Two-phase flow equations with outflow boundary conditions in the hydrophobichydrophilic case

Nonlinear Analysis, Theory, Methods and Applications

Volumn 73, Issue 4, 2010, Pages 840-853

  Lenzinger, Michael ^a   Schweizer, Ben ^a  

^a TU DORTMUND UNIVERSITY   (Germany)

Author keywords

Maximum principle; Outflow boundary; Porous media; Two phase flow; Variational inequality

Indexed keywords

APPROXIMATION PROCEDURE; CAPILLARY PRESSURE FUNCTION; EXISTENCE RESULTS; HYDROPHOBIC AND HYDROPHILIC; HYDROPHOBIC-HYDROPHILIC; LIMITING SYSTEM; NUMERICAL SCHEME; OPEN SPACE; OUTFLOW BOUNDARY; POROUS MEDIA; VARIATIONAL INEQUALITIES; VARIATIONAL INEQUALITY;

MAXIMUM PRINCIPLE; POROUS MATERIALS; TWO PHASE FLOW; VARIATIONAL TECHNIQUES;

BOUNDARY CONDITIONS;

EID: 77955314156     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.na.2010.03.040     Document Type: Article

References (21)

1. A.Yu. Beliaev, and S.M. Hassanizadeh A theoretical model of hysteresis and dynamic effects in the capillary relation for two-phase flow in porous media Transp. Porous Media 43 3 2001 487 510
2. B. Schweizer Averaging of flows with capillary hysteresis in stochastic porous media European J. Appl. Math. 18 3 2007 389 415
3. D. Kröner, and S. Luckhaus Flow of oil and water in a porous medium J. Differential Equations 55 2 1984 276 288
4. T. Arbogast The existence of weak solutions to single porosity and simple dual-porosity models of two-phase incompressible flow Nonlinear Anal. 19 11 1992 1009 1031
5. Z. Chen Degenerate two-phase incompressible flow. I. Existence, uniqueness and regularity of a weak solution J. Differential Equations 171 2 2001 203 232
6. H.W. Alt, and E. DiBenedetto Nonsteady flow of water and oil through inhomogeneous porous media Ann. Sc. Norm. Super Pisa Cl. Sci. (4) 12 3 1985 335 392
7. M. Ohlberger, B. Schweizer, Modelling of interfaces in unsaturated porous media, in: Discrete and continuous dynamical systems, Supplement Volume. Conference Proceedings of the AIMS, www.aimSciences.org, 2007.
8. H.W. Alt, S. Luckhaus, and A. Visintin On nonstationary flow through porous media Ann. Mat. Pura Appl. (4) 136 1984 303 316
9. B. Schweizer Regularization of outflow problems in unsaturated porous media with dry regions J. Differential Equations 237 2007 278 306
10. Z. Chen Degenerate two-phase incompressible flow. II. Regularity, stabiltiy and stabilization J. Differential Equations 186 2 2002 345 376 (Pubitemid 36006074)
11. A. Beliaev Homogenization of two-phase flows in porous media with hysteresis in the capillary relation European J. Appl. Math. 14 1 2003 61 84
12. A. Bourgeat, S. Luckhaus, and A. Mikelić Convergence of the homogenization process for a double-porosity model of immiscible two-phase flow SIAM J. Math. Anal. 27 6 1996 1520 1543
13. B. Schweizer Homogenization of degenerate two-phase flow equations with oil trapping SIAM J. Math. Anal. 39 6 2008 1740 1763
14. A. Michel A finite volume scheme for two-phase immiscible flow in porous media SIAM J. Numer. Anal. 41 4 2003 1301 1317 (electronic)
15. M. Ohlberger Convergence of a mixed finite elementsfinite volume method for the two phase flow in porous media EastWest J. Numer. Math. 5 3 1997 183 210
16. R. Herbin, R. Eymard, and A. Michel Mathematical study of a petroleum-engineering scheme ESAIM: M2AN 37 6 2003 937 972
17. J.H. Nam, and M. Kaviany Effective diffusivity and water-saturation distribution in single- and two-layer PEMFC diffusion medium Int. J. Heat Mass Transfer 46 2003 4595 4611
18. U. Pasaogullari, and C.Y. Wang Liquid water transport in gas diffusion layer of polymer electrolyte fuel cells J. Electrochem. Soc. 151 3 2004 A399 A406
19. O.A. Ladyzenskaja, and N.N. Uralceva Linear and quasilinear elliptic equations Mathematics in Science and Engineering vol. 46 1968 Academic Press
20. B. Schweizer A well-posed model for dynamic contact angles Nonlinear Anal. 43 1 2001 109 125
21. R.E. Showalter Monotone operators in Banach space and nonlinear partial differential equations Mathematical Surveys and Monographs vol. 49 1997 American Mathematical Society Providence, RI