A benchmark problem for the two- and three-dimensional Cahn–Hilliard equations

Darae Jeong, Yongho Choi, Junseok Kim

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

This paper proposes a benchmark problem for the two- and three-dimensional Cahn–Hilliard (CH) equations, which describe the process of phase separation. The CH equation is highly nonlinear and an analytical solution does not exist except trivial solutions. Therefore, we have to approximate the CH equation numerically. To test the accuracy of a numerical scheme, we have to resort to convergence tests, which consist of consecutive relative errors or a very fine solution from the numerical scheme. For a fair convergence test, we provide benchmark problems which are of the shrinking annulus and spherical shell type. We show numerical results by using the explicit Euler's scheme with a very fine time step size and also present a comparison test with Eyre's convex splitting schemes.

Original languageEnglish
Pages (from-to)149-159
Number of pages11
JournalCommunications in Nonlinear Science and Numerical Simulation
Volume61
DOIs
Publication statusPublished - 2018 Aug 1

Fingerprint

Cahn-Hilliard Equation
Benchmark
Three-dimensional
Phase separation
Numerical Scheme
Euler Scheme
Spherical Shell
Explicit Scheme
Phase Separation
Shrinking
Ring or annulus
Relative Error
Consecutive
Analytical Solution
Trivial
Numerical Results

Keywords

  • Benchmark problem
  • Cahn–Hilliard equation
  • Finite difference method
  • Multigrid method

ASJC Scopus subject areas

  • Numerical Analysis
  • Modelling and Simulation
  • Applied Mathematics

Cite this

A benchmark problem for the two- and three-dimensional Cahn–Hilliard equations. / Jeong, Darae; Choi, Yongho; Kim, Junseok.

In: Communications in Nonlinear Science and Numerical Simulation, Vol. 61, 01.08.2018, p. 149-159.

Research output: Contribution to journalArticle

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