Pinning boundary conditions for phase-field models

Hyun Geun Lee, Junxiang Yang, Junseok Kim

Research output: Contribution to journalArticle

Abstract

In this paper, we present pinning boundary conditions for two- (2D) and three-dimensional (3D) phase-field models. For the 2D and axisymmetric domains in the neighborhood of the pinning boundaries, we apply an odd-function-type treatment and use a local gradient of the phase-field for points away from the pinning boundaries. For the 3D domain, we propose a simple treatment that fixes the values on the ghost grid points beyond the discrete computational domain. As examples of the phase-field models, we consider the Allen–Cahn and conservative Allen–Cahn equations with the pinning boundary conditions. We present various numerical experiments to demonstrate the performance of the proposed pinning boundary treatment. The computational results confirm the efficiency of the proposed method.

Original languageEnglish
Article number105060
JournalCommunications in Nonlinear Science and Numerical Simulation
Volume82
DOIs
Publication statusPublished - 2020 Mar

Fingerprint

Phase Field Model
Boundary conditions
Allen-Cahn Equation
Odd function
Phase Field
3D Model
Experiments
Computational Results
Numerical Experiment
Gradient
Grid
Three-dimensional
Demonstrate

Keywords

  • Allen–Cahn equation
  • Conservative Allen–Cahn equation
  • Pinning boundary condition

ASJC Scopus subject areas

  • Numerical Analysis
  • Modelling and Simulation
  • Applied Mathematics

Cite this

Pinning boundary conditions for phase-field models. / Lee, Hyun Geun; Yang, Junxiang; Kim, Junseok.

In: Communications in Nonlinear Science and Numerical Simulation, Vol. 82, 105060, 03.2020.

Research output: Contribution to journalArticle

@article{d37add3707f149679e5551fb08cbaa41,
title = "Pinning boundary conditions for phase-field models",
abstract = "In this paper, we present pinning boundary conditions for two- (2D) and three-dimensional (3D) phase-field models. For the 2D and axisymmetric domains in the neighborhood of the pinning boundaries, we apply an odd-function-type treatment and use a local gradient of the phase-field for points away from the pinning boundaries. For the 3D domain, we propose a simple treatment that fixes the values on the ghost grid points beyond the discrete computational domain. As examples of the phase-field models, we consider the Allen–Cahn and conservative Allen–Cahn equations with the pinning boundary conditions. We present various numerical experiments to demonstrate the performance of the proposed pinning boundary treatment. The computational results confirm the efficiency of the proposed method.",
keywords = "Allen–Cahn equation, Conservative Allen–Cahn equation, Pinning boundary condition",
author = "Lee, {Hyun Geun} and Junxiang Yang and Junseok Kim",
year = "2020",
month = "3",
doi = "10.1016/j.cnsns.2019.105060",
language = "English",
volume = "82",
journal = "Communications in Nonlinear Science and Numerical Simulation",
issn = "1007-5704",
publisher = "Elsevier",

}

TY - JOUR

T1 - Pinning boundary conditions for phase-field models

AU - Lee, Hyun Geun

AU - Yang, Junxiang

AU - Kim, Junseok

PY - 2020/3

Y1 - 2020/3

N2 - In this paper, we present pinning boundary conditions for two- (2D) and three-dimensional (3D) phase-field models. For the 2D and axisymmetric domains in the neighborhood of the pinning boundaries, we apply an odd-function-type treatment and use a local gradient of the phase-field for points away from the pinning boundaries. For the 3D domain, we propose a simple treatment that fixes the values on the ghost grid points beyond the discrete computational domain. As examples of the phase-field models, we consider the Allen–Cahn and conservative Allen–Cahn equations with the pinning boundary conditions. We present various numerical experiments to demonstrate the performance of the proposed pinning boundary treatment. The computational results confirm the efficiency of the proposed method.

AB - In this paper, we present pinning boundary conditions for two- (2D) and three-dimensional (3D) phase-field models. For the 2D and axisymmetric domains in the neighborhood of the pinning boundaries, we apply an odd-function-type treatment and use a local gradient of the phase-field for points away from the pinning boundaries. For the 3D domain, we propose a simple treatment that fixes the values on the ghost grid points beyond the discrete computational domain. As examples of the phase-field models, we consider the Allen–Cahn and conservative Allen–Cahn equations with the pinning boundary conditions. We present various numerical experiments to demonstrate the performance of the proposed pinning boundary treatment. The computational results confirm the efficiency of the proposed method.

KW - Allen–Cahn equation

KW - Conservative Allen–Cahn equation

KW - Pinning boundary condition

UR - http://www.scopus.com/inward/record.url?scp=85073597476&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85073597476&partnerID=8YFLogxK

U2 - 10.1016/j.cnsns.2019.105060

DO - 10.1016/j.cnsns.2019.105060

M3 - Article

AN - SCOPUS:85073597476

VL - 82

JO - Communications in Nonlinear Science and Numerical Simulation

JF - Communications in Nonlinear Science and Numerical Simulation

SN - 1007-5704

M1 - 105060

ER -