Multi-scale computational heat transfer with moving solidification boundaries

In order to develop computational strategies for solidification processing of advanced engineering materials, one must address several fundamental issues, including (i) a moving solid–fluid interface, (ii) geometrical complexities of both processing components and solid–fluid interfaces, and (iii) disparate scales in length and time, ranging from the dimension of the processing system, to the convection and diffusion scales, to the morphological scale, and to the capillary scale. Main implications from these observations are that dynamic similarity can not be maintained in virtually any scale-up processes, and, even for laminar flows, direct numerical simulation of a solidification problem can not be handled with current computing resources. In this article, we highlight recent efforts in developing suitable computational techniques to facilitate a multi-scale approach which handles micro-, meso-, and macro-scale phenomena in a coupled framework. Relevant modeling and computational techniques are summarized along with selected examples at macroscopic and morphological scales.