A NONLINEARLY PRECONDITIONED INEXACT NEWTON ALGORITHM FOR STEADY STATE LATTICE BOLTZMANN EQUATIONS

doi:10.1137/15M1028078

	A NONLINEARLY PRECONDITIONED INEXACT NEWTON ALGORITHM FOR STEADY STATE LATTICE BOLTZMANN EQUATIONS
	Huang, Jizu1 ; Yang, Chao 2,3; Cai, Xiao-Chuan 4
	2016
发表期刊	SIAM JOURNAL ON SCIENTIFIC COMPUTING
ISSN	1064-8275
卷号	38 期号:3 页码:A1701-A1724
摘要	Most existing methods for calculating the steady state solution of the lattice Boltzmann equations are based on pseudo time stepping, which often requires a large number of time steps especially for high Reynolds number problems. To calculate the steady state solution directly without the time integration, in this paper we propose and study a nonlinearly preconditioned inexact Newton algorithm with a domain decomposition based linear solver for parallelization. More precisely, the proposed algorithmic framework involves an implicit, second-order discretization, a two-level inexact Newton method, and a nonlinear elimination preconditioner to accelerate the convergence of Newton iteration. A nonstandard, pollution removing, coarse space is introduced for the two-level method. Numerical experiments are presented to demonstrate the robustness and efficiency of the algorithm, especially for problems at a high Reynolds number. A comparison is also included to show the superiority of the proposed approach over other explicit and implicit methods in terms of the total compute time measured on a parallel computer.
关键词	steady state lattice Boltzmann equations inexact Newton algorithm nonlinear preconditioning pollution removing coarse space parallel scalability
DOI	10.1137/15M1028078
语种	英语
资助项目	NSFC[11501554] ; NSFC[91530323] ; NSFC[91530103] ; NSFC[91330111] ; NSFC[6151101105] ; NSFC[61120106005] ; 863 program[2015AA01A302] ; NSF[CCF-1216314]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000385282800019
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/23725
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.Chinese Acad Sci, 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 NONLINEARLY PRECONDITIONED INEXACT NEWTON ALGORITHM FOR STEADY STATE LATTICE BOLTZMANN EQUATIONS[J]. SIAM JOURNAL ON SCIENTIFIC COMPUTING,2016,38(3):A1701-A1724.
APA	Huang, Jizu,Yang, Chao,&Cai, Xiao-Chuan.(2016).A NONLINEARLY PRECONDITIONED INEXACT NEWTON ALGORITHM FOR STEADY STATE LATTICE BOLTZMANN EQUATIONS.SIAM JOURNAL ON SCIENTIFIC COMPUTING,38(3),A1701-A1724.
MLA	Huang, Jizu,et al."A NONLINEARLY PRECONDITIONED INEXACT NEWTON ALGORITHM FOR STEADY STATE LATTICE BOLTZMANN EQUATIONS".SIAM JOURNAL ON SCIENTIFIC COMPUTING 38.3(2016):A1701-A1724.