Convergence Analysis of a FV-FE Scheme for Partially Miscible Two-Phase Flow in Anisotropic Porous Media

dc.conference.date15 June 2014 through 20 June 2014
dc.conference.name7th International Symposium on Finite Volumes for Complex Applications-Problems and Perspectives, FVCA7
dc.contributor.authorSaad, Bilal Mohammed
dc.contributor.authorSaad, Mazen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
dc.contributor.institutionEcole Centrale de Nantes, 1, rue de la Noé, BP 92101Nantes, France
dc.date.accessioned2016-01-19T14:45:33Z
dc.date.available2016-01-19T14:45:33Z
dc.date.issued2014-05-16
dc.date.published-online2014-05-16
dc.date.published-print2014
dc.description.abstractWe study the convergence of a combined finite volume nonconforming finite element scheme on general meshes for a partially miscible two-phase flow model in anisotropic porous media. This model includes capillary effects and exchange between the phase. The diffusion term,which can be anisotropic and heterogeneous, is discretized by piecewise linear nonconforming triangular finite elements. The other terms are discretized by means of a cell-centered finite volume scheme on a dual mesh. The relative permeability of each phase is decentred according the sign of the velocity at the dual interface. The convergence of the scheme is proved thanks to an estimate on the two pressures which allows to show estimates on the discrete time and compactness results in the case of degenerate relative permeabilities. A key point in the scheme is to use particular averaging formula for the dissolution function arising in the diffusion term. We show also a simulation of CO2 injection in a water saturated reservoir and nuclear waste management. Numerical results are obtained by in-house numerical code. © Springer International Publishing Switzerland 2014.
dc.identifier.citationSaad B, Saad M (2014) Convergence Analysis of a FV-FE Scheme for Partially Miscible Two-Phase Flow in Anisotropic Porous Media. Springer Proceedings in Mathematics & Statistics: 713–721. Available: http://dx.doi.org/10.1007/978-3-319-05591-6_71.
dc.identifier.doi10.1007/978-3-319-05591-6_71
dc.identifier.isbn9783319055909
dc.identifier.issn2194-1009
dc.identifier.issn2194-1017
dc.identifier.journalFinite Volumes for Complex Applications VII-Elliptic, Parabolic and Hyperbolic Problems
dc.identifier.urihttp://hdl.handle.net/10754/594301
dc.publisherSpringer Nature
dc.titleConvergence Analysis of a FV-FE Scheme for Partially Miscible Two-Phase Flow in Anisotropic Porous Media
dc.typeConference Paper
display.details.left<span><h5>Type</h5>Conference Paper<br><br><h5>Authors</h5><a href="https://repository.kaust.edu.sa/search?query=orcid.id:0000-0002-9509-7604&spc.sf=dc.date.issued&spc.sd=DESC">Saad, Bilal Mohammed</a> <a href="https://orcid.org/0000-0002-9509-7604" target="_blank"><img src="https://repository.kaust.edu.sa/server/api/core/bitstreams/82a625b4-ed4b-40c8-865a-d6a5225a26a4/content" width="16" height="16"/></a><br><a href="https://repository.kaust.edu.sa/search?spc.sf=dc.date.issued&spc.sd=DESC&f.author=Saad, Mazen,equals">Saad, Mazen</a><br><br><h5>KAUST Department</h5><a href="https://repository.kaust.edu.sa/search?spc.sf=dc.date.issued&spc.sd=DESC&f.department=Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division,equals">Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division</a><br><br><h5>Online Publication Date</h5>2014-05-16<br><br><h5>Print Publication Date</h5>2014<br><br><h5>Date</h5>2014-05-16</span>
display.details.right<span><h5>Abstract</h5>We study the convergence of a combined finite volume nonconforming finite element scheme on general meshes for a partially miscible two-phase flow model in anisotropic porous media. This model includes capillary effects and exchange between the phase. The diffusion term,which can be anisotropic and heterogeneous, is discretized by piecewise linear nonconforming triangular finite elements. The other terms are discretized by means of a cell-centered finite volume scheme on a dual mesh. The relative permeability of each phase is decentred according the sign of the velocity at the dual interface. The convergence of the scheme is proved thanks to an estimate on the two pressures which allows to show estimates on the discrete time and compactness results in the case of degenerate relative permeabilities. A key point in the scheme is to use particular averaging formula for the dissolution function arising in the diffusion term. We show also a simulation of CO2 injection in a water saturated reservoir and nuclear waste management. Numerical results are obtained by in-house numerical code. © Springer International Publishing Switzerland 2014.<br><br><h5>Citation</h5>Saad B, Saad M (2014) Convergence Analysis of a FV-FE Scheme for Partially Miscible Two-Phase Flow in Anisotropic Porous Media. Springer Proceedings in Mathematics & Statistics: 713–721. Available: http://dx.doi.org/10.1007/978-3-319-05591-6_71.<br><br><h5>Publisher</h5><a href="https://repository.kaust.edu.sa/search?spc.sf=dc.date.issued&spc.sd=DESC&f.publisher=Springer Nature,equals">Springer Nature</a><br><br><h5>Journal</h5><a href="https://repository.kaust.edu.sa/search?spc.sf=dc.date.issued&spc.sd=DESC&f.journal=Finite Volumes for Complex Applications VII-Elliptic, Parabolic and Hyperbolic Problems,equals">Finite Volumes for Complex Applications VII-Elliptic, Parabolic and Hyperbolic Problems</a><br><br><h5>Conference/Event Name</h5><a href="https://repository.kaust.edu.sa/search?spc.sf=dc.date.issued&spc.sd=DESC&f.conference=7th International Symposium on Finite Volumes for Complex Applications-Problems and Perspectives, FVCA7,equals">7th International Symposium on Finite Volumes for Complex Applications-Problems and Perspectives, FVCA7</a><br><br><h5>DOI</h5><a href="https://doi.org/10.1007/978-3-319-05591-6_71">10.1007/978-3-319-05591-6_71</a></span>
kaust.personSaad, Bilal Mohammed
orcid.authorSaad, Bilal Mohammed::0000-0002-9509-7604
orcid.authorSaad, Mazen
orcid.id0000-0002-9509-7604
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