Linear Stability Analysis of the Cahn–Hilliard Equation in Spinodal Region

We study a linear stability analysis for the Cahn–Hilliard (CH) equation at critical and off-critical compositions. The CH equation is solved by the linearly stabilized splitting scheme and the Fourier-spectral method. We define the analytic and numerical growth rates and compare these growth rates...

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Bibliographic Details
Published in:Journal of function spaces 2022, Vol.2022, p.1-11
Main Authors: Ham, Seokjun, Jeong, Darae, Kim, Hyundong, Lee, Chaeyoung, Kwak, Soobin, Hwang, Youngjin, Kim, Junseok
Format: Article
Language:English
Subjects:
Composition
Critical point
Energy
Experiments
Free energy
Growth rate
Numerical analysis
Partial differential equations
Spectral methods
Stability analysis
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Summary:We study a linear stability analysis for the Cahn–Hilliard (CH) equation at critical and off-critical compositions. The CH equation is solved by the linearly stabilized splitting scheme and the Fourier-spectral method. We define the analytic and numerical growth rates and compare these growth rates with respect to the different average levels. In this study, the linear stability analysis is conducted by classifying three average levels such as zero average, spinodal average, and near critical point levels of free energy function, in the one-dimensional (1D) space. The numerical results provide insight for the dynamics of CH equation at critical and off-critical compositions.
ISSN:2314-8896
2314-8888
DOI:10.1155/2022/2970876