Numerical analysis of a non equilibrium two-component two-compressible flow in porous media

Handle URI:
http://hdl.handle.net/10754/562951
Title:
Numerical analysis of a non equilibrium two-component two-compressible flow in porous media
Authors:
Saad, Bilal Mohammed ( 0000-0002-9509-7604 ) ; Saad, Mazen Naufal B M
Abstract:
We propose and analyze a finite volume scheme to simulate a non equilibrium two components (water and hydrogen) two phase flow (liquid and gas) model. In this model, the assumption of local mass non equilibrium is ensured and thus the velocity of the mass exchange between dissolved hydrogen and hydrogen in the gas phase is supposed finite. The proposed finite volume scheme is fully implicit in time together with a phase-by-phase upwind approach in space and it is discretize the equations in their general form with gravity and capillary terms We show that the proposed scheme satisfies the maximum principle for the saturation and the concentration of the dissolved hydrogen. We establish stability results on the velocity of each phase and on the discrete gradient of the concentration. We show the convergence of a subsequence to a weak solution of the continuous equations as the size of the discretization tends to zero. At our knowledge, this is the first convergence result of finite volume scheme in the case of two component two phase compressible flow in several space dimensions.
KAUST Department:
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division; Applied Mathematics and Computational Science Program
Publisher:
American Institute of Mathematical Sciences (AIMS)
Journal:
Discrete and Continuous Dynamical Systems - Series S
Issue Date:
Sep-2013
DOI:
10.3934/dcdss.2014.7.317
Type:
Article
ISSN:
19371632
Sponsors:
This work was partially supported by GNR MOMAS.
Appears in Collections:
Articles; Applied Mathematics and Computational Science Program; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorSaad, Bilal Mohammeden
dc.contributor.authorSaad, Mazen Naufal B Men
dc.date.accessioned2015-08-03T11:16:46Zen
dc.date.available2015-08-03T11:16:46Zen
dc.date.issued2013-09en
dc.identifier.issn19371632en
dc.identifier.doi10.3934/dcdss.2014.7.317en
dc.identifier.urihttp://hdl.handle.net/10754/562951en
dc.description.abstractWe propose and analyze a finite volume scheme to simulate a non equilibrium two components (water and hydrogen) two phase flow (liquid and gas) model. In this model, the assumption of local mass non equilibrium is ensured and thus the velocity of the mass exchange between dissolved hydrogen and hydrogen in the gas phase is supposed finite. The proposed finite volume scheme is fully implicit in time together with a phase-by-phase upwind approach in space and it is discretize the equations in their general form with gravity and capillary terms We show that the proposed scheme satisfies the maximum principle for the saturation and the concentration of the dissolved hydrogen. We establish stability results on the velocity of each phase and on the discrete gradient of the concentration. We show the convergence of a subsequence to a weak solution of the continuous equations as the size of the discretization tends to zero. At our knowledge, this is the first convergence result of finite volume scheme in the case of two component two phase compressible flow in several space dimensions.en
dc.description.sponsorshipThis work was partially supported by GNR MOMAS.en
dc.publisherAmerican Institute of Mathematical Sciences (AIMS)en
dc.subjectComponenten
dc.subjectCompressibleen
dc.subjectDegenerate problemen
dc.subjectFinite volume schemeen
dc.subjectPorous mediaen
dc.titleNumerical analysis of a non equilibrium two-component two-compressible flow in porous mediaen
dc.typeArticleen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.contributor.departmentApplied Mathematics and Computational Science Programen
dc.identifier.journalDiscrete and Continuous Dynamical Systems - Series Sen
dc.contributor.institutionEcole Centrale de Nantes, Laboratoire de Mathématiques Jean Leray, UMR 6629 CNRS, 1 Rue De La Noé, BP 92101, 44321 Nantes, Franceen
kaust.authorSaad, Bilal Mohammeden
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