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Title:
ACTIVE-SET REDUCED-SPACE METHODS WITH NONLINEAR ELIMINATION FOR TWO-PHASE FLOW PROBLEMS IN POROUS MEDIA
Author: Yang, HJ ; Yang, C ; Sun, SY
Keyword: two-phase flow ; variational inequality ; active-set reduced-space methods ; nonlinear preconditioners ; nonlinear elimination ; parallel computing
Source: SIAM JOURNAL ON SCIENTIFIC COMPUTING
Issued Date: 2016
Volume: 38, Issue:4, Pages:B593-B618
Indexed Type: SCI
Department: Hunan Univ, Coll Math & Econ, Changsha 410082, Hunan, 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. KAUST, Div Phys Sci & Engn PSE, Thuwal 239556900, Saudi Arabia.
Abstract: Fully implicit methods are drawing more attention in scientific and engineering applications due to the allowance of large time steps in extreme-scale simulations. When using a fully implicit method to solve two-phase flow problems in porous media, one major challenge is the solution of the resultant nonlinear system at each time step. To solve such nonlinear systems, traditional nonlinear iterative methods, such as the class of the Newton methods, often fail to achieve the desired convergent rate due to the high nonlinearity of the system and/or the violation of the boundedness requirement of the saturation. In the paper, we reformulate the two-phase model as a variational inequality that naturally ensures the physical feasibility of the saturation variable. The variational inequality is then solved by an active-set reduced-space method with a nonlinear elimination preconditioner to remove the high nonlinear components that often causes the failure of the nonlinear iteration for convergence. To validate the effectiveness of the proposed method, we compare it with the classical implicit pressure-explicit saturation method for two-phase flow problems with strong heterogeneity. The numerical results show that our nonlinear solver overcomes the often severe limits on the time step associated with existing methods, results in superior convergence performance, and achieves reduction in the total computing time by more than one order of magnitude.
English Abstract: Fully implicit methods are drawing more attention in scientific and engineering applications due to the allowance of large time steps in extreme-scale simulations. When using a fully implicit method to solve two-phase flow problems in porous media, one major challenge is the solution of the resultant nonlinear system at each time step. To solve such nonlinear systems, traditional nonlinear iterative methods, such as the class of the Newton methods, often fail to achieve the desired convergent rate due to the high nonlinearity of the system and/or the violation of the boundedness requirement of the saturation. In the paper, we reformulate the two-phase model as a variational inequality that naturally ensures the physical feasibility of the saturation variable. The variational inequality is then solved by an active-set reduced-space method with a nonlinear elimination preconditioner to remove the high nonlinear components that often causes the failure of the nonlinear iteration for convergence. To validate the effectiveness of the proposed method, we compare it with the classical implicit pressure-explicit saturation method for two-phase flow problems with strong heterogeneity. The numerical results show that our nonlinear solver overcomes the often severe limits on the time step associated with existing methods, results in superior convergence performance, and achieves reduction in the total computing time by more than one order of magnitude.
Language: 英语
WOS ID: WOS:000385283400033
Citation statistics:
Content Type: 期刊论文
URI: http://ir.iscas.ac.cn/handle/311060/17419
Appears in Collections:软件所图书馆_期刊论文

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Recommended Citation:
Yang, HJ,Yang, C,Sun, SY. ACTIVE-SET REDUCED-SPACE METHODS WITH NONLINEAR ELIMINATION FOR TWO-PHASE FLOW PROBLEMS IN POROUS MEDIA[J]. SIAM JOURNAL ON SCIENTIFIC COMPUTING,2016-01-01,38(4):B593-B618.
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