Journal of the Korean Society for Industrial and Applied Mathematics

  • 제17권3호
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  • Pages.197-207
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  • 2013
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  • 1226-9433(pISSN)
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  • 1229-0645(eISSN)
한국산업응용수학회 (Korean Society for Industrial and Applied Mathematics)
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COMPARISON OF DIFFERENT NUMERICAL SCHEMES FOR THE CAHN-HILLIARD EQUATION

  • 투고 : 2013.06.08
  • 심사 : 2013.07.01
  • 발행 : 2013.09.25
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초록

The Cahn-Hilliard equation was proposed as a phenomenological model for describing the process of phase separation of a binary alloy. The equation has been applied to many physical applications such as amorphological instability caused by elastic non-equilibrium, image inpainting, two- and three-phase fluid flow, phase separation, flow visualization and the formation of the quantum dots. To solve the Cahn-Hillard equation, many numerical methods have been proposed such as the explicit Euler's, the implicit Euler's, the Crank-Nicolson, the semi-implicit Euler's, the linearly stabilized splitting and the non-linearly stabilized splitting schemes. In this paper, we investigate each scheme in finite-difference schemes by comparing their performances, especially stability and efficiency. Except the explicit Euler's method, we use the fast solver which is called a multigrid method. Our numerical investigation shows that the linearly stabilized stabilized splitting scheme is not unconditionally gradient stable in time unlike the known result. And the Crank-Nicolson scheme is accurate but unstable in time, whereas the non-linearly stabilized splitting scheme has advantage over other schemes on the time step restriction.

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피인용 문헌

  1. A MODIFIED CAHN-HILLIARD EQUATION FOR 3D VOLUME RECONSTRUCTION FROM TWO PLANAR CROSS SECTIONS vol.19, pp.1, 2015, https://doi.org/10.12941/jksiam.2015.19.047
  2. A Simple Benchmark Problem for the Numerical Methods of the Cahn-Hilliard Equation vol.2021, pp.None, 2013, https://doi.org/10.1155/2021/8889603