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A second-order accurate non-linear difference scheme for the N -component Cahn–Hilliard system

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  • Lee, Hyun Geun
  • Kim, Junseok

Abstract

We consider a second-order conservative nonlinear numerical scheme for the N-component Cahn–Hilliard system modeling the phase separation of a N-component mixture. The scheme is based on a Crank–Nicolson finite-difference method and is solved by an efficient and accurate nonlinear multigrid method. We numerically demonstrate the second-order accuracy of the numerical scheme. We observe that our numerical solutions are consistent with the exact solutions of linear stability analysis results. We also describe numerical experiments such as the evolution of triple junctions and the spinodal decomposition in a quaternary mixture. We investigate the effects of a concentration dependent mobility on phase separation.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:phsmap:v:387:y:2008:i:19:p:4787-4799
    DOI: 10.1016/j.physa.2008.03.023
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    Citations

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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 & 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.
    4. 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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