Active-Set Reduced-Space Methods with Nonlinear Elimination for Two-Phase Flow Problems in Porous Media

Handle URI:
http://hdl.handle.net/10754/619780
Title:
Active-Set Reduced-Space Methods with Nonlinear Elimination for Two-Phase Flow Problems in Porous Media
Authors:
Yang, Haijian; Yang, Chao; Sun, Shuyu ( 0000-0002-3078-864X )
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.
KAUST Department:
Physical Sciences and Engineering (PSE) Division
Citation:
Active-Set Reduced-Space Methods with Nonlinear Elimination for Two-Phase Flow Problems in Porous Media 2016, 38 (4):B593 SIAM Journal on Scientific Computing
Publisher:
Society for Industrial & Applied Mathematics (SIAM)
Journal:
SIAM Journal on Scientific Computing
Issue Date:
26-Jul-2016
DOI:
10.1137/15M1041882
Type:
Article
ISSN:
1064-8275; 1095-7197
Sponsors:
The authors would like to thank the anonymous reviewers for the valuable suggestions leading to the improvement of the paper.
Additional Links:
http://epubs.siam.org/doi/10.1137/15M1041882
Appears in Collections:
Articles

Full metadata record

DC FieldValue Language
dc.contributor.authorYang, Haijianen
dc.contributor.authorYang, Chaoen
dc.contributor.authorSun, Shuyuen
dc.date.accessioned2016-09-04T11:28:56Z-
dc.date.available2016-09-04T11:28:56Z-
dc.date.issued2016-07-26-
dc.identifier.citationActive-Set Reduced-Space Methods with Nonlinear Elimination for Two-Phase Flow Problems in Porous Media 2016, 38 (4):B593 SIAM Journal on Scientific Computingen
dc.identifier.issn1064-8275-
dc.identifier.issn1095-7197-
dc.identifier.doi10.1137/15M1041882-
dc.identifier.urihttp://hdl.handle.net/10754/619780-
dc.description.abstractFully 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.en
dc.description.sponsorshipThe authors would like to thank the anonymous reviewers for the valuable suggestions leading to the improvement of the paper.en
dc.language.isoenen
dc.publisherSociety for Industrial & Applied Mathematics (SIAM)en
dc.relation.urlhttp://epubs.siam.org/doi/10.1137/15M1041882en
dc.rightsArchived with thanks to SIAM Journal on Scientific Computingen
dc.subjecttwo-phase flowen
dc.subjectvariational inequalityen
dc.subjectactive-set reduced-space methodsen
dc.subjectnonlinear preconditionersen
dc.subjectnonlinear eliminationen
dc.subjectparallel computingen
dc.titleActive-Set Reduced-Space Methods with Nonlinear Elimination for Two-Phase Flow Problems in Porous Mediaen
dc.typeArticleen
dc.contributor.departmentPhysical Sciences and Engineering (PSE) Divisionen
dc.identifier.journalSIAM Journal on Scientific Computingen
dc.eprint.versionPublisher's Version/PDFen
dc.contributor.institutionCollege of Mathematics and Econometrics, Hunan University, Changsha, Hunan, 410082, Chinaen
dc.contributor.institutionInstitute of Software, Chinese Academy of Sciences, Beijing 100190, China, and State Key Laboratory of Computer Science, Chinese Academy of Sciences, Beijing 100190, Chinaen
dc.contributor.affiliationKing Abdullah University of Science and Technology (KAUST)en
kaust.authorSun, Shuyuen
All Items in KAUST are protected by copyright, with all rights reserved, unless otherwise indicated.