Novel energy dissipative method on the adaptive spatial discretization for the Allen-Cahn equation

doi:10.1088/1674-1056/abe37b

中国物理B ›› 2021, Vol. 30 ›› Issue (7): 70201-070201.doi: 10.1088/1674-1056/abe37b

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Novel energy dissipative method on the adaptive spatial discretization for the Allen-Cahn equation

Jing-Wei Sun(孙竟巍)¹, Xu Qian(钱旭)^1,†, Hong Zhang(张弘)¹, and Song-He Song(宋松和)^1,2

1 Department of Mathematics, National University of Defense Technology, Changsha 410073, China;
2 State Key Laboratory of High Performance Computing, National University of Defense Technology, Changsha 410073, China

收稿日期:2020-12-25 修回日期:2021-01-23 接受日期:2021-02-05 出版日期:2021-06-22 发布日期:2021-06-24
通讯作者: Xu Qian E-mail:qianxu@nudt.edu.cn
基金资助:
Project supported by the National Key R&D Program of China (Grant No. 2020YFA0709800), the National Natural Science Foundation of China (Grant Nos. 11901577, 11971481, 12071481, and 12001539), the Natural Science Foundation of Hunan, China (Grant Nos. S2017JJQNJJ0764 and 2020JJ5652), the fund from Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering (Grant No. 2018MMAEZD004), the Basic Research Foundation of National Numerical Wind Tunnel Project, China (Grant No. NNW2018-ZT4A08), and the Research Fund of National University of Defense Technology (Grant No. ZK19-37).

Novel energy dissipative method on the adaptive spatial discretization for the Allen-Cahn equation

Jing-Wei Sun(孙竟巍)¹, Xu Qian(钱旭)^1,†, Hong Zhang(张弘)¹, and Song-He Song(宋松和)^1,2

1 Department of Mathematics, National University of Defense Technology, Changsha 410073, China;
2 State Key Laboratory of High Performance Computing, National University of Defense Technology, Changsha 410073, China

Received:2020-12-25 Revised:2021-01-23 Accepted:2021-02-05 Online:2021-06-22 Published:2021-06-24
Contact: Xu Qian E-mail:qianxu@nudt.edu.cn
Supported by:
Project supported by the National Key R&D Program of China (Grant No. 2020YFA0709800), the National Natural Science Foundation of China (Grant Nos. 11901577, 11971481, 12071481, and 12001539), the Natural Science Foundation of Hunan, China (Grant Nos. S2017JJQNJJ0764 and 2020JJ5652), the fund from Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering (Grant No. 2018MMAEZD004), the Basic Research Foundation of National Numerical Wind Tunnel Project, China (Grant No. NNW2018-ZT4A08), and the Research Fund of National University of Defense Technology (Grant No. ZK19-37).

摘要/Abstract

摘要： We propose a novel energy dissipative method for the Allen-Cahn equation on nonuniform grids. For spatial discretization, the classical central difference method is utilized, while the average vector field method is applied for time discretization. Compared with the average vector field method on the uniform mesh, the proposed method can involve fewer grid points and achieve better numerical performance over long time simulation. This is due to the moving mesh method, which can concentrate the grid points more densely where the solution changes drastically. Numerical experiments are provided to illustrate the advantages of the proposed concrete adaptive energy dissipative scheme under large time and space steps over a long time.

关键词: moving mesh, energy dissipative, average vector field method, Allen-Cahn equation

Abstract: We propose a novel energy dissipative method for the Allen-Cahn equation on nonuniform grids. For spatial discretization, the classical central difference method is utilized, while the average vector field method is applied for time discretization. Compared with the average vector field method on the uniform mesh, the proposed method can involve fewer grid points and achieve better numerical performance over long time simulation. This is due to the moving mesh method, which can concentrate the grid points more densely where the solution changes drastically. Numerical experiments are provided to illustrate the advantages of the proposed concrete adaptive energy dissipative scheme under large time and space steps over a long time.

Key words: moving mesh, energy dissipative, average vector field method, Allen-Cahn equation

中图分类号: (Numerical simulation; solution of equations)

02.60.Cb

05.70.Fh (Phase transitions: general studies) 02.70.Bf (Finite-difference methods)

Jing-Wei Sun(孙竟巍), Xu Qian(钱旭), Hong Zhang(张弘), and Song-He Song(宋松和). Novel energy dissipative method on the adaptive spatial discretization for the Allen-Cahn equation[J]. 中国物理B, 2021, 30(7): 70201-070201.

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Novel energy dissipative method on the adaptive spatial discretization for the Allen-Cahn equation

Novel energy dissipative method on the adaptive spatial discretization for the Allen-Cahn equation

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