CSpace
ENERGY STABLE SECOND ORDER LINEAR SCHEMES FOR THE ALLEN-CAHN PHASE-FIELD EQUATION
Wang, Lin1; Yu, Haijun2,3
2019
Source PublicationCOMMUNICATIONS IN MATHEMATICAL SCIENCES
ISSN1539-6746
Volume17Issue:3Pages:609-635
AbstractPhase-field model is a powerful mathematical tool to study the dynamics of interface and morphology changes in fluid mechanics and material sciences. However, numerically solving a phase field model for a real problem is a challenging task due to the non-convexity of the bulk energy and the small interface thickness parameter in the equation. In this paper, we propose two stabilized second order semi-implicit linear schemes for the Allen-Cahn phase-field equation based on backward differentiation formula and Crank-Nicolson method, respectively. In both schemes, the nonlinear bulk force is treated explicitly with two second-order stabilization terms, which make the schemes unconditionally energy stable and numerically efficient. By using a known result of the spectrum estimate of the linearized Allen-Cahn operator and some regularity estimates of the exact solution, we obtain an optimal second order convergence in time with a prefactor depending on the inverse of the characteristic interface thickness only in some lower polynomial order. Both 2-dimensional and 3-dimensional numerical results are presented to verify the accuracy and efficiency of proposed schemes.
KeywordAllen-Cahn equation energy stable stabilized semi-implicit scheme second order scheme error estimate
Language英语
Funding ProjectNNSFC[11771439] ; NNSFC[U1530401] ; NNSFC[91852116] ; China National Program on Key Basic Research Project[2015CB856003]
WOS Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000485624800002
PublisherINT PRESS BOSTON, INC
Citation statistics
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/35537
Collection中国科学院数学与系统科学研究院
Affiliation1.Beijing Computat Sci Res Ctr, CSRC, Beijing 100193, Peoples R China
2.Acad Math & Syst Sci, Inst Computat Math & Sci Engn Comp, NCMIS & LSEC, Beijing 100190, Peoples R China
3.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China
Recommended Citation
GB/T 7714
Wang, Lin,Yu, Haijun. ENERGY STABLE SECOND ORDER LINEAR SCHEMES FOR THE ALLEN-CAHN PHASE-FIELD EQUATION[J]. COMMUNICATIONS IN MATHEMATICAL SCIENCES,2019,17(3):609-635.
APA Wang, Lin,&Yu, Haijun.(2019).ENERGY STABLE SECOND ORDER LINEAR SCHEMES FOR THE ALLEN-CAHN PHASE-FIELD EQUATION.COMMUNICATIONS IN MATHEMATICAL SCIENCES,17(3),609-635.
MLA Wang, Lin,et al."ENERGY STABLE SECOND ORDER LINEAR SCHEMES FOR THE ALLEN-CAHN PHASE-FIELD EQUATION".COMMUNICATIONS IN MATHEMATICAL SCIENCES 17.3(2019):609-635.
Files in This Item:
There are no files associated with this item.
Related Services
Recommend this item
Bookmark
Usage statistics
Export to Endnote
Google Scholar
Similar articles in Google Scholar
[Wang, Lin]'s Articles
[Yu, Haijun]'s Articles
Baidu academic
Similar articles in Baidu academic
[Wang, Lin]'s Articles
[Yu, Haijun]'s Articles
Bing Scholar
Similar articles in Bing Scholar
[Wang, Lin]'s Articles
[Yu, Haijun]'s Articles
Terms of Use
No data!
Social Bookmark/Share
All comments (0)
No comment.
 

Items in the repository are protected by copyright, with all rights reserved, unless otherwise indicated.