A numerical method for the Cahn-Hilliard equation with a variable mobility

Research output: Contribution to journalArticle

48 Citations (Scopus)

Abstract

We consider a conservative nonlinear multigrid method for the Cahn-Hilliard equation with a variable mobility of a model for phase separation in a binary mixture. The method uses the standard finite difference approximation in spatial discretization and the Crank-Nicholson semi-implicit scheme in temporal discretization. And the resulting discretized equations are solved by an efficient nonlinear multigrid method. The continuous problem has the conservation of mass and the decrease of the total energy. It is proved that these properties hold for the discrete problem. Also, we show the proposed scheme has a second-order convergence in space and time numerically. For numerical experiments, we investigate the effects of a variable mobility.

Original languageEnglish
Pages (from-to)1560-1571
Number of pages12
JournalCommunications in Nonlinear Science and Numerical Simulation
Volume12
Issue number8
DOIs
Publication statusPublished - 2007 Dec 1
Externally publishedYes

Fingerprint

multigrid methods
Cahn-Hilliard Equation
Multigrid Method
Binary mixtures
Phase separation
Conservation
Numerical methods
Discretization
Numerical Methods
Semi-implicit Scheme
Finite Difference Approximation
Binary Mixtures
eccentrics
Phase Separation
binary mixtures
conservation
Experiments
Numerical Experiment
Decrease
Energy

Keywords

  • Cahn-Hilliard equation
  • Nonlinear multigrid method
  • Phase separation
  • Variable mobility

ASJC Scopus subject areas

  • Mechanical Engineering
  • Statistical and Nonlinear Physics

Cite this

A numerical method for the Cahn-Hilliard equation with a variable mobility. / Kim, Junseok.

In: Communications in Nonlinear Science and Numerical Simulation, Vol. 12, No. 8, 01.12.2007, p. 1560-1571.

Research output: Contribution to journalArticle

@article{0911f4bd86d44e5f88ee0c0f5ca9b0c7,
title = "A numerical method for the Cahn-Hilliard equation with a variable mobility",
abstract = "We consider a conservative nonlinear multigrid method for the Cahn-Hilliard equation with a variable mobility of a model for phase separation in a binary mixture. The method uses the standard finite difference approximation in spatial discretization and the Crank-Nicholson semi-implicit scheme in temporal discretization. And the resulting discretized equations are solved by an efficient nonlinear multigrid method. The continuous problem has the conservation of mass and the decrease of the total energy. It is proved that these properties hold for the discrete problem. Also, we show the proposed scheme has a second-order convergence in space and time numerically. For numerical experiments, we investigate the effects of a variable mobility.",
keywords = "Cahn-Hilliard equation, Nonlinear multigrid method, Phase separation, Variable mobility",
author = "Junseok Kim",
year = "2007",
month = "12",
day = "1",
doi = "10.1016/j.cnsns.2006.02.010",
language = "English",
volume = "12",
pages = "1560--1571",
journal = "Communications in Nonlinear Science and Numerical Simulation",
issn = "1007-5704",
publisher = "Elsevier",
number = "8",

}

TY - JOUR

T1 - A numerical method for the Cahn-Hilliard equation with a variable mobility

AU - Kim, Junseok

PY - 2007/12/1

Y1 - 2007/12/1

N2 - We consider a conservative nonlinear multigrid method for the Cahn-Hilliard equation with a variable mobility of a model for phase separation in a binary mixture. The method uses the standard finite difference approximation in spatial discretization and the Crank-Nicholson semi-implicit scheme in temporal discretization. And the resulting discretized equations are solved by an efficient nonlinear multigrid method. The continuous problem has the conservation of mass and the decrease of the total energy. It is proved that these properties hold for the discrete problem. Also, we show the proposed scheme has a second-order convergence in space and time numerically. For numerical experiments, we investigate the effects of a variable mobility.

AB - We consider a conservative nonlinear multigrid method for the Cahn-Hilliard equation with a variable mobility of a model for phase separation in a binary mixture. The method uses the standard finite difference approximation in spatial discretization and the Crank-Nicholson semi-implicit scheme in temporal discretization. And the resulting discretized equations are solved by an efficient nonlinear multigrid method. The continuous problem has the conservation of mass and the decrease of the total energy. It is proved that these properties hold for the discrete problem. Also, we show the proposed scheme has a second-order convergence in space and time numerically. For numerical experiments, we investigate the effects of a variable mobility.

KW - Cahn-Hilliard equation

KW - Nonlinear multigrid method

KW - Phase separation

KW - Variable mobility

UR - http://www.scopus.com/inward/record.url?scp=34249662156&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=34249662156&partnerID=8YFLogxK

U2 - 10.1016/j.cnsns.2006.02.010

DO - 10.1016/j.cnsns.2006.02.010

M3 - Article

AN - SCOPUS:34249662156

VL - 12

SP - 1560

EP - 1571

JO - Communications in Nonlinear Science and Numerical Simulation

JF - Communications in Nonlinear Science and Numerical Simulation

SN - 1007-5704

IS - 8

ER -