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Applicable Analysis
An International Journal
Volume 92, 2013 - Issue 7
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Articles

Homogenization results for a coupled system modelling immiscible compressible two-phase flow in porous media by the concept of global pressure

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Pages 1417-1433 | Received 20 Jan 2012, Accepted 28 Mar 2012, Published online: 08 May 2012

References

  • OECD/NEA, Safety of Geological Disposal of High-level and Long-lived Radioactive Waste in France, An International Peer Review of the ‘Dossier 2005 Argile’ Concerning Disposal in the Callovo-Oxfordian Formation, OECD Publishing, Paris, 2006; available online at http://www.nea.fr/html/rwm/reports/2006/nea6178-argile.pdf
  • Croisé , J , Mayer , G , Talandier , J and Wendling , J . 2011 . Impact of water consumption and saturation-dependent corrosion rate on hydrogen generation and migration from an intermediate-level radioactive waste repository . Transp. Porous Media , 90 : 59 – 75 .
  • Senger , R , Ewing , J , Zhang , K , Avis , J , Marschall , P and Gauss , I . 2011 . Modeling approaches for investigating gas migration from a deep low/intermediate level waste repository (Switzerland) . Transp. Porous Media , 90 ( 1 ) : 113 – 133 .
  • ANDRA, Dossier 2005 Argile, les recherches de l'Andra sur le stockage géologique des déchets radioactifs à haute activité et à vie longue, Collection les Rapports, Andra, Châtenay-Malabry, 2005
  • Hornung , U . 1997 . Homogenization and Porous Media , New York : Springer-Verlag .
  • Amaziane , B , Antontsev , S , Pankratov , L and Piatnitski , A . 2010 . Homogenization of immiscible compressible two-phase flow in porous media: application to gas migration in a nuclear waste repository . Multiscale Model. Simul. , 8 : 2023 – 2047 .
  • Bourgeat , A , Gipouloux , O and Marušić-Paloka , E . 2004 . Mathematical modelling of an under- ground waste disposal site by upscaling . Math. Methods Appl. Sci. , 27 : 381 – 403 .
  • Bourgeat , A , Gipouloux , O and Smai , F . 2010 . Scaling up of source terms with random behaviour for modelling transport migration of contaminants in aquifers . Nonlinear Anal. Real World Appl. , 11 ( 6 ) : 4513 – 4523 .
  • Bourgeat , A and Marušić-Paloka , E . 2005 . A homogenized model of an underground waste repository including a disturbed zone . Multiscale Model. Simul. , 3 : 918 – 939 .
  • Bourgeat , A , Marušić-Paloka , E and Piatnitski , A . 2010 . Scaling up of an underground nuclear waste repository including a possibly damaged zone . Asymptot. Anal. , 67 : 147 – 165 .
  • Bourgeat , A and Piatnitski , A . 2010 . Averaging of a singular random source term in a diffusion convection equation . SIAM J. Math. Anal. , 42 ( 6 ) : 2626 – 2651 .
  • Gipouloux , O and Smai , F . 2008 . Scaling up of an underground waste disposal model with random source terms . Int. J. Multiscale Comput. Eng. , 6 : 309 – 325 .
  • Amaziane , B and Jurak , M . 2008 . A new formulation of immiscible compressible two-phase flow in porous media . C. R. Mecanique , 336 : 600 – 605 .
  • Amaziane , B , Jurak , M and Keko , AŽgaljić . 2010 . Modeling and numerical simulations of immiscible compressible two-phase flow in porous media by the concept of global pressure . Transp. Porous Media , 84 ( 1 ) : 133 – 152 .
  • Chavent , G . 2009 . A fully equivalent global pressure formulation for three-phases compressible flows . Appl. Anal. , 88 ( 10–11 ) : 1527 – 1541 .
  • Amaziane , B , Jurak , M and Keko , AŽgaljić . 2011 . An existence result for a coupled system modelling a fully equivalent global pressure formulation for immiscible compressible two-phase flow in porous media . J. Differ. Eqns , 250 ( 3 ) : 1685 – 1718 .
  • Galusinski , C and Saad , M . 2009 . Weak solutions for immiscible compressible multifluid flows in porous media . C. R. Math. Acad. Sci. Paris , 347 ( 5–6 ) : 249 – 254 .
  • Allaire , G . 1992 . Homogenization and two-scale convergence . SIAM J. Math. Anal. , 23 ( 6 ) : 1482 – 1518 .
  • Clark , GW and Showalter , RE . 1999 . Two-scale convergence of a model for flow in a partially fissured medium . Electron. J. Differ. Eqns , 1999 ( 2 ) : 1 – 20 .
  • Lukkassen , D , Nguetseng , G and Wall , P . 2002 . Two-scale convergence . Int. J. Pure Appl. Math. , 2 ( 1 ) : 35 – 86 .

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