A combined finite volume-nonconforming finite element scheme for compressible two phase flow in porous media

Handle URI:
http://hdl.handle.net/10754/566060
Title:
A combined finite volume-nonconforming finite element scheme for compressible two phase flow in porous media
Authors:
Saad, Bilal Mohammed ( 0000-0002-9509-7604 ) ; Saad, Mazen Naufal B M
Abstract:
We propose and analyze a combined finite volume-nonconforming finite element scheme on general meshes to simulate the two compressible phase flow in porous media. 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, where the dual volumes are constructed around the sides of the original mesh. The relative permeability of each phase is decentred according the sign of the velocity at the dual interface. This technique also ensures the validity of the discrete maximum principle for the saturation under a non restrictive shape regularity of the space mesh and the positiveness of all transmissibilities. Next, a priori estimates on the pressures and a function of the saturation that denote capillary terms are established. These stabilities results lead to some compactness arguments based on the use of the Kolmogorov compactness theorem, and allow us to derive the convergence of a subsequence of the sequence of approximate solutions to a weak solution of the continuous equations, provided the mesh size tends to zero. The proof is given for the complete system when the density of the each phase depends on its own pressure. © 2014 Springer-Verlag Berlin Heidelberg.
KAUST Department:
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Publisher:
Springer Nature
Journal:
Numerische Mathematik
Issue Date:
28-Jun-2014
DOI:
10.1007/s00211-014-0651-z
ARXIV:
arXiv:1202.5274v1
Type:
Article
ISSN:
0029599X
Sponsors:
Research reported in this publication was supported by the King Abdullah University of Science and Technology (KAUST) and this work is partially supported by GDR MOMAS.
Appears in Collections:
Articles; 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.accessioned2015-08-12T09:26:33Zen
dc.date.available2015-08-12T09:26:33Zen
dc.date.issued2014-06-28en
dc.identifier.issn0029599Xen
dc.identifier.doi10.1007/s00211-014-0651-zen
dc.identifier.urihttp://hdl.handle.net/10754/566060en
dc.description.abstractWe propose and analyze a combined finite volume-nonconforming finite element scheme on general meshes to simulate the two compressible phase flow in porous media. 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, where the dual volumes are constructed around the sides of the original mesh. The relative permeability of each phase is decentred according the sign of the velocity at the dual interface. This technique also ensures the validity of the discrete maximum principle for the saturation under a non restrictive shape regularity of the space mesh and the positiveness of all transmissibilities. Next, a priori estimates on the pressures and a function of the saturation that denote capillary terms are established. These stabilities results lead to some compactness arguments based on the use of the Kolmogorov compactness theorem, and allow us to derive the convergence of a subsequence of the sequence of approximate solutions to a weak solution of the continuous equations, provided the mesh size tends to zero. The proof is given for the complete system when the density of the each phase depends on its own pressure. © 2014 Springer-Verlag Berlin Heidelberg.en
dc.description.sponsorshipResearch reported in this publication was supported by the King Abdullah University of Science and Technology (KAUST) and this work is partially supported by GDR MOMAS.en
dc.publisherSpringer Natureen
dc.titleA combined finite volume-nonconforming finite element scheme for compressible two phase flow in porous mediaen
dc.typeArticleen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.identifier.journalNumerische Mathematiken
dc.contributor.institutionEcole Cent Nantes, Dept Informat & Math, CNRS, Lab Math Jean Leray,UMR 6629, F-44321 Nantes, Franceen
dc.identifier.arxividarXiv:1202.5274v1en
kaust.authorSaad, Bilal Mohammeden
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