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A multigrid solution for the Cahn–Hilliard equation on nonuniform grids

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  • Choi, Yongho
  • Jeong, Darae
  • Kim, Junseok

Abstract

We present a nonlinear multigrid method to solve the Cahn–Hilliard (CH) equation on nonuniform grids. The CH equation was originally proposed as a mathematical model to describe phase separation phenomena after the quenching of binary alloys. The model has the characteristics of thin diffusive interfaces. To resolve the sharp interfacial transition, we need a very fine grid, which is computationally expensive. To reduce the cost, we can use a fine grid around the interfacial transition region and a relatively coarser grid in the bulk region. The CH equation is discretized by a conservative finite difference scheme in space and an unconditionally gradient stable type scheme in time. We use a conservative restriction in the nonlinear multigrid method to conserve the total mass in the coarser grid levels. Various numerical results on one-, two-, and three-dimensional spaces are presented to demonstrate the accuracy and effectiveness of the nonuniform grids for the CH equation.

Suggested Citation

  • Choi, Yongho & Jeong, Darae & Kim, Junseok, 2017. "A multigrid solution for the Cahn–Hilliard equation on nonuniform grids," Applied Mathematics and Computation, Elsevier, vol. 293(C), pages 320-333.
    • Handle: RePEc:eee:apmaco:v:293:y:2017:i:c:p:320-333
    DOI: 10.1016/j.amc.2016.08.026
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    References listed on IDEAS

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    1. Choi, Jeong-Whan & Lee, Hyun Geun & Jeong, Darae & Kim, Junseok, 2009. "An unconditionally gradient stable numerical method for solving the Allen–Cahn equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(9), pages 1791-1803.
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    Cited by:

    1. Liu, Tao, 2018. "A nonlinear multigrid method for inverse problem in the multiphase porous media flow," Applied Mathematics and Computation, Elsevier, vol. 320(C), pages 271-281.

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