A Locally Conservative Eulerian--Lagrangian Method for a Model Two-Phase Flow Problem in a One-Dimensional Porous Medium

Handle URI:
http://hdl.handle.net/10754/597295
Title:
A Locally Conservative Eulerian--Lagrangian Method for a Model Two-Phase Flow Problem in a One-Dimensional Porous Medium
Authors:
Arbogast, Todd; Huang, Chieh-Sen; Russell, Thomas F.
Abstract:
Motivated by possible generalizations to more complex multiphase multicomponent systems in higher dimensions, we develop an Eulerian-Lagrangian numerical approximation for a system of two conservation laws in one space dimension modeling a simplified two-phase flow problem in a porous medium. The method is based on following tracelines, so it is stable independent of any CFL constraint. The main difficulty is that it is not possible to follow individual tracelines independently. We approximate tracing along the tracelines by using local mass conservation principles and self-consistency. The two-phase flow problem is governed by a system of equations representing mass conservation of each phase, so there are two local mass conservation principles. Our numerical method respects both of these conservation principles over the computational mesh (i.e., locally), and so is a fully conservative traceline method. We present numerical results that demonstrate the ability of the method to handle problems with shocks and rarefactions, and to do so with very coarse spatial grids and time steps larger than the CFL limit. © 2012 Society for Industrial and Applied Mathematics.
Citation:
Arbogast T, Huang C-S, Russell TF (2012) A Locally Conservative Eulerian--Lagrangian Method for a Model Two-Phase Flow Problem in a One-Dimensional Porous Medium. SIAM Journal on Scientific Computing 34: A1950–A1974. Available: http://dx.doi.org/10.1137/090778079.
Publisher:
Society for Industrial & Applied Mathematics (SIAM)
Journal:
SIAM Journal on Scientific Computing
Issue Date:
Jan-2012
DOI:
10.1137/090778079
Type:
Article
ISSN:
1064-8275; 1095-7197
Sponsors:
This author was supported in part by U.S. National Science Foundation grants DMS-0713815 and DMS-0835745, the King Abdullah University of Science and Technology (KAUST) Academic Excellence Alliance program, and the Mathematics Research Promotion Center of Taiwan.This author was supported in part under Taiwan National Science Council grants 96-2115-M-110-002-MY3 and 99-2115-M-110-006-MY3.
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Full metadata record

DC FieldValue Language
dc.contributor.authorArbogast, Todden
dc.contributor.authorHuang, Chieh-Senen
dc.contributor.authorRussell, Thomas F.en
dc.date.accessioned2016-02-25T12:30:03Zen
dc.date.available2016-02-25T12:30:03Zen
dc.date.issued2012-01en
dc.identifier.citationArbogast T, Huang C-S, Russell TF (2012) A Locally Conservative Eulerian--Lagrangian Method for a Model Two-Phase Flow Problem in a One-Dimensional Porous Medium. SIAM Journal on Scientific Computing 34: A1950–A1974. Available: http://dx.doi.org/10.1137/090778079.en
dc.identifier.issn1064-8275en
dc.identifier.issn1095-7197en
dc.identifier.doi10.1137/090778079en
dc.identifier.urihttp://hdl.handle.net/10754/597295en
dc.description.abstractMotivated by possible generalizations to more complex multiphase multicomponent systems in higher dimensions, we develop an Eulerian-Lagrangian numerical approximation for a system of two conservation laws in one space dimension modeling a simplified two-phase flow problem in a porous medium. The method is based on following tracelines, so it is stable independent of any CFL constraint. The main difficulty is that it is not possible to follow individual tracelines independently. We approximate tracing along the tracelines by using local mass conservation principles and self-consistency. The two-phase flow problem is governed by a system of equations representing mass conservation of each phase, so there are two local mass conservation principles. Our numerical method respects both of these conservation principles over the computational mesh (i.e., locally), and so is a fully conservative traceline method. We present numerical results that demonstrate the ability of the method to handle problems with shocks and rarefactions, and to do so with very coarse spatial grids and time steps larger than the CFL limit. © 2012 Society for Industrial and Applied Mathematics.en
dc.description.sponsorshipThis author was supported in part by U.S. National Science Foundation grants DMS-0713815 and DMS-0835745, the King Abdullah University of Science and Technology (KAUST) Academic Excellence Alliance program, and the Mathematics Research Promotion Center of Taiwan.This author was supported in part under Taiwan National Science Council grants 96-2115-M-110-002-MY3 and 99-2115-M-110-006-MY3.en
dc.publisherSociety for Industrial & Applied Mathematics (SIAM)en
dc.subjectAdvection-diffusionen
dc.subjectCharacteristicsen
dc.subjectLocal conservationen
dc.subjectRarefactionsen
dc.subjectShocksen
dc.subjectStreamlinesen
dc.subjectTracelinesen
dc.subjectTwo-phaseen
dc.titleA Locally Conservative Eulerian--Lagrangian Method for a Model Two-Phase Flow Problem in a One-Dimensional Porous Mediumen
dc.typeArticleen
dc.identifier.journalSIAM Journal on Scientific Computingen
dc.contributor.institutionUniversity of Texas at Austin, Austin, United Statesen
dc.contributor.institutionNational Sun Yat-Sen University Taiwan, Kaohsiung, Taiwanen
dc.contributor.institutionNational Science Foundation, Arlington, United Statesen
kaust.grant.programAcademic Excellence Alliance (AEA)en
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