A second-order unconditionally stable method for the anisotropic dendritic crystal growth model with an orientation-field

Yibao Li; Kang Qin; Qing Xia; Junseok Kim

doi:10.1016/j.apnum.2022.11.006

A second-order unconditionally stable method for the anisotropic dendritic crystal growth model with an orientation-field

Yibao Li, Kang Qin, Qing Xia, Junseok Kim

Department of Mathematics

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

6 Citations (Scopus)

Abstract

In this article, we develop a linear, unconditionally energy stable computational scheme for solving the dendritic crystal growth model with the orientational field. We apply the phase field model to describe the evolution of crystal with rotation. The model, which couples the heat equation and anisotropic Allen–Cahn type equation, is a complicated nonlinear system. The time integration is based on the second-order Crank–Nicolson method. The anisotropic coefficient is treated by using the invariant energy quadratization. We mathematically prove that the proposed method is unconditionally energy stable. The second-order spatial and temporal accuracy will be preserved for the numerical approximation. Various computational tests are performed to show the accuracy, stability, and efficiency of the proposed scheme.

Original language	English
Pages (from-to)	512-526
Number of pages	15
Journal	Applied Numerical Mathematics
Volume	184
DOIs	https://doi.org/10.1016/j.apnum.2022.11.006
Publication status	Published - 2023 Feb

Bibliographical note

Funding Information:
Y.B. Li is supported by the Fundamental Research Funds for the Central Universities (No. XTR042019005 ). The corresponding author (J.S. Kim) was supported by Korea University Grant. The authors are grateful to the reviewers whose valuable suggestions and comments significantly improved the quality of this paper.

Publisher Copyright:
© 2022 IMACS

Keywords

Anisotropy
Crystal growth model
Orientational field model
Phase field model
Unconditionally energy-stable

ASJC Scopus subject areas

Numerical Analysis
Computational Mathematics
Applied Mathematics

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10.1016/j.apnum.2022.11.006

Cite this

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title = "A second-order unconditionally stable method for the anisotropic dendritic crystal growth model with an orientation-field",

abstract = "In this article, we develop a linear, unconditionally energy stable computational scheme for solving the dendritic crystal growth model with the orientational field. We apply the phase field model to describe the evolution of crystal with rotation. The model, which couples the heat equation and anisotropic Allen–Cahn type equation, is a complicated nonlinear system. The time integration is based on the second-order Crank–Nicolson method. The anisotropic coefficient is treated by using the invariant energy quadratization. We mathematically prove that the proposed method is unconditionally energy stable. The second-order spatial and temporal accuracy will be preserved for the numerical approximation. Various computational tests are performed to show the accuracy, stability, and efficiency of the proposed scheme.",

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author = "Yibao Li and Kang Qin and Qing Xia and Junseok Kim",

note = "Funding Information: Y.B. Li is supported by the Fundamental Research Funds for the Central Universities (No. XTR042019005 ). The corresponding author (J.S. Kim) was supported by Korea University Grant. The authors are grateful to the reviewers whose valuable suggestions and comments significantly improved the quality of this paper. Publisher Copyright: {\textcopyright} 2022 IMACS",

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doi = "10.1016/j.apnum.2022.11.006",

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AU - Li, Yibao

AU - Qin, Kang

AU - Xia, Qing

AU - Kim, Junseok

N1 - Funding Information: Y.B. Li is supported by the Fundamental Research Funds for the Central Universities (No. XTR042019005 ). The corresponding author (J.S. Kim) was supported by Korea University Grant. The authors are grateful to the reviewers whose valuable suggestions and comments significantly improved the quality of this paper. Publisher Copyright: © 2022 IMACS

PY - 2023/2

Y1 - 2023/2

N2 - In this article, we develop a linear, unconditionally energy stable computational scheme for solving the dendritic crystal growth model with the orientational field. We apply the phase field model to describe the evolution of crystal with rotation. The model, which couples the heat equation and anisotropic Allen–Cahn type equation, is a complicated nonlinear system. The time integration is based on the second-order Crank–Nicolson method. The anisotropic coefficient is treated by using the invariant energy quadratization. We mathematically prove that the proposed method is unconditionally energy stable. The second-order spatial and temporal accuracy will be preserved for the numerical approximation. Various computational tests are performed to show the accuracy, stability, and efficiency of the proposed scheme.

AB - In this article, we develop a linear, unconditionally energy stable computational scheme for solving the dendritic crystal growth model with the orientational field. We apply the phase field model to describe the evolution of crystal with rotation. The model, which couples the heat equation and anisotropic Allen–Cahn type equation, is a complicated nonlinear system. The time integration is based on the second-order Crank–Nicolson method. The anisotropic coefficient is treated by using the invariant energy quadratization. We mathematically prove that the proposed method is unconditionally energy stable. The second-order spatial and temporal accuracy will be preserved for the numerical approximation. Various computational tests are performed to show the accuracy, stability, and efficiency of the proposed scheme.

KW - Anisotropy

KW - Crystal growth model

KW - Orientational field model

KW - Phase field model

KW - Unconditionally energy-stable

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DO - 10.1016/j.apnum.2022.11.006

M3 - Article

AN - SCOPUS:85141915242

SN - 0168-9274

VL - 184

SP - 512

EP - 526

JO - Applied Numerical Mathematics

JF - Applied Numerical Mathematics

ER -

A second-order unconditionally stable method for the anisotropic dendritic crystal growth model with an orientation-field

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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