A numerical method for the ternary Cahn-Hilliard system with a degenerate mobility

Junseok Kim, Kyungkeun Kang

Research output: Contribution to journalArticle

16 Citations (Scopus)

Abstract

We applied a second-order conservative nonlinear multigrid method for the ternary Cahn-Hilliard system with a concentration dependent degenerate mobility for a model for phase separation in a ternary mixture. First, we used a standard finite difference approximation for spatial discretization and a Crank-Nicolson semi-implicit scheme for the temporal discretization. Then, we solved the resulting discretized equations using an efficient nonlinear multigrid method. We proved stability of the numerical solution for a sufficiently small time step. We demonstrate the second-order accuracy of the numerical scheme. We also show that our numerical solutions of the ternary Cahn-Hilliard system are consistent with the exact solutions of the linear stability analysis results in a linear regime. We demonstrate that the multigrid solver can straightforwardly deal with different boundary conditions such as Neumann, periodic, mixed, and Dirichlet. Finally, we describe numerical experiments highlighting differences of constant mobility and degenerate mobility in one, two, and three spatial dimensions.

Original languageEnglish
Pages (from-to)1029-1042
Number of pages14
JournalApplied Numerical Mathematics
Volume59
Issue number5
DOIs
Publication statusPublished - 2009 May 1

Fingerprint

Cahn-Hilliard
Linear stability analysis
Ternary
Phase separation
Numerical methods
Numerical Methods
Multigrid Method
Boundary conditions
Discretization
Numerical Solution
Semi-implicit Scheme
Crank-Nicolson Scheme
Second-order Accuracy
Finite Difference Approximation
Experiments
Linear Stability Analysis
Phase Separation
Numerical Scheme
Demonstrate
Dirichlet

Keywords

  • Degenerate mobility
  • Nonlinear multigrid
  • Phase separation
  • Ternary Cahn-Hilliard

ASJC Scopus subject areas

  • Applied Mathematics
  • Computational Mathematics
  • Numerical Analysis

Cite this

A numerical method for the ternary Cahn-Hilliard system with a degenerate mobility. / Kim, Junseok; Kang, Kyungkeun.

In: Applied Numerical Mathematics, Vol. 59, No. 5, 01.05.2009, p. 1029-1042.

Research output: Contribution to journalArticle

@article{c20781c385344b16a377197e13848a31,
title = "A numerical method for the ternary Cahn-Hilliard system with a degenerate mobility",
abstract = "We applied a second-order conservative nonlinear multigrid method for the ternary Cahn-Hilliard system with a concentration dependent degenerate mobility for a model for phase separation in a ternary mixture. First, we used a standard finite difference approximation for spatial discretization and a Crank-Nicolson semi-implicit scheme for the temporal discretization. Then, we solved the resulting discretized equations using an efficient nonlinear multigrid method. We proved stability of the numerical solution for a sufficiently small time step. We demonstrate the second-order accuracy of the numerical scheme. We also show that our numerical solutions of the ternary Cahn-Hilliard system are consistent with the exact solutions of the linear stability analysis results in a linear regime. We demonstrate that the multigrid solver can straightforwardly deal with different boundary conditions such as Neumann, periodic, mixed, and Dirichlet. Finally, we describe numerical experiments highlighting differences of constant mobility and degenerate mobility in one, two, and three spatial dimensions.",
keywords = "Degenerate mobility, Nonlinear multigrid, Phase separation, Ternary Cahn-Hilliard",
author = "Junseok Kim and Kyungkeun Kang",
year = "2009",
month = "5",
day = "1",
doi = "10.1016/j.apnum.2008.04.004",
language = "English",
volume = "59",
pages = "1029--1042",
journal = "Applied Numerical Mathematics",
issn = "0168-9274",
publisher = "Elsevier",
number = "5",

}

TY - JOUR

T1 - A numerical method for the ternary Cahn-Hilliard system with a degenerate mobility

AU - Kim, Junseok

AU - Kang, Kyungkeun

PY - 2009/5/1

Y1 - 2009/5/1

N2 - We applied a second-order conservative nonlinear multigrid method for the ternary Cahn-Hilliard system with a concentration dependent degenerate mobility for a model for phase separation in a ternary mixture. First, we used a standard finite difference approximation for spatial discretization and a Crank-Nicolson semi-implicit scheme for the temporal discretization. Then, we solved the resulting discretized equations using an efficient nonlinear multigrid method. We proved stability of the numerical solution for a sufficiently small time step. We demonstrate the second-order accuracy of the numerical scheme. We also show that our numerical solutions of the ternary Cahn-Hilliard system are consistent with the exact solutions of the linear stability analysis results in a linear regime. We demonstrate that the multigrid solver can straightforwardly deal with different boundary conditions such as Neumann, periodic, mixed, and Dirichlet. Finally, we describe numerical experiments highlighting differences of constant mobility and degenerate mobility in one, two, and three spatial dimensions.

AB - We applied a second-order conservative nonlinear multigrid method for the ternary Cahn-Hilliard system with a concentration dependent degenerate mobility for a model for phase separation in a ternary mixture. First, we used a standard finite difference approximation for spatial discretization and a Crank-Nicolson semi-implicit scheme for the temporal discretization. Then, we solved the resulting discretized equations using an efficient nonlinear multigrid method. We proved stability of the numerical solution for a sufficiently small time step. We demonstrate the second-order accuracy of the numerical scheme. We also show that our numerical solutions of the ternary Cahn-Hilliard system are consistent with the exact solutions of the linear stability analysis results in a linear regime. We demonstrate that the multigrid solver can straightforwardly deal with different boundary conditions such as Neumann, periodic, mixed, and Dirichlet. Finally, we describe numerical experiments highlighting differences of constant mobility and degenerate mobility in one, two, and three spatial dimensions.

KW - Degenerate mobility

KW - Nonlinear multigrid

KW - Phase separation

KW - Ternary Cahn-Hilliard

UR - http://www.scopus.com/inward/record.url?scp=61549141683&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=61549141683&partnerID=8YFLogxK

U2 - 10.1016/j.apnum.2008.04.004

DO - 10.1016/j.apnum.2008.04.004

M3 - Article

AN - SCOPUS:61549141683

VL - 59

SP - 1029

EP - 1042

JO - Applied Numerical Mathematics

JF - Applied Numerical Mathematics

SN - 0168-9274

IS - 5

ER -