KMS Of Academy of mathematics and systems sciences, CAS
| ENERGY STABLE SECOND ORDER LINEAR SCHEMES FOR THE ALLEN-CAHN PHASE-FIELD EQUATION | |
| Wang, Lin1; Yu, Haijun2,3 | |
| 2019 | |
| Source Publication | COMMUNICATIONS IN MATHEMATICAL SCIENCES
 |
| ISSN | 1539-6746 |
| Volume | 17Issue:3Pages:609-635 |
| Abstract | Phase-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. |
| Keyword | Allen-Cahn equation energy stable stabilized semi-implicit scheme second order scheme error estimate |
| Language | 英语 |
| Funding Project | NNSFC[11771439] ; NNSFC[U1530401] ; NNSFC[91852116] ; China National Program on Key Basic Research Project[2015CB856003] |
| WOS Research Area | Mathematics |
| WOS Subject | Mathematics, Applied |
| WOS ID | WOS:000485624800002 |
| Publisher | INT PRESS BOSTON, INC |
| Citation statistics | |
| Document Type | 期刊论文 |
| Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/35537 |
| Collection | 中国科学院数学与系统科学研究院 |
| Corresponding Author | Wang, Lin |
| Affiliation | 1.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. |
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