TY - JOUR
T1 - A compact fourth-order finite difference scheme for the three-dimensional Cahn-Hilliard equation
AU - Li, Yibao
AU - Lee, Hyun Geun
AU - Xia, Binhu
AU - Kim, Junseok
N1 - Funding Information:
Y.B. Li is supported by the Fundamental Research Funds for the Central Universities, China (No. XJJ2015068 ) and supported by China Postdoctoral Science Foundation (No. 2015M572541 ). The corresponding author (J.S. Kim) was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) ( NRF-2014R1A2A2A01003683 ).
Publisher Copyright:
© 2015 Elsevier B.V.
Copyright:
Copyright 2016 Elsevier B.V., All rights reserved.
PY - 2016/3/1
Y1 - 2016/3/1
N2 - This work extends the previous two-dimensional compact scheme for the Cahn-Hilliard equation (Lee et al., 2014) to three-dimensional space. The proposed scheme, derived by combining a compact formula and a linearly stabilized splitting scheme, has second-order accuracy in time and fourth-order accuracy in space. The discrete system is conservative and practically stable. We also implement the compact scheme in a three-dimensional adaptive mesh refinement framework. The resulting system of discrete equations is solved by using a multigrid. We demonstrate the performance of our proposed algorithm by several numerical experiments.
AB - This work extends the previous two-dimensional compact scheme for the Cahn-Hilliard equation (Lee et al., 2014) to three-dimensional space. The proposed scheme, derived by combining a compact formula and a linearly stabilized splitting scheme, has second-order accuracy in time and fourth-order accuracy in space. The discrete system is conservative and practically stable. We also implement the compact scheme in a three-dimensional adaptive mesh refinement framework. The resulting system of discrete equations is solved by using a multigrid. We demonstrate the performance of our proposed algorithm by several numerical experiments.
KW - Adaptive mesh refinement
KW - Cahn-Hilliard equation
KW - Finite difference method
KW - Fourth-order compact scheme
KW - Multigrid
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U2 - 10.1016/j.cpc.2015.11.006
DO - 10.1016/j.cpc.2015.11.006
M3 - Article
AN - SCOPUS:84957428815
SN - 0010-4655
VL - 200
SP - 108
EP - 116
JO - Computer Physics Communications
JF - Computer Physics Communications
ER -