Micro-Macro Modeling of Solidification Processes and Phenomena

"The wide range of length and time scales found in solidification processes are outlined and discussed. Methods for Direct Microstructure Simulation (DMS) are introduced. Key features in sharp interface and phase field models are presented. Concepts in micro-macro solidification modeling are covered. Basic details of microstructure and segregation models are provided. A description of a recent segregation micro-macro model is presented in detail.IntroductionA solidification process involves the containment of a liquid region, which, due to cooling, transforms over time to form a fully solid product. The development of the solid microstructure and the segregation of solute components during this transformation are controlled by phenomena that occur across a wide range of length and time scales. A ""successful"" model of a given solidification process needs to account for these phenomena. Standard models of solidification employ a discrete grid of node points and associated volume elements in the special domain, with a discrete time step to track the transient changes of nodal values, describing the composition and microstructure. Through the use of such models significant progress has been made towards a complete understanding of solidification process and phenomena (see the conference proceedings in Refs [1-9]). As solidification models become more sophisticated, however, they all run into the problem of resolving the full range of disparate space and time scales.Two approaches can deal with this problem1. Direct Microstructure Simulation (DMS) where the grid size and time step are chosen to scale with the smallest length and time scales of the given problem.2. Micro-macro modeling where the grid size and time step scale with the macroscopic process scale and phenomena at smaller scales are accounted for via sub-grid modeling and volume averaging.Currently full DMS of solidification is beyond the reach of available computer power and the application and development of micro-macro models is an important and critical research area."