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Comparison study of the conservative Allen–Cahn and the Cahn–Hilliard equations

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  • Lee, Dongsun
  • Kim, Junseok

Abstract

In this paper, a comparison study of conservative Allen–Cahn and Cahn–Hilliard equations is presented. We consider two mass-conservative Allen–Cahn equations and two Cahn–Hilliard equations with constant and variable mobilities. The equations are discretized using finite difference schemes, and discrete systems of the equations are solved using a nonlinear multigrid method. The generation and motion of interface are investigated for the conservative equations. We then present numerical experiments which highlight different dynamics of the four equations.

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  • Lee, Dongsun & Kim, Junseok, 2016. "Comparison study of the conservative Allen–Cahn and the Cahn–Hilliard equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 119(C), pages 35-56.
    • Handle: RePEc:eee:matcom:v:119:y:2016:i:c:p:35-56
    DOI: 10.1016/j.matcom.2015.08.018
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    References listed on IDEAS

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    1. Vanherpe, Liesbeth & Wendler, Frank & Nestler, Britta & Vandewalle, Stefan, 2010. "A multigrid solver for phase field simulation of microstructure evolution," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 80(7), pages 1438-1448.
    2. Do-Quang, Minh & Amberg, Gustav, 2010. "Numerical simulation of the coupling problems of a solid sphere impacting on a liquid free surface," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 80(8), pages 1664-1673.
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    Cited by:

    1. Lee, Seunggyu & Lee, Dongsun, 2019. "The fractional Allen–Cahn equation with the sextic potential," Applied Mathematics and Computation, Elsevier, vol. 351(C), pages 176-192.

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