A FULLY IMPLICIT METHOD FOR LATTICE BOLTZMANN EQUATIONS

doi:10.1137/140975346

	A FULLY IMPLICIT METHOD FOR LATTICE BOLTZMANN EQUATIONS
	Huang, Jizu1 ; Yang, Chao 2,3; Cai, Xiao-Chuan 4
	2015
发表期刊	SIAM JOURNAL ON SCIENTIFIC COMPUTING
ISSN	1064-8275
卷号	37 期号:5 页码:S291-S313
摘要	Existing approaches for solving the lattice Boltzmann equations with finite difference methods are explicit and semi-implicit; both have certain stability constraints on the time step size. In this work, a fully implicit second-order finite difference scheme is developed. We focus on a parallel, highly scalable, Newton-Krylov-RAS algorithm for the solution of a large sparse nonlinear system of equations arising at each time step. Here, RAS is a restricted additive Schwarz preconditioner based on a first-order spatial discretization. We show numerically that by using the fully implicit method the time step size is no longer constrained by the CFL condition, and the Newton-Krylov-RAS algorithm is scalable on a supercomputer with more than ten thousand processors. Moreover, to calculate the steady state solution we investigate an adaptive time stepping strategy. The total compute time required by the implicit method with adaptive time stepping is much smaller than that of an explicit method for several test cases.
关键词	lattice Boltzmann equations fully implicit method Newton-Krylov-RAS domain decomposition parallel scalability
DOI	10.1137/140975346
语种	英语
资助项目	NSFC[61170075] ; NSFC[61120106005] ; NSFC[91330111] ; 973 program[2011CB309701] ; NSF[CCF-1216314] ; 863 program[2015AA01A302] ; Shenzhen grant[KQCX20130628112914303]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000364457000033
出版者	SIAM PUBLICATIONS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/21217
专题	计算数学与科学工程计算研究所
通讯作者	Cai, Xiao-Chuan
作者单位	1.Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math & Sci Engn Comp, Beijing 100190, Peoples R China 2.Chinese Acad Sci, Inst Software, Beijing 100190, Peoples R China 3.State Key Lab Comp Sci, Beijing 100190, Peoples R China 4.Univ Colorado, Dept Comp Sci, Boulder, CO 80309 USA
推荐引用方式 GB/T 7714	Huang, Jizu,Yang, Chao,Cai, Xiao-Chuan. A FULLY IMPLICIT METHOD FOR LATTICE BOLTZMANN EQUATIONS[J]. SIAM JOURNAL ON SCIENTIFIC COMPUTING,2015,37(5):S291-S313.
APA	Huang, Jizu,Yang, Chao,&Cai, Xiao-Chuan.(2015).A FULLY IMPLICIT METHOD FOR LATTICE BOLTZMANN EQUATIONS.SIAM JOURNAL ON SCIENTIFIC COMPUTING,37(5),S291-S313.
MLA	Huang, Jizu,et al."A FULLY IMPLICIT METHOD FOR LATTICE BOLTZMANN EQUATIONS".SIAM JOURNAL ON SCIENTIFIC COMPUTING 37.5(2015):S291-S313.