Kinetic equations and level-set approach for simulating solid-state microstructure evolutions at the mesoscopic scale: state of the art, limitations, and prospects

For over three decades, the front-capturing level-set method has demonstrated its prowess for the simulation, at the mesoscopic scale, of numerous mechanisms in the context of microstructure evolution occurring during complex thermomechanical paths. This review delves into the foundations of this numerical framework, charting its evolution concerning polycrystalline materials, examining its recent advancements, scrutinizing its current shortcomings, and exploring future possibilities. Special attention will be given to the context of hot metal forming processes. In this context, this article also aims to reintroduce, as simply as possible, the kinetic equations related to the grain boundary migration.