KMS Of Academy of mathematics and systems sciences, CAS
| A FULLY IMPLICIT METHOD FOR LATTICE BOLTZMANN EQUATIONS | |
Huang, Jizu1 ; Yang, Chao2,3; Cai, Xiao-Chuan4
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| 2015 | |
| Source Publication | SIAM JOURNAL ON SCIENTIFIC COMPUTING
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| ISSN | 1064-8275 |
| Volume | 37Issue:5Pages:S291-S313 |
| Abstract | 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. |
| Keyword | lattice Boltzmann equations fully implicit method Newton-Krylov-RAS domain decomposition parallel scalability |
| DOI | 10.1137/140975346 |
| Language | 英语 |
| Funding Project | NSFC[61170075] ; NSFC[61120106005] ; NSFC[91330111] ; 973 program[2011CB309701] ; NSF[CCF-1216314] ; 863 program[2015AA01A302] ; Shenzhen grant[KQCX20130628112914303] |
| WOS Research Area | Mathematics |
| WOS Subject | Mathematics, Applied |
| WOS ID | WOS:000364457000033 |
| Publisher | SIAM PUBLICATIONS |
| Citation statistics | |
| Document Type | 期刊论文 |
| Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/21217 |
| Collection | 计算数学与科学工程计算研究所 |
| Corresponding Author | Cai, Xiao-Chuan |
| Affiliation | 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 |
| Recommended Citation 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. |
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