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A fourth-order spatial accurate and practically stable compact scheme for the Cahn–Hilliard equation

Author

Listed:
  • Lee, Chaeyoung
  • Jeong, Darae
  • Shin, Jaemin
  • Li, Yibao
  • Kim, Junseok

Abstract

We present a fourth-order spatial accurate and practically stable compact difference scheme for the Cahn–Hilliard equation. The compact scheme is derived by combining a compact nine-point formula and linearly stabilized splitting scheme. The resulting system of discrete equations is solved by a multigrid method. Numerical experiments are conducted to verify the practical stability and fourth-order accuracy of the proposed scheme. We also demonstrate that the compact scheme is more robust and efficient than the non-compact fourth-order scheme by applying to parallel computing and adaptive mesh refinement.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:phsmap:v:409:y:2014:i:c:p:17-28
    DOI: 10.1016/j.physa.2014.04.038
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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. 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.
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    Cited by:

    1. Koike, Yukito & Nakamula, Atsushi & Nishie, Akihiro & Obuse, Kiori & Sawado, Nobuyuki & Suda, Yamato & Toda, Kouichi, 2022. "Mock-integrability and stable solitary vortices," Chaos, Solitons & Fractals, Elsevier, vol. 165(P1).
    2. Chaeyoung Lee & Darae Jeong & Junxiang Yang & Junseok Kim, 2020. "Nonlinear Multigrid Implementation for the Two-Dimensional Cahn–Hilliard Equation," Mathematics, MDPI, vol. 8(1), pages 1-23, January.
    3. Sinhababu, Arijit & Bhattacharya, Anirban, 2022. "A pseudo-spectral based efficient volume penalization scheme for Cahn–Hilliard equation in complex geometries," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 199(C), pages 1-24.
    4. Qiming Huang & Junxiang Yang, 2022. "Linear and Energy-Stable Method with Enhanced Consistency for the Incompressible Cahn–Hilliard–Navier–Stokes Two-Phase Flow Model," Mathematics, MDPI, vol. 10(24), pages 1-16, December.

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