Benchmark Problems for the Numerical Discretization of the Cahn–Hilliard Equation with a Source Term
In this paper, we present benchmark problems for the numerical discretization of the Cahn–Hilliard equation with a source term. If the source term includes an isotropic growth term, then initially circular and spherical shapes should grow with their original shapes. However, there is numerical aniso...
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Published in | Discrete dynamics in nature and society Vol. 2021; pp. 1 - 11 |
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Main Authors | , , , , , , , |
Format | Journal Article |
Language | English |
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New York
Hindawi
06.12.2021
John Wiley & Sons, Inc Hindawi Limited |
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Abstract | In this paper, we present benchmark problems for the numerical discretization of the Cahn–Hilliard equation with a source term. If the source term includes an isotropic growth term, then initially circular and spherical shapes should grow with their original shapes. However, there is numerical anisotropic error and this error results in anisotropic evolutions. Therefore, it is essential to use isotropic space discretization in the simulation of growth phenomenon such as tumor growth. To test numerical discretization, we present two benchmark problems: one is the growth of a disk or a sphere and the other is the growth of a rotated ellipse or a rotated ellipsoid. The computational results show that the standard discrete Laplace operator has severe grid orientation dependence. However, the isotropic discrete Laplace operator generates good results. |
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AbstractList | In this paper, we present benchmark problems for the numerical discretization of the Cahn–Hilliard equation with a source term. If the source term includes an isotropic growth term, then initially circular and spherical shapes should grow with their original shapes. However, there is numerical anisotropic error and this error results in anisotropic evolutions. Therefore, it is essential to use isotropic space discretization in the simulation of growth phenomenon such as tumor growth. To test numerical discretization, we present two benchmark problems: one is the growth of a disk or a sphere and the other is the growth of a rotated ellipse or a rotated ellipsoid. The computational results show that the standard discrete Laplace operator has severe grid orientation dependence. However, the isotropic discrete Laplace operator generates good results. |
Audience | Academic |
Author | Yoon, Sungha Park, Jintae Kim, Junseok Lee, Hyun Geun Kim, Hyundong Kim, Sangkwon Lee, Chaeyoung Li, Yibao |
Author_xml | – sequence: 1 givenname: Sungha surname: Yoon fullname: Yoon, Sungha organization: Department of MathematicsKorea UniversitySeoul 02 841Republic of Koreakorea.ac.kr – sequence: 2 givenname: Hyun Geun surname: Lee fullname: Lee, Hyun Geun organization: Department of MathematicsKwangwoon UniversitySeoul 01 897Republic of Koreakw.ac.kr – sequence: 3 givenname: Yibao surname: Li fullname: Li, Yibao organization: School of Mathematics and StatisticsXi’an Jiaotong UniversityXi’an 710 049Chinaxjtu.edu.cn – sequence: 4 givenname: Chaeyoung surname: Lee fullname: Lee, Chaeyoung organization: Department of MathematicsKorea UniversitySeoul 02 841Republic of Koreakorea.ac.kr – sequence: 5 givenname: Jintae surname: Park fullname: Park, Jintae organization: Department of MathematicsKorea UniversitySeoul 02 841Republic of Koreakorea.ac.kr – sequence: 6 givenname: Sangkwon surname: Kim fullname: Kim, Sangkwon organization: Department of MathematicsKorea UniversitySeoul 02 841Republic of Koreakorea.ac.kr – sequence: 7 givenname: Hyundong surname: Kim fullname: Kim, Hyundong organization: Department of MathematicsKorea UniversitySeoul 02 841Republic of Koreakorea.ac.kr – sequence: 8 givenname: Junseok orcidid: 0000-0002-0484-9189 surname: Kim fullname: Kim, Junseok organization: Department of MathematicsKorea UniversitySeoul 02 841Republic of Koreakorea.ac.kr |
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Copyright | Copyright © 2021 Sungha Yoon et al. COPYRIGHT 2021 John Wiley & Sons, Inc. Copyright © 2021 Sungha Yoon et al. This is an open access article distributed under the Creative Commons Attribution License (the “License”), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License. https://creativecommons.org/licenses/by/4.0 |
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References | 22 24 25 26 28 U. Trottenberg (30) 2000 10 11 12 13 14 15 16 17 18 W. L. Briggs (29) 2000 19 1 2 3 4 5 6 D. J. Eyre (27) 1997 7 8 9 M. Smoka (23) 2021 20 21 |
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Snippet | In this paper, we present benchmark problems for the numerical discretization of the Cahn–Hilliard equation with a source term. If the source term includes an... In this paper, we present benchmark problems for the numerical discretization of the Cahn-Hilliard equation with a source term. If the source term includes an... |
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Title | Benchmark Problems for the Numerical Discretization of the Cahn–Hilliard Equation with a Source Term |
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