A practically unconditionally gradient stable scheme for the N-component CahnHilliard system

Hyun Geun Lee; Jeong Whan Choi; Junseok Kim

doi:10.1016/j.physa.2011.11.032

A practically unconditionally gradient stable scheme for the N-component CahnHilliard system

Hyun Geun Lee, Jeong Whan Choi, Junseok Kim

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

45 Citations (Scopus)

Abstract

We present a practically unconditionally gradient stable conservative nonlinear numerical scheme for the N-component CahnHilliard system modeling the phase separation of an N-component mixture. The scheme is based on a nonlinear splitting method and is solved by an efficient and accurate nonlinear multigrid method. The scheme allows us to convert the N-component CahnHilliard system into a system of N-1 binary CahnHilliard equations and significantly reduces the required computer memory and CPU time. We observe that our numerical solutions are consistent with the linear stability analysis results. We also demonstrate the efficiency of the proposed scheme with various numerical experiments.

Original language	English
Pages (from-to)	1009-1019
Number of pages	11
Journal	Physica A: Statistical Mechanics and its Applications
Volume	391
Issue number	4
DOIs	https://doi.org/10.1016/j.physa.2011.11.032
Publication status	Published - 2012 Feb 15

Keywords

Finite difference
N-component CahnHilliard system
Nonlinear multigrid
Phase separation
Practically unconditionally gradient stable

ASJC Scopus subject areas

Statistics and Probability
Condensed Matter Physics

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10.1016/j.physa.2011.11.032

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title = "A practically unconditionally gradient stable scheme for the N-component CahnHilliard system",

abstract = "We present a practically unconditionally gradient stable conservative nonlinear numerical scheme for the N-component CahnHilliard system modeling the phase separation of an N-component mixture. The scheme is based on a nonlinear splitting method and is solved by an efficient and accurate nonlinear multigrid method. The scheme allows us to convert the N-component CahnHilliard system into a system of N-1 binary CahnHilliard equations and significantly reduces the required computer memory and CPU time. We observe that our numerical solutions are consistent with the linear stability analysis results. We also demonstrate the efficiency of the proposed scheme with various numerical experiments.",

keywords = "Finite difference, N-component CahnHilliard system, Nonlinear multigrid, Phase separation, Practically unconditionally gradient stable",

author = "Lee, {Hyun Geun} and Choi, {Jeong Whan} and Junseok Kim",

note = "Funding Information: This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (No. 2011-0023794 ).",

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AU - Lee, Hyun Geun

AU - Choi, Jeong Whan

AU - Kim, Junseok

N1 - Funding Information: This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (No. 2011-0023794 ).

PY - 2012/2/15

Y1 - 2012/2/15

N2 - We present a practically unconditionally gradient stable conservative nonlinear numerical scheme for the N-component CahnHilliard system modeling the phase separation of an N-component mixture. The scheme is based on a nonlinear splitting method and is solved by an efficient and accurate nonlinear multigrid method. The scheme allows us to convert the N-component CahnHilliard system into a system of N-1 binary CahnHilliard equations and significantly reduces the required computer memory and CPU time. We observe that our numerical solutions are consistent with the linear stability analysis results. We also demonstrate the efficiency of the proposed scheme with various numerical experiments.

AB - We present a practically unconditionally gradient stable conservative nonlinear numerical scheme for the N-component CahnHilliard system modeling the phase separation of an N-component mixture. The scheme is based on a nonlinear splitting method and is solved by an efficient and accurate nonlinear multigrid method. The scheme allows us to convert the N-component CahnHilliard system into a system of N-1 binary CahnHilliard equations and significantly reduces the required computer memory and CPU time. We observe that our numerical solutions are consistent with the linear stability analysis results. We also demonstrate the efficiency of the proposed scheme with various numerical experiments.

KW - Finite difference

KW - N-component CahnHilliard system

KW - Nonlinear multigrid

KW - Phase separation

KW - Practically unconditionally gradient stable

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M3 - Article

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JO - Physica A: Statistical Mechanics and its Applications

JF - Physica A: Statistical Mechanics and its Applications

IS - 4

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A practically unconditionally gradient stable scheme for the N-component CahnHilliard system

Abstract

Keywords

ASJC Scopus subject areas

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