Numerical approximation of a two-phase flow problem in a porous medium with discontinuous capillary forces

SIAM Journal on Numerical Analysis

Volumn 43, Issue 6, 2006, Pages 2402-2422

  Enchéry, Guillaume ^a   Eymard, R ^b   Michel, A ^c  

^a WEIERSTRASS INSTITUTE FOR APPLIED ANALYSIS AND STOCHASTICS   (Germany)

^b UNIVERSITÉ GUSTAVE EIFFEL   (France)

^c IFP ENERGIES NOUVELLES   (France)

Author keywords

Capillarity; Finite volume methods; Flows in porous media; Nonlinear PDE of parabolic type

Indexed keywords

APPROXIMATION THEORY; CAPILLARITY; CAPILLARY FLOW; FINITE VOLUME METHOD; MECHANICAL PERMEABILITY; NUMERICAL ANALYSIS; POROUS MATERIALS;

CONSERVATION EQUATIONS; NONLINEAR DEGENERATE PARABOLIC PROBLEM;

TWO PHASE FLOW;

EID: 33845518637     PISSN: 00361429     EISSN: None     Source Type: Journal    
DOI: 10.1137/040602936     Document Type: Article

References (14)

1. H. W. ALT AND S. LUCKHAUS, Quasilinear elliptic-parabolic differential equations, Math. Z., (1983), pp. 311-341.
2. K. AZIZ AND A. SETTARI, Petroleum Reservoir Simulation, Elsevier Applied Science Publishers, London, 1979.
3. J. BEAR, Dynamic of Fluids in Porous Media, Dover, New York, 1972.
4. J. BEAR, Modeling Transport Phenomena in Porous Media, Springer, New York, 1996, pp. 27-63.
5. M. BERTSCH, R. D. PASSO, AND C. VAN DUIJN, Analysis of oil trapping in porous media flow, SIAM J. Math. Anal., 35 (2003), pp. 245-267.
6. J. CARILLO, Entropy solutions for nonlinear degenerate problems, Arch. Ration. Mech. Anal., 147 (1999), pp. 269-361.
7. G. CHAVENT AND J. JAFFRÉ, Mathematical Models and Finite Elements for Reservoir Simulation, Stud. Math. Appl., vol. 17, North-Holland, Amsterdam, 1986.
8. G. ENCHÉRY, Modèles et schémas numériques pour la simulation de bassin, Ph.D. thesis, Université de Marne-La-Vallée, 2004.
9. B. G. ERSLAND, M. S. ESPEDAL, AND R. NYBO, Numerical methods for flow in a porous medium with internal boundaries, Comput. Geosci., 2 (1998), pp. 217-240.
10. R. EYMARD AND T. GALLOUËT, H-convergence and numerical schemes for elliptic equations, SIAM J. Numer. Anal., 41 (2003), pp. 539-562.
11. R. EYMARD, T. GALLOUËT, AND R. HERBIN, The Finite Volume Method, Ph. Ciarlet and J. L. Lions, eds., North-Holland, Amsterdam, 2000.
12. R. EYMARD, T. GALLOUËT, D. HILHORST, AND Y. N. SLIMANE, Finite volumes and nonlinear diffusion equations, M2AN, 32 (1998), pp. 747-761.
13. A. MICHEL, Convergence de schémas volumes finis pour des problèmes de convection diffusion non linéaires, Ph.D. thesis, Université de Provence, 2001.
14. C. J. VAN DUIJN, J. MOLENAAR, AND M. J. DE NEEF, The effect of capillary forces on immiscible two-phase flow in heterogeneous porous media, Transport in Porous Media, 21 (1995), pp. 71-93.