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

Shen，Jie1,2; Xu，Jie2; Yang，Jiang3

2019

10.1137/17M1150153

SIAM REVIEW   影响因子和分区

0036-1445

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.

Allen-Cahn and Cahn-Hilliard equations Energy stability Gradient flows Nonlocal models Phase field models

SCI ; EI

英语

ESI高被引

其他

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:000478968600005

Society for Industrial and Applied Mathematics Publications

20193707435783

Free energy ; Nonlinear equations

Energy Conservation:525.2 ; Thermodynamics:641.1

MATHEMATICS

2-s2.0-85071698907

Scopus

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

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.

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.

Shen，Jie,et al."A new class of efficient and robust energy stable schemes for gradient flows".SIAM REVIEW 61.3(2019):474-506.