On Efficient Second Order Stabilized Semi-implicit Schemes for the Cahn-Hilliard Phase-Field Equation

doi:10.1007/s10915-018-0746-2

	On Efficient Second Order Stabilized Semi-implicit Schemes for the Cahn-Hilliard Phase-Field Equation
	Wang, Lin 1,2; Yu, Haijun1,2
	2018-11-01
发表期刊	JOURNAL OF SCIENTIFIC COMPUTING
ISSN	0885-7474
卷号	77 期号:2 页码:1185-1209
摘要	Efficient and energy stable high order time marching schemes are very important but not easy to construct for the study of nonlinear phase dynamics. In this paper, we propose and study two linearly stabilized second order semi-implicit schemes for the Cahn-Hilliard phase-field equation. One uses backward differentiation formula and the other uses Crank-Nicolson method to discretize linear terms. In both schemes, the nonlinear bulk forces are treated explicitly with two second-order stabilization terms. This treatment leads to linear elliptic systems with constant coefficients, for which lots of robust and efficient solvers are available. The discrete energy dissipation properties are proved for both schemes. Rigorous error analysis is carried out to show that, when the time step-size is small enough, second order accuracy in time is obtained with a prefactor controlled by a fixed power of , where is the characteristic interface thickness. Numerical results are presented to verify the accuracy and efficiency of proposed schemes.
关键词	Phase field model Cahn-Hilliard equation Energy stable Stabilized semi-implicit scheme Second order time marching
DOI	10.1007/s10915-018-0746-2
语种	英语
资助项目	NNSFC[11771439] ; NNSFC[11371358] ; NNSFC[91530322]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000446594600022
出版者	SPRINGER/PLENUM PUBLISHERS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/31454
专题	计算数学与科学工程计算研究所
通讯作者	Yu, Haijun
作者单位	1.Acad Math & Syst Sci, Inst Computat Math & Sci Engn Comp, NCMIS & LSEC, Beijing 100190, Peoples R China 2.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China
推荐引用方式 GB/T 7714	Wang, Lin,Yu, Haijun. On Efficient Second Order Stabilized Semi-implicit Schemes for the Cahn-Hilliard Phase-Field Equation[J]. JOURNAL OF SCIENTIFIC COMPUTING,2018,77(2):1185-1209.
APA	Wang, Lin,&Yu, Haijun.(2018).On Efficient Second Order Stabilized Semi-implicit Schemes for the Cahn-Hilliard Phase-Field Equation.JOURNAL OF SCIENTIFIC COMPUTING,77(2),1185-1209.
MLA	Wang, Lin,et al."On Efficient Second Order Stabilized Semi-implicit Schemes for the Cahn-Hilliard Phase-Field Equation".JOURNAL OF SCIENTIFIC COMPUTING 77.2(2018):1185-1209.