An accurate and robust level-set formulation for multiple junction kinetics

The front-capturing Level-Set (LS) method is widely employed in academia and industry to model grain boundary (GB) migration during the microstructure evolution of polycrystalline materials under thermo-mechanical treatments. During capillarity-driven grain growth, the conventional mean curvature flow equation, $\vec{v} = - \mu \gamma \kappa \vec{n}$, is used to compute the GB normal migration velocity. Over recent decades, extensive efforts have been made to incorporate polycrystalline heterogeneity into this framework. However, despite increased complexity and computational costs, these approaches have yet to achieve fully satisfactory performance. This paper introduces a simple yet robust LS formulation that accurately captures multiple junction kinetics, even with extreme GB energy ratios. Validation against existing analytical solutions highlights the method's accuracy and efficiency. This novel approach offers significant potential for advancing the study of highly heterogeneous interface systems.