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Title:
A NONLINEARLY PRECONDITIONED INEXACT NEWTON ALGORITHM FOR STEADY STATE LATTICE BOLTZMANN EQUATIONS
Author: Huang, JZ ; Yang, C ; Cai, XC
Keyword: steady state lattice Boltzmann equations ; inexact Newton algorithm ; nonlinear preconditioning ; pollution removing coarse space ; parallel scalability
Source: SIAM JOURNAL ON SCIENTIFIC COMPUTING
Issued Date: 2016
Volume: 38, Issue:3, Pages:A1701-A1724
Indexed Type: SCI
Department: Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math & Sci Engn Comp, Beijing 100190, Peoples R China. Chinese Acad Sci, Inst Software, Beijing 100190, Peoples R China. Chinese Acad Sci, State Key Lab Comp Sci, Beijing 100190, Peoples R China. Univ Colorado, Dept Comp Sci, Boulder, CO 80309 USA.
Abstract: 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.
English Abstract: 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.
Language: 英语
WOS ID: WOS:000385282800019
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Content Type: 期刊论文
URI: http://ir.iscas.ac.cn/handle/311060/17421
Appears in Collections:软件所图书馆_期刊论文

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Recommended Citation:
Huang, JZ,Yang, C,Cai, XC. A NONLINEARLY PRECONDITIONED INEXACT NEWTON ALGORITHM FOR STEADY STATE LATTICE BOLTZMANN EQUATIONS[J]. SIAM JOURNAL ON SCIENTIFIC COMPUTING,2016-01-01,38(3):A1701-A1724.
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