A nonlinear convex splitting fourier spectral scheme for the Cahn–Hilliard equation with a logarithmic free energy

Junseok Kim, Hyun Geun Lee

Research output: Contribution to journalArticle

Abstract

For a simple implementation, a linear convex splitting scheme was coupled with the Fourier spectral method for the Cahn–Hilliard equation with a logarithmic free energy. However, an inappropriate value of the splitting parameter of the linear scheme may lead to incorrect morphologies in the phase separation process. In order to overcome this problem, we present a nonlinear convex splitting Fourier spectral scheme for the Cahn–Hilliard equation with a logarithmic free energy, which is an appropriate extension of Eyre’s idea of convex-concave decomposition of the energy functional. Using the nonlinear scheme, we derive a useful formula for the relation between the gradient energy coefficient and the thickness of the interfacial layer. And we present numerical simulations showing the different evolution of the solution using the linear and nonlinear schemes. The numerical results demonstrate that the nonlinear scheme is more accurate than the linear one.

Original languageEnglish
Pages (from-to)265-276
Number of pages12
JournalBulletin of the Korean Mathematical Society
Volume56
Issue number1
DOIs
Publication statusPublished - 2019 Jan 1

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Cahn-Hilliard Equation
Free Energy
Logarithmic
Fourier Method
Phase Separation
Energy Functional
Spectral Methods
Gradient
Decompose
Numerical Simulation
Numerical Results
Coefficient
Energy
Demonstrate

Keywords

  • Cahn
  • Fourier spectral method
  • Hilliard equation
  • Logarithmic free energy
  • Nonlinear convex splitting scheme
  • Phase separation

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

A nonlinear convex splitting fourier spectral scheme for the Cahn–Hilliard equation with a logarithmic free energy. / Kim, Junseok; Lee, Hyun Geun.

In: Bulletin of the Korean Mathematical Society, Vol. 56, No. 1, 01.01.2019, p. 265-276.

Research output: Contribution to journalArticle

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