TY - JOUR
T1 - A fast, robust, and accurate operator splitting method for phase-field simulations of crystal growth
AU - Li, Yibao
AU - Geun Lee, Hyun
AU - Kim, Junseok
N1 - Funding Information:
This work was supported by the National Research Foundation of Korea Grant funded by the Korean Government (MEST) ( NRF-2010-0003989 ). The authors thank anonymous referee for very useful comments on this paper.
Copyright:
Copyright 2011 Elsevier B.V., All rights reserved.
PY - 2011/4/15
Y1 - 2011/4/15
N2 - In this paper we propose a fast, robust, and accurate operator splitting method for phase-field simulations of dendritic growth in both two- and three-dimensional space. The proposed method is based on operator splitting techniques. We split the governing phase-field equation into three parts: the first equation is calculated by using an explicit Euler's method. The second is a heat equation with a source term and is solved by a fast solver such as a multigrid method. The third is a nonlinear equation and is evaluated using a closed form solution. We also present a set of representative numerical experiments for crystal growth simulation to demonstrate the accuracy and efficiency of the proposed method. Our simulation results are also consistent with previous numerical experiments.
AB - In this paper we propose a fast, robust, and accurate operator splitting method for phase-field simulations of dendritic growth in both two- and three-dimensional space. The proposed method is based on operator splitting techniques. We split the governing phase-field equation into three parts: the first equation is calculated by using an explicit Euler's method. The second is a heat equation with a source term and is solved by a fast solver such as a multigrid method. The third is a nonlinear equation and is evaluated using a closed form solution. We also present a set of representative numerical experiments for crystal growth simulation to demonstrate the accuracy and efficiency of the proposed method. Our simulation results are also consistent with previous numerical experiments.
KW - A1. Multigrid method
KW - A1. Operator splitting
KW - A1. Phase-field simulation
KW - A2. Crystal growth
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U2 - 10.1016/j.jcrysgro.2011.02.042
DO - 10.1016/j.jcrysgro.2011.02.042
M3 - Article
AN - SCOPUS:79953249318
SN - 0022-0248
VL - 321
SP - 176
EP - 182
JO - Journal of Crystal Growth
JF - Journal of Crystal Growth
IS - 1
ER -