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A practically unconditionally gradient stable scheme for the N-component Cahn–Hilliard system

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  • Lee, Hyun Geun
  • Choi, Jeong-Whan
  • Kim, Junseok

Abstract

We present a practically unconditionally gradient stable conservative nonlinear numerical scheme for the N-component Cahn–Hilliard system modeling the phase separation of an N-component mixture. The scheme is based on a nonlinear splitting method and is solved by an efficient and accurate nonlinear multigrid method. The scheme allows us to convert the N-component Cahn–Hilliard system into a system of N−1 binary Cahn–Hilliard equations and significantly reduces the required computer memory and CPU time. We observe that our numerical solutions are consistent with the linear stability analysis results. We also demonstrate the efficiency of the proposed scheme with various numerical experiments.

Suggested Citation

  • Lee, Hyun Geun & Choi, Jeong-Whan & Kim, Junseok, 2012. "A practically unconditionally gradient stable scheme for the N-component Cahn–Hilliard system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(4), pages 1009-1019.
    • Handle: RePEc:eee:phsmap:v:391:y:2012:i:4:p:1009-1019
    DOI: 10.1016/j.physa.2011.11.032
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    References listed on IDEAS

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    1. Lee, Hyun Geun & Kim, Junseok, 2008. "A second-order accurate non-linear difference scheme for the N -component Cahn–Hilliard system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(19), pages 4787-4799.
    2. Copetti, M.I.M., 2000. "Numerical experiments of phase separation in ternary mixtures," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 52(1), pages 41-51.
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    Cited by:

    1. Lee, Chaeyoung & Jeong, Darae & Shin, Jaemin & Li, Yibao & Kim, Junseok, 2014. "A fourth-order spatial accurate and practically stable compact scheme for the Cahn–Hilliard equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 409(C), pages 17-28.
    2. Hyun Geun Lee & Jaemin Shin & June-Yub Lee, 2019. "A High-Order Convex Splitting Method for a Non-Additive Cahn–Hilliard Energy Functional," Mathematics, MDPI, vol. 7(12), pages 1-13, December.
    3. Lee, Hyun Geun & Kim, Junseok, 2015. "An efficient numerical method for simulating multiphase flows using a diffuse interface model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 423(C), pages 33-50.

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    1. Hyun Geun Lee & Jaemin Shin & June-Yub Lee, 2019. "A High-Order Convex Splitting Method for a Non-Additive Cahn–Hilliard Energy Functional," Mathematics, MDPI, vol. 7(12), pages 1-13, December.
    2. Lee, Chaeyoung & Jeong, Darae & Shin, Jaemin & Li, Yibao & Kim, Junseok, 2014. "A fourth-order spatial accurate and practically stable compact scheme for the Cahn–Hilliard equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 409(C), pages 17-28.
    3. Lee, Hyun Geun & Kim, Junseok, 2015. "An efficient numerical method for simulating multiphase flows using a diffuse interface model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 423(C), pages 33-50.

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