Modeling of Microstructure Evolution in the Solidification of Multi-component Alloys Using Level Set Methods

A level set method combining features of front tracking methods and fixed domain methods is presented to model microstructure evolution in the solidification of multi-component multiphase alloy systems. Phase boundaries are explicitly tracked by solving the multi-phase level set equations. Diffused interfaces are constructed by extending a small width in both directions from these explicitly tracked phase boundaries. Based on the constructed artificial diffused interfaces, volume-averaging techniques are applied for energy, species and momentum transport. This sacrifice of accuracy by adopting a diffused interface for computational convenience is small considering that the interfaces are still explicitly tracked. By avoiding explicit application of temperature essential boundary conditions on the freezing front, the numerical scheme is energy conserving and the numerical results insensitive to the mesh size. For the numerical analysis of melt flow, a SUPG (streamline-upwind/Petrov-Galerkin), PSPG (pressure stabilizing/Petrov-Galerkin) and DSPG (Darcy stabilizing/ Petrov-Galerkin) stabilized velocity-pressure finite element algorithm is adopted. Microstructure evolution in multicomponent alloy systems is solved directly using input from phase diagrams. This avoids the difficulty of parameter identification needed in most diffused interface models, and allows easy application to the solidification of various practical alloy systems. Comparable accuracy is observed to front tracking and phase field models in a number of examples available in the literature. Computational techniques including fast marching and narrow band computing are utilized to speed up the level set computations. Adaptive mesh refinement in the rapidly varying interface region makes the method practical for coupling phenomena in mesoand macro-scales during the solidification process.