problems

A phase change is the transformation of a material from one phase or state of matter to another. It includes phase changes between solid, liquid and gaseous states of matter. Phase change problems, including melting and solidification, are very important in many engineering applications such as food freezing, metal processing, and solidification of castings. Numerical modeling has been one of important tools to study physical phenomena in phase change problems at various scales. Initially, the material phase change problems were studied at the macroscale, and the thermal diffusion equation was usually employed as one of governing equations: