An $h$-Adaptive Operator Splitting Method for Two-Phase Flow in 3D Heterogeneous Porous Media

Handle URI:
http://hdl.handle.net/10754/597503
Title:
An $h$-Adaptive Operator Splitting Method for Two-Phase Flow in 3D Heterogeneous Porous Media
Authors:
Chueh, Chih-Che; Djilali, Ned; Bangerth, Wolfgang
Abstract:
The simulation of multiphase flow in porous media is a ubiquitous problem in a wide variety of fields, such as fuel cell modeling, oil reservoir simulation, magma dynamics, and tumor modeling. However, it is computationally expensive. This paper presents an interconnected set of algorithms which we show can accelerate computations by more than two orders of magnitude compared to traditional techniques, yet retains the high accuracy necessary for practical applications. Specifically, we base our approach on a new adaptive operator splitting technique driven by an a posteriori criterion to separate the flow from the transport equations, adaptive meshing to reduce the size of the discretized problem, efficient block preconditioned solver techniques for fast solution of the discrete equations, and a recently developed artificial diffusion strategy to stabilize the numerical solution of the transport equation. We demonstrate the accuracy and efficiency of our approach using numerical experiments in one, two, and three dimensions using a program that is made available as part of a large open source library. © 2013 Society for Industrial and Applied Mathematics.
Citation:
Chueh C-C, Djilali N, Bangerth W (2013) An $h$-Adaptive Operator Splitting Method for Two-Phase Flow in 3D Heterogeneous Porous Media. SIAM Journal on Scientific Computing 35: B149–B175. Available: http://dx.doi.org/10.1137/120866208.
Publisher:
Society for Industrial & Applied Mathematics (SIAM)
Journal:
SIAM Journal on Scientific Computing
KAUST Grant Number:
KUS-C1-016-04
Issue Date:
Jan-2013
DOI:
10.1137/120866208
Type:
Article
ISSN:
1064-8275; 1095-7197
Sponsors:
This author’s work was supported by award KUS-C1-016-04, made by the King Abdullah University of Science and Technology, by the ComputationalInfrastructure in Geodynamics initiative through the NSF under award EAR-0949446 and The Universityof California–Davis, and through an Alfred P. Sloan Research Fellowship.
Appears in Collections:
Publications Acknowledging KAUST Support

Full metadata record

DC FieldValue Language
dc.contributor.authorChueh, Chih-Cheen
dc.contributor.authorDjilali, Neden
dc.contributor.authorBangerth, Wolfgangen
dc.date.accessioned2016-02-25T12:41:00Zen
dc.date.available2016-02-25T12:41:00Zen
dc.date.issued2013-01en
dc.identifier.citationChueh C-C, Djilali N, Bangerth W (2013) An $h$-Adaptive Operator Splitting Method for Two-Phase Flow in 3D Heterogeneous Porous Media. SIAM Journal on Scientific Computing 35: B149–B175. Available: http://dx.doi.org/10.1137/120866208.en
dc.identifier.issn1064-8275en
dc.identifier.issn1095-7197en
dc.identifier.doi10.1137/120866208en
dc.identifier.urihttp://hdl.handle.net/10754/597503en
dc.description.abstractThe simulation of multiphase flow in porous media is a ubiquitous problem in a wide variety of fields, such as fuel cell modeling, oil reservoir simulation, magma dynamics, and tumor modeling. However, it is computationally expensive. This paper presents an interconnected set of algorithms which we show can accelerate computations by more than two orders of magnitude compared to traditional techniques, yet retains the high accuracy necessary for practical applications. Specifically, we base our approach on a new adaptive operator splitting technique driven by an a posteriori criterion to separate the flow from the transport equations, adaptive meshing to reduce the size of the discretized problem, efficient block preconditioned solver techniques for fast solution of the discrete equations, and a recently developed artificial diffusion strategy to stabilize the numerical solution of the transport equation. We demonstrate the accuracy and efficiency of our approach using numerical experiments in one, two, and three dimensions using a program that is made available as part of a large open source library. © 2013 Society for Industrial and Applied Mathematics.en
dc.description.sponsorshipThis author’s work was supported by award KUS-C1-016-04, made by the King Abdullah University of Science and Technology, by the ComputationalInfrastructure in Geodynamics initiative through the NSF under award EAR-0949446 and The Universityof California–Davis, and through an Alfred P. Sloan Research Fellowship.en
dc.publisherSociety for Industrial & Applied Mathematics (SIAM)en
dc.subjectAdaptive mesh refinementen
dc.subjectFuel cellsen
dc.subjectHeterogeneous porous mediaen
dc.subjectOperator splittingen
dc.subjectPreconditioningen
dc.subjectStabilized finite element methoden
dc.subjectTwo-phase flowen
dc.titleAn $h$-Adaptive Operator Splitting Method for Two-Phase Flow in 3D Heterogeneous Porous Mediaen
dc.typeArticleen
dc.identifier.journalSIAM Journal on Scientific Computingen
dc.contributor.institutionUniversity of Victoria, Victoria, Canadaen
dc.contributor.institutionQueen's University, Kingston, Kingston, Canadaen
dc.contributor.institutionTexas A and M University, College Station, United Statesen
kaust.grant.numberKUS-C1-016-04en
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