A dynamic-solver-consistent minimum action method: With an application to 2D Navier-Stokes equations

doi:10.1016/j.jcp.2016.11.019

CSpace

	A dynamic-solver-consistent minimum action method: With an application to 2D Navier-Stokes equations
	Wan, Xiaoliang 1,2; Yu, Haijun 3,4
	2017-02-15
发表期刊	JOURNAL OF COMPUTATIONAL PHYSICS
ISSN	0021-9991
卷号	331 页码:209-226
摘要	This paper discusses the necessity and strategy to unify the development of a dynamic solver and a minimum action method (MAM) for a spatially extended system when employing the large deviation principle (LDP) to study the effects of small random perturbations. A dynamic solver is used to approximate the unperturbed system, and a minimum action method is used to approximate the LDP, which corresponds to solving an Euler-Lagrange equation related to but more complicated than the unperturbed system. We will clarify possible inconsistencies induced by independent numerical approximations of the unperturbed system and the LDP, based on which we propose to define both the dynamic solver and the MAM on the same approximation space for spatial discretization. The semi-discrete LDP can then be regarded as the exact LDP of the semi-discrete unperturbed system, which is a finite-dimensional ODE system. We achieve this methodology for the two-dimensional Navier-Stokes equations using a divergence free approximation space. The method developed can be used to study the nonlinear instability of wall-bounded parallel shear flows, and be generalized straightforwardly to three-dimensional cases. Numerical experiments are presented. (C) 2016 Elsevier Inc. All rights reserved.
关键词	Minimum action method Rare events White noise Colored noise Finite element method Numerical adaptivity
DOI	10.1016/j.jcp.2016.11.019
语种	英语
资助项目	AFOSR Grant[FA9550-15-1-0051] ; NSF Grant[DMS-1620026] ; NNSFC Grants[11101413] ; NNSFC Grants[11371358] ; Major Program of NNSFC Grant[91530322]
WOS研究方向	Computer Science ; Physics
WOS类目	Computer Science, Interdisciplinary Applications ; Physics, Mathematical
WOS记录号	WOS:000393250700011
出版者	ACADEMIC PRESS INC ELSEVIER SCIENCE
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/24681
专题	中国科学院数学与系统科学研究院
通讯作者	Wan, Xiaoliang
作者单位	1.Louisiana State Univ, Dept Math, Baton Rouge, LA 70803 USA 2.Louisiana State Univ, Ctr Computat & Technol, Baton Rouge, LA 70803 USA 3.Acad Math & Syst Sci, Inst Computat Math & Sci Engn Comp, NCMIS, Beijing 100190, Peoples R China 4.Acad Math & Syst Sci, Inst Computat Math & Sci Engn Comp, LSEC, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Wan, Xiaoliang,Yu, Haijun. A dynamic-solver-consistent minimum action method: With an application to 2D Navier-Stokes equations[J]. JOURNAL OF COMPUTATIONAL PHYSICS,2017,331:209-226.
APA	Wan, Xiaoliang,&Yu, Haijun.(2017).A dynamic-solver-consistent minimum action method: With an application to 2D Navier-Stokes equations.JOURNAL OF COMPUTATIONAL PHYSICS,331,209-226.
MLA	Wan, Xiaoliang,et al."A dynamic-solver-consistent minimum action method: With an application to 2D Navier-Stokes equations".JOURNAL OF COMPUTATIONAL PHYSICS 331(2017):209-226.