A review of level-set modeling in epitaxial growth and alloys solidification

Level-set methods provide a powerful computational framework for simulating free boundary problems in materials science. This paper presents a unified perspective on their application to two distinct phenomena: multicomponent alloy solidification and epitaxial island growth. Although these problems differ significantly in physical mechanisms and characteristic length scales, they can both be effectively addressed within the level-set framework, highlighting the versatility of the method across diverse applications. We outline the mathematical formulations and highlight computational advances and common features across applications. This overview highlights the role of level-set methods as a foundational tool in predictive materials modeling.