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A Sharp Computational Method for the Simulation of the Solidification of Binary Alloys

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Abstract

We present a numerical method for the simulation of binary alloys. We make use of the level-set method to capture the evolution of the solidification front and of an adaptive mesh refinement framework based on non-graded quadtree grids to efficiently capture the multiscale nature of the alloys’ concentration profile. In addition, our approach is based on a sharp treatment of the boundary conditions at the solidification front. We apply this algorithm to the solidification of an Ni–Cu alloy and report results that agree quantitatively with theoretical analyses. We also apply this algorithm to show that solidification mechanism maps predicting growth regimes as a function of tip velocities and thermal gradients can be accurately computed with this method; these include the important transitions from planar to cellular to dendritic regimes.

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Acknowledgments

We would like to thank Dr. Jonathan Miller for stimulating discussions at UCSB and AFRL about solidification of binary alloys. We also thank Christopher Harrel for running some simulations while interning in the Computational Applied Science Laboratory as part of the CNSI INSET program at UCSB. The research of M. Theillard and F. Gibou was supported in part by ONR N00014-11-1-0027, NSF CHE 1027817 and by the W.M. Keck Foundation. In addition M. Theillard acknowledges support from a Dean’s fellowship at UCSB. T. Pollock was supported in part by NSF DMREF Grant DMR 1233704.

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  1. Mechanical Engineering Department, University of California, Santa Barbara, CA, 93106, USA

    Maxime Theillard

  2. Mechanical Engineering Department and Computer Science Department, University of California, Santa Barbara, CA, 93106, USA

    Frédéric Gibou

  3. Materials Department, University of California, Santa Barbara, CA, 93106, USA

    Tresa Pollock

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  1. Maxime Theillard
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  2. Frédéric Gibou
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Theillard, M., Gibou, F. & Pollock, T. A Sharp Computational Method for the Simulation of the Solidification of Binary Alloys. J Sci Comput 63, 330–354 (2015). https://doi.org/10.1007/s10915-014-9895-0

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