Comparison study of the conservative Allen-Cahn and the Cahn-Hilliard equations

Dongsun Lee; Junseok Kim

doi:10.1016/j.matcom.2015.08.018

Comparison study of the conservative Allen-Cahn and the Cahn-Hilliard equations

Dongsun Lee, Junseok Kim

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

21 Citations (Scopus)

Abstract

In this paper, a comparison study of conservative Allen-Cahn and Cahn-Hilliard equations is presented. We consider two mass-conservative Allen-Cahn equations and two Cahn-Hilliard equations with constant and variable mobilities. The equations are discretized using finite difference schemes, and discrete systems of the equations are solved using a nonlinear multigrid method. The generation and motion of interface are investigated for the conservative equations. We then present numerical experiments which highlight different dynamics of the four equations.

Original language	English
Pages (from-to)	35-56
Number of pages	22
Journal	Mathematics and Computers in Simulation
Volume	119
DOIs	https://doi.org/10.1016/j.matcom.2015.08.018
Publication status	Published - 2016 Jan 1

Keywords

Cahn-Hilliard equation
Conservation of mass
Conservative Allen-Cahn equation

ASJC Scopus subject areas

Modelling and Simulation
Numerical Analysis
Applied Mathematics
Theoretical Computer Science
Computer Science(all)

Access to Document

10.1016/j.matcom.2015.08.018

Fingerprint Dive into the research topics of 'Comparison study of the conservative Allen-Cahn and the Cahn-Hilliard equations'. Together they form a unique fingerprint.

Cite this

@article{916534d144174433abcf6fb648e7759d,

title = "Comparison study of the conservative Allen-Cahn and the Cahn-Hilliard equations",

abstract = "In this paper, a comparison study of conservative Allen-Cahn and Cahn-Hilliard equations is presented. We consider two mass-conservative Allen-Cahn equations and two Cahn-Hilliard equations with constant and variable mobilities. The equations are discretized using finite difference schemes, and discrete systems of the equations are solved using a nonlinear multigrid method. The generation and motion of interface are investigated for the conservative equations. We then present numerical experiments which highlight different dynamics of the four equations.",

keywords = "Cahn-Hilliard equation, Conservation of mass, Conservative Allen-Cahn equation",

author = "Dongsun Lee and Junseok Kim",

year = "2016",

month = jan,

day = "1",

doi = "10.1016/j.matcom.2015.08.018",

language = "English",

volume = "119",

pages = "35--56",

journal = "Mathematics and Computers in Simulation",

issn = "0378-4754",

publisher = "Elsevier",

}

TY - JOUR

T1 - Comparison study of the conservative Allen-Cahn and the Cahn-Hilliard equations

AU - Lee, Dongsun

AU - Kim, Junseok

PY - 2016/1/1

Y1 - 2016/1/1

N2 - In this paper, a comparison study of conservative Allen-Cahn and Cahn-Hilliard equations is presented. We consider two mass-conservative Allen-Cahn equations and two Cahn-Hilliard equations with constant and variable mobilities. The equations are discretized using finite difference schemes, and discrete systems of the equations are solved using a nonlinear multigrid method. The generation and motion of interface are investigated for the conservative equations. We then present numerical experiments which highlight different dynamics of the four equations.

AB - In this paper, a comparison study of conservative Allen-Cahn and Cahn-Hilliard equations is presented. We consider two mass-conservative Allen-Cahn equations and two Cahn-Hilliard equations with constant and variable mobilities. The equations are discretized using finite difference schemes, and discrete systems of the equations are solved using a nonlinear multigrid method. The generation and motion of interface are investigated for the conservative equations. We then present numerical experiments which highlight different dynamics of the four equations.

KW - Cahn-Hilliard equation

KW - Conservation of mass

KW - Conservative Allen-Cahn equation

UR - http://www.scopus.com/inward/record.url?scp=84945470967&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84945470967&partnerID=8YFLogxK

U2 - 10.1016/j.matcom.2015.08.018

DO - 10.1016/j.matcom.2015.08.018

M3 - Article

AN - SCOPUS:84945470967

VL - 119

SP - 35

EP - 56

JO - Mathematics and Computers in Simulation

JF - Mathematics and Computers in Simulation

SN - 0378-4754

ER -