Convergence of Discontinuous Galerkin Methods for Incompressible Two-Phase Flow in Heterogeneous Media

Handle URI:
http://hdl.handle.net/10754/555745
Title:
Convergence of Discontinuous Galerkin Methods for Incompressible Two-Phase Flow in Heterogeneous Media
Authors:
Kou, Jisheng; Sun, Shuyu ( 0000-0002-3078-864X )
Abstract:
A class of discontinuous Galerkin methods with interior penalties is presented for incompressible two-phase flow in heterogeneous porous media with capillary pressures. The semidiscrete approximate schemes for fully coupled system of two-phase flow are formulated. In highly heterogeneous permeable media, the saturation is discontinuous due to different capillary pressures, and therefore, the proposed methods incorporate the capillary pressures in the pressure equation instead of saturation equation. By introducing a coupling approach for stability and error estimates instead of the conventional separate analysis for pressure and saturation, the stability of the schemes in space and time and a priori hp error estimates are presented in the L2(H 1) for pressure and in the L∞(L2) and L2(H1) for saturation. Two time discretization schemes are introduced for effectively computing the discrete solutions. © 2013 Societ y for Industrial and Applied Mathematics.
KAUST Department:
Computational Transport Phenomena Lab; Physical Sciences and Engineering (PSE) Division
Citation:
Convergence of Discontinuous Galerkin Methods for Incompressible Two-Phase Flow in Heterogeneous Media 2013, 51 (6):3280 SIAM Journal on Numerical Analysis
Journal:
SIAM Journal on Numerical Analysis
Issue Date:
Jan-2013
DOI:
10.1137/120898358
Type:
Article
ISSN:
0036-1429; 1095-7170
Additional Links:
http://epubs.siam.org/doi/abs/10.1137/120898358
Appears in Collections:
Articles; Physical Sciences and Engineering (PSE) Division; Physical Sciences and Engineering (PSE) Division; Computational Transport Phenomena Lab; Computational Transport Phenomena Lab

Full metadata record

DC FieldValue Language
dc.contributor.authorKou, Jishengen
dc.contributor.authorSun, Shuyuen
dc.date.accessioned2015-05-26T07:02:40Zen
dc.date.available2015-05-26T07:02:40Zen
dc.date.issued2013-01en
dc.identifier.citationConvergence of Discontinuous Galerkin Methods for Incompressible Two-Phase Flow in Heterogeneous Media 2013, 51 (6):3280 SIAM Journal on Numerical Analysisen
dc.identifier.issn0036-1429en
dc.identifier.issn1095-7170en
dc.identifier.doi10.1137/120898358en
dc.identifier.urihttp://hdl.handle.net/10754/555745en
dc.description.abstractA class of discontinuous Galerkin methods with interior penalties is presented for incompressible two-phase flow in heterogeneous porous media with capillary pressures. The semidiscrete approximate schemes for fully coupled system of two-phase flow are formulated. In highly heterogeneous permeable media, the saturation is discontinuous due to different capillary pressures, and therefore, the proposed methods incorporate the capillary pressures in the pressure equation instead of saturation equation. By introducing a coupling approach for stability and error estimates instead of the conventional separate analysis for pressure and saturation, the stability of the schemes in space and time and a priori hp error estimates are presented in the L2(H 1) for pressure and in the L∞(L2) and L2(H1) for saturation. Two time discretization schemes are introduced for effectively computing the discrete solutions. © 2013 Societ y for Industrial and Applied Mathematics.en
dc.relation.urlhttp://epubs.siam.org/doi/abs/10.1137/120898358en
dc.rightsArchived with thanks to SIAM Journal on Numerical Analysisen
dc.subjecttwo-phase flowen
dc.subjectdiscontinuous Galerkin methoden
dc.subjectstabilityen
dc.subjecterror estimatesen
dc.titleConvergence of Discontinuous Galerkin Methods for Incompressible Two-Phase Flow in Heterogeneous Mediaen
dc.typeArticleen
dc.contributor.departmentComputational Transport Phenomena Laben
dc.contributor.departmentPhysical Sciences and Engineering (PSE) Divisionen
dc.identifier.journalSIAM Journal on Numerical Analysisen
dc.eprint.versionPublisher's Version/PDFen
dc.contributor.institutionSchool of Mathematics and Statistics, Hubei Engineering University, Xiaogan 432000, Hubei, Chinaen
kaust.authorSun, Shuyuen
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