Nonlinearly preconditioned semismooth Newton methods for variational inequality solution of two-phase flow in porous media

Handle URI:
http://hdl.handle.net/10754/621999
Title:
Nonlinearly preconditioned semismooth Newton methods for variational inequality solution of two-phase flow in porous media
Authors:
Yang, Haijian; Sun, Shuyu ( 0000-0002-3078-864X ) ; Yang, Chao
Abstract:
Most existing methods for solving two-phase flow problems in porous media do not take the physically feasible saturation fractions between 0 and 1 into account, which often destroys the numerical accuracy and physical interpretability of the simulation. To calculate the solution without the loss of this basic requirement, we introduce a variational inequality formulation of the saturation equilibrium with a box inequality constraint, and use a conservative finite element method for the spatial discretization and a backward differentiation formula with adaptive time stepping for the temporal integration. The resulting variational inequality system at each time step is solved by using a semismooth Newton algorithm. To accelerate the Newton convergence and improve the robustness, we employ a family of adaptive nonlinear elimination methods as a nonlinear preconditioner. Some numerical results are presented to demonstrate the robustness and efficiency of the proposed algorithm. A comparison is also included to show the superiority of the proposed fully implicit approach over the classical IMplicit Pressure-Explicit Saturation (IMPES) method in terms of the time step size and the total execution time measured on a parallel computer.
KAUST Department:
Applied Mathematics and Computational Science Program; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Citation:
Yang H, Sun S, Yang C (2016) Nonlinearly preconditioned semismooth Newton methods for variational inequality solution of two-phase flow in porous media. Journal of Computational Physics. Available: http://dx.doi.org/10.1016/j.jcp.2016.11.036.
Publisher:
Elsevier BV
Journal:
Journal of Computational Physics
KAUST Grant Number:
BAS/1/1351-01-01
Issue Date:
10-Dec-2016
DOI:
10.1016/j.jcp.2016.11.036
Type:
Article
ISSN:
0021-9991
Sponsors:
The authors would like to express their appreciation to the anonymous reviewers for their invaluable comments, which have greatly improved the quality of the paper. The work was supported in part by Special Project on High-Performance Computing under the National Key R&D Program (2016YFB0200603) and National Natural Science Foundation of China (11571100, 91530323, 11272352). S. Sun was also supported by KAUST through the grant BAS/1/1351-01-01. C. Yang was also supported by Key Research Program of Frontier Sciences from CAS through the grant QYZDB-SSW-SYS006.
Additional Links:
http://www.sciencedirect.com/science/article/pii/S0021999116306283
Appears in Collections:
Articles; Applied Mathematics and Computational Science Program; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorYang, Haijianen
dc.contributor.authorSun, Shuyuen
dc.contributor.authorYang, Chaoen
dc.date.accessioned2016-12-12T08:35:47Z-
dc.date.available2016-12-12T08:35:47Z-
dc.date.issued2016-12-10en
dc.identifier.citationYang H, Sun S, Yang C (2016) Nonlinearly preconditioned semismooth Newton methods for variational inequality solution of two-phase flow in porous media. Journal of Computational Physics. Available: http://dx.doi.org/10.1016/j.jcp.2016.11.036.en
dc.identifier.issn0021-9991en
dc.identifier.doi10.1016/j.jcp.2016.11.036en
dc.identifier.urihttp://hdl.handle.net/10754/621999-
dc.description.abstractMost existing methods for solving two-phase flow problems in porous media do not take the physically feasible saturation fractions between 0 and 1 into account, which often destroys the numerical accuracy and physical interpretability of the simulation. To calculate the solution without the loss of this basic requirement, we introduce a variational inequality formulation of the saturation equilibrium with a box inequality constraint, and use a conservative finite element method for the spatial discretization and a backward differentiation formula with adaptive time stepping for the temporal integration. The resulting variational inequality system at each time step is solved by using a semismooth Newton algorithm. To accelerate the Newton convergence and improve the robustness, we employ a family of adaptive nonlinear elimination methods as a nonlinear preconditioner. Some numerical results are presented to demonstrate the robustness and efficiency of the proposed algorithm. A comparison is also included to show the superiority of the proposed fully implicit approach over the classical IMplicit Pressure-Explicit Saturation (IMPES) method in terms of the time step size and the total execution time measured on a parallel computer.en
dc.description.sponsorshipThe authors would like to express their appreciation to the anonymous reviewers for their invaluable comments, which have greatly improved the quality of the paper. The work was supported in part by Special Project on High-Performance Computing under the National Key R&D Program (2016YFB0200603) and National Natural Science Foundation of China (11571100, 91530323, 11272352). S. Sun was also supported by KAUST through the grant BAS/1/1351-01-01. C. Yang was also supported by Key Research Program of Frontier Sciences from CAS through the grant QYZDB-SSW-SYS006.en
dc.publisherElsevier BVen
dc.relation.urlhttp://www.sciencedirect.com/science/article/pii/S0021999116306283en
dc.rightsNOTICE: this is the author’s version of a work that was accepted for publication in Journal of Computational Physics. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Journal of Computational Physics, 10 December 2016. DOI: 10.1016/j.jcp.2016.11.036en
dc.subjectTwo-phase flowen
dc.subjectFully implicit methoden
dc.subjectVariational inequalityen
dc.subjectSemismooth Newton methoden
dc.subjectNonlinear preconditioneren
dc.subjectParallel computingen
dc.titleNonlinearly preconditioned semismooth Newton methods for variational inequality solution of two-phase flow in porous mediaen
dc.typeArticleen
dc.contributor.departmentApplied Mathematics and Computational Science Programen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.identifier.journalJournal of Computational Physicsen
dc.eprint.versionPost-printen
dc.contributor.institutionCollege of Mathematics and Econometrics, Hunan University, Changsha, Hunan 410082, PR Chinaen
dc.contributor.institutionInstitute of Software, Chinese Academy of Sciences, Beijing 100190, PR Chinaen
dc.contributor.institutionState Key Laboratory of Computer Science, Chinese Academy of Sciences, Beijing 100190, PR Chinaen
kaust.authorSun, Shuyuen
kaust.grant.numberBAS/1/1351-01-01en
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