A Level Set Approach for the Numerical Simulation of Dendritic Growth

In this paper, we 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, see [12]. 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. ∗Mathematics Department & Computer Science Department, Stanford University, Stanford, CA 94305. Supported in part by an NSF postdoctoral fellowship # DMS0102029, a Focused Research Group grant # DMS0074152 from the NSF and by ONR N00014-01-1-0620. †Computer Science Department, Stanford University, Stanford, CA 94305. Supported in part by an ONR YIP and PECASE award N00014-01-1-0620 and NSF -0106694. ‡Mathematics Department, University of California, Los Angeles, CA 90095-1555. Supported in part by a Focused Research Group grant # DMS0074152 from the NSF. §Mathematics Department, University of California, Los Angeles, CA 90095-1555. Supported in part by ONR N00014-97-0027 and NSF DMS-0074735.