Phase field simulations of coupled microstructure solidification problems via the strong form particle difference method

Jeong Hoon Song, Yao Fu, Tae Yeon Kim, Yeong Cheol Yoon, John G. Michopoulos, Timon Rabczuk

Research output: Contribution to journalArticle

10 Citations (Scopus)

Abstract

This paper presents the development of a strong form-based collocation method called the particle difference method (PDM), capable of predicting the spatiotemporal evolution of polycrystalline material solidification through coupling of multi-phase and temperature fields. Cross coupled phase field evolution and heat transfer equations are discretized via the PDM to obtain the interface kinematics of polycrystalline boundary during solidification. A distinct feature of the PDM is its ability to represent derivative operators via a moving least-square approximation of the Taylor expansion through point-wise computations at collocation points. The method discretizes directly the strong forms using the pre-computed derivative operators at each collocation point and elegantly overcomes the topological difficulty in modeling intricate moving interfaces. To verify the efficacy of the PDM, numerical results are compared with those obtained from the conventional finite difference method for uniform and irregular distributions of the collocation points. The scalability of the parallelized PDM is tested by measuring its efficiency with increasing the number of processors. We also provide a solidification simulation with two ellipsoidal inclusions to demonstrate the capability of the PDM in complex moving interface problems with high curvature.

Original languageEnglish
Pages (from-to)1-19
Number of pages19
JournalInternational Journal of Mechanics and Materials in Design
DOIs
Publication statusAccepted/In press - 2017 Sep 8
Externally publishedYes

Fingerprint

Solidification
Microstructure
Least squares approximations
Derivatives
Polycrystalline materials
Finite difference method
Mathematical operators
Scalability
Numerical methods
Kinematics
Temperature distribution
Heat transfer

Keywords

  • Microstructure
  • Phase field model
  • Point collocation
  • Polycrystalline
  • Solidification
  • Strong form

ASJC Scopus subject areas

  • Materials Science(all)
  • Mechanics of Materials
  • Mechanical Engineering

Cite this

Phase field simulations of coupled microstructure solidification problems via the strong form particle difference method. / Song, Jeong Hoon; Fu, Yao; Kim, Tae Yeon; Yoon, Yeong Cheol; Michopoulos, John G.; Rabczuk, Timon.

In: International Journal of Mechanics and Materials in Design, 08.09.2017, p. 1-19.

Research output: Contribution to journalArticle

Song, Jeong Hoon ; Fu, Yao ; Kim, Tae Yeon ; Yoon, Yeong Cheol ; Michopoulos, John G. ; Rabczuk, Timon. / Phase field simulations of coupled microstructure solidification problems via the strong form particle difference method. In: International Journal of Mechanics and Materials in Design. 2017 ; pp. 1-19.
@article{ec458117135941dea3a69021c8c6d42a,
title = "Phase field simulations of coupled microstructure solidification problems via the strong form particle difference method",
abstract = "This paper presents the development of a strong form-based collocation method called the particle difference method (PDM), capable of predicting the spatiotemporal evolution of polycrystalline material solidification through coupling of multi-phase and temperature fields. Cross coupled phase field evolution and heat transfer equations are discretized via the PDM to obtain the interface kinematics of polycrystalline boundary during solidification. A distinct feature of the PDM is its ability to represent derivative operators via a moving least-square approximation of the Taylor expansion through point-wise computations at collocation points. The method discretizes directly the strong forms using the pre-computed derivative operators at each collocation point and elegantly overcomes the topological difficulty in modeling intricate moving interfaces. To verify the efficacy of the PDM, numerical results are compared with those obtained from the conventional finite difference method for uniform and irregular distributions of the collocation points. The scalability of the parallelized PDM is tested by measuring its efficiency with increasing the number of processors. We also provide a solidification simulation with two ellipsoidal inclusions to demonstrate the capability of the PDM in complex moving interface problems with high curvature.",
keywords = "Microstructure, Phase field model, Point collocation, Polycrystalline, Solidification, Strong form",
author = "Song, {Jeong Hoon} and Yao Fu and Kim, {Tae Yeon} and Yoon, {Yeong Cheol} and Michopoulos, {John G.} and Timon Rabczuk",
year = "2017",
month = "9",
day = "8",
doi = "10.1007/s10999-017-9386-1",
language = "English",
pages = "1--19",
journal = "International Journal of Mechanics and Materials in Design",
issn = "1569-1713",
publisher = "Springer Netherlands",

}

TY - JOUR

T1 - Phase field simulations of coupled microstructure solidification problems via the strong form particle difference method

AU - Song, Jeong Hoon

AU - Fu, Yao

AU - Kim, Tae Yeon

AU - Yoon, Yeong Cheol

AU - Michopoulos, John G.

AU - Rabczuk, Timon

PY - 2017/9/8

Y1 - 2017/9/8

N2 - This paper presents the development of a strong form-based collocation method called the particle difference method (PDM), capable of predicting the spatiotemporal evolution of polycrystalline material solidification through coupling of multi-phase and temperature fields. Cross coupled phase field evolution and heat transfer equations are discretized via the PDM to obtain the interface kinematics of polycrystalline boundary during solidification. A distinct feature of the PDM is its ability to represent derivative operators via a moving least-square approximation of the Taylor expansion through point-wise computations at collocation points. The method discretizes directly the strong forms using the pre-computed derivative operators at each collocation point and elegantly overcomes the topological difficulty in modeling intricate moving interfaces. To verify the efficacy of the PDM, numerical results are compared with those obtained from the conventional finite difference method for uniform and irregular distributions of the collocation points. The scalability of the parallelized PDM is tested by measuring its efficiency with increasing the number of processors. We also provide a solidification simulation with two ellipsoidal inclusions to demonstrate the capability of the PDM in complex moving interface problems with high curvature.

AB - This paper presents the development of a strong form-based collocation method called the particle difference method (PDM), capable of predicting the spatiotemporal evolution of polycrystalline material solidification through coupling of multi-phase and temperature fields. Cross coupled phase field evolution and heat transfer equations are discretized via the PDM to obtain the interface kinematics of polycrystalline boundary during solidification. A distinct feature of the PDM is its ability to represent derivative operators via a moving least-square approximation of the Taylor expansion through point-wise computations at collocation points. The method discretizes directly the strong forms using the pre-computed derivative operators at each collocation point and elegantly overcomes the topological difficulty in modeling intricate moving interfaces. To verify the efficacy of the PDM, numerical results are compared with those obtained from the conventional finite difference method for uniform and irregular distributions of the collocation points. The scalability of the parallelized PDM is tested by measuring its efficiency with increasing the number of processors. We also provide a solidification simulation with two ellipsoidal inclusions to demonstrate the capability of the PDM in complex moving interface problems with high curvature.

KW - Microstructure

KW - Phase field model

KW - Point collocation

KW - Polycrystalline

KW - Solidification

KW - Strong form

UR - http://www.scopus.com/inward/record.url?scp=85028995995&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85028995995&partnerID=8YFLogxK

U2 - 10.1007/s10999-017-9386-1

DO - 10.1007/s10999-017-9386-1

M3 - Article

AN - SCOPUS:85028995995

SP - 1

EP - 19

JO - International Journal of Mechanics and Materials in Design

JF - International Journal of Mechanics and Materials in Design

SN - 1569-1713

ER -