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dc.contributor.authorYang, Haijian
dc.contributor.authorSun, Shuyu
dc.contributor.authorYang, Chao-he
dc.date.accessioned2016-12-12T08:35:47Z
dc.date.available2016-12-12T08:35:47Z
dc.date.issued2016-12-10
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.
dc.identifier.issn0021-9991
dc.identifier.doi10.1016/j.jcp.2016.11.036
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.
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.
dc.publisherElsevier BV
dc.relation.urlhttp://www.sciencedirect.com/science/article/pii/S0021999116306283
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.2016.11.036
dc.subjectTwo-phase flow
dc.subjectFully implicit method
dc.subjectVariational inequality
dc.subjectSemismooth Newton method
dc.subjectNonlinear preconditioner
dc.subjectParallel computing
dc.titleNonlinearly preconditioned semismooth Newton methods for variational inequality solution of two-phase flow in porous media
dc.typeArticle
dc.contributor.departmentApplied Mathematics and Computational Science Program
dc.contributor.departmentComputational Transport Phenomena Lab
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
dc.contributor.departmentEarth Science and Engineering Program
dc.contributor.departmentPhysical Science and Engineering (PSE) Division
dc.identifier.journalJournal of Computational Physics
dc.eprint.versionPost-print
dc.contributor.institutionCollege of Mathematics and Econometrics, Hunan University, Changsha, Hunan 410082, PR China
dc.contributor.institutionInstitute of Software, Chinese Academy of Sciences, Beijing 100190, PR China
dc.contributor.institutionState Key Laboratory of Computer Science, Chinese Academy of Sciences, Beijing 100190, PR China
kaust.personSun, Shuyu
kaust.grant.numberBAS/1/1351-01-01
dc.date.published-online2016-12-10
dc.date.published-print2017-03


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