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题名

A new class of efficient and robust energy stable schemes for gradient flows

作者
发表日期
2019
DOI
发表期刊
ISSN
0036-1445
卷号61期号:3页码:474-506
摘要
We propose a new numerical technique to deal with nonlinear terms in gradient flows. By introducing a scalar auxiliary variable (SAV), we construct efficient and robust energy stable schemes for a large class of gradient flows. The SAV approach is not restricted to specific forms of the nonlinear part of the free energy and only requires solving decoupled linear equations with constant coefficients. We use this technique to deal with several challenging applications which cannot be easily handled by existing approaches, and we present convincing numerical results to show that our schemes are not only much more efficient and easy to implement, but can also better capture the physical properties in these models. Based on this SAV approach, we can construct unconditionally second-order energy stable schemes, and we can easily construct even third- or fourth-order BDF schemes which, although not unconditionally stable, are very robust in practice. In particular, when coupled with an adaptive time stepping strategy, the SAV approach can be extremely efficient and accurate.
关键词
相关链接[Scopus记录] ; [来源记录]
收录类别
SCI ; EI
语种
英语
重要成果
ESI高被引
学校署名
其他
资助项目
National Natural Science Foundation of China[51661135011] ; National Natural Science Foundation of China[91630204] ; National Science Foundation[DMS-1620262] ; National Science Foundation[DMS-1720442] ; Air Force Office of Scientific Research[FA9550-16-1-0102]
WOS记录号
WOS:000478968600005
出版者
EI入藏号
20193707435783
EI主题词
Free energy ; Nonlinear equations
EI分类号
Energy Conservation:525.2 ; Thermodynamics:641.1
ESI学科分类
MATHEMATICS
Scopus记录号
2-s2.0-85071698907
来源库
Scopus
引用统计
被引频次[WOS]:380
成果类型期刊论文
条目标识符http://kc.sustech.edu.cn/handle/2SGJ60CL/44072
专题理学院_数学系
作者单位
1.Fujian Provincial Key Laboratory of Mathematical Modeling and High-Performance Scientific ComputingSchool of Mathematical SciencesXiamen University,Xiamen,361005,China
2.Department of MathematicsPurdue University,West Lafayette,47907,United States
3.Department of MathematicsSouthern University of Science and Technology,Shenzhen, Guang-dong,518000,China
推荐引用方式
GB/T 7714
Shen,Jie,Xu,Jie,Yang,Jiang. A new class of efficient and robust energy stable schemes for gradient flows[J]. SIAM REVIEW,2019,61(3):474-506.
APA
Shen,Jie,Xu,Jie,&Yang,Jiang.(2019).A new class of efficient and robust energy stable schemes for gradient flows.SIAM REVIEW,61(3),474-506.
MLA
Shen,Jie,et al."A new class of efficient and robust energy stable schemes for gradient flows".SIAM REVIEW 61.3(2019):474-506.
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