Many problems in the physical or life sciences can be adressed by solving the modified Stefan problem, for which an interface motion is governed by external physical properties. In this talk, I will present a level set approach for the modeling of dendritic solidification. These simulations exploit a recently developed second order accurate symmetric discretization of the Poisson equation. Numerical results indicate that this method can be used successfully on complex interfacial shapes and can simulate many of the physical features of dendritic solidification. We apply this algorithm to the simulation of the dendritic crystallization of a pure melt and find that the
dendrite tip velocity and tip shapes are in excellent agreement with solvability theory. Numerical results are presented in both two and three spatial dimensions. If time permits, I will discuss the possibilities of deriving an algorithm with accuracy greater than 1.
Copyright. All Rights Reserved.