A level set method combining features of front tracking methods and
fixed domain methods is presented to model three-dimensional
microstructure evolution in the solidification of multi-component
alloys. Phase boundaries are tracked by solving the multi-phase level
set equations. Diffused interfaces are constructed from these tracked
phase boundaries using the level set functions. Based on the assumed
diffused interfaces, volume-averaging techniques are applied for
energy, species and momentum transport. Techniques including fast
marching, narrow band computing, parallel computation using domain
decomposition and adaptive meshing are utilized to allow simulation of
physically realistic systems. In closing, we will discuss a number of
mathematical and computational issues related to multiscale
solidification modeling and design and the role that uncertainty plays
in such systems.