Homogenization of a Darcy-Stokes system modeling vuggy porous media

Computational Geosciences

Volumn 10, Issue 3, 2006, Pages 291-302

  Arbogast, Todd ^a   Lehr, Heather L ^b  

^a UNIVERSITY OF TEXAS AT AUSTIN   (United States)

^b OHIO STATE UNIVERSITY   (United States)

Author keywords

Beavers Joseph boundary condition; Darcy Stokes system; Homogenization; Two scale convergence; Vuggy porous media

Indexed keywords

BOUNDARY CONDITIONS; COMPUTER SIMULATION; INCOMPRESSIBLE FLOW; MATHEMATICAL MODELS; NAVIER STOKES EQUATIONS; OPEN CHANNEL FLOW; POROUS MATERIALS; VISCOUS FLOW;

ANALYTICAL METHOD; DARCY LAW; FLUID FLOW; HOMOGENEITY; POROUS MEDIUM; STOKES FORMULA;

CASTORIDAE;

EID: 33748526177     PISSN: 14200597     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10596-006-9024-8     Document Type: Article

References (29)

1. Allaire, G.: Homogenization and two-scale convergence. SIAM J. Math. Anal. 23, 1482-1518 (1992)
2. Allaire, G., Damlamain, A., Hornung, U.: Two-scale convergence on periodic surfaces and applications. In: Bourgeat, A. et al. (eds.) Proceedings of the International Conference on Mathematical Modelling of Flow Through Porous Media (May 1995), pp. 15-25. World Scientific Pub., Singapore (1996)
3. Arbogast, T., Brunson, D.S.: A computational method for approximating a Darcy-Stokes system governing a vuggy porous medium (in press).
4. Arbogast, T., Douglas Jr., J., Hornung, U.: Derivation of the double porosity model of single phase flow via homogenization theory. SIAM J. Math. Anal. 21, 823-836 (1990)
5. Babuška, I.: The finite element method with Lagrangian multipliers. Numer. Math. 20, 179-192 (1973)
6. Bear, J.: Dynamics of Fluids in Porous Media. Dover, New York (1972)
7. Beavers, G.S., Joseph, D.D.: Boundary conditions at a naturally permeable wall. J. Fluid Mech. 30, 197-207 (1967)
8. Bensoussan, A., Lions, J.L., Papanicolaou, G.: Asymptotic Analysis for Periodic Structure. North Holland, Amsterdam (1978)
9. Bouchitté, G., Fragala, I.: Homogenization of thin structures by the two-scale method with respect to measures. SIAM J. Math. Anal. 32(6), 1198-1226 (2001)
10. Brenner, S.C., Scott, L.R.: The Mathematical Theory of Finite Element Methods. Springer-Verlag, New York (1994)
11. Brezzi, F.: On the existence, uniqueness and approximation of saddle-point problems arising from Lagrangian multipliers. RAIRO 8, 129-151 (1974)
12. Brezzi, F., Fortin, M.: Mixed and Hybrid Finite Element Methods. Springer-Verlag, New York (1991)
13. Gartling, D.K., Hickox, C.E., Givler, R.C.: Simulation of coupled viscous and porous flow problems. Comp. Fluid Dyn. 7, 23-48 (1996)
14. Hornung, U. (ed.): Homogenization and Porous Media, Interdisciplinary Applied Mathematics Series. Springer-Verlag, New York (1997)
15. Jäger, W., Mikelić, A.: On the boundary conditions at the contact interface between a porous medium and a free fluid. Ann. Sc. Norm. Super. Pisa, Classe Fis. Mat. Ser. IV 23, 403-465 (1996)
16. Jäger, W., Mikelić, A.: On the interface boundary condition of Beavers, Joseph, and Saffman. SIAM J. Appl. Math. 60, 1111-1127 (2000)
17. Jikov, V.V., Kozlov, S.M., Oleinik, O.A.: Homogenization of Differential Operators and Integral Functions. Springer-Verlag, New York (1994)
18. Jones, I.P.: Low Reynolds number flow past a porous spherical shell. Proc. Camb. Philol. Soc. 73, 231-238 (1973)
19. Layton, W.J., Schieweck, F., Yotov, I.: Coupling fluid flow with porous media flow. SIAM J. Numer. Anal. 40, 2195-2218 (2003)
20. Lions, J.L., Magenes, E.: Non-Homogeneous Boundary Value Problems and Applications 1. Springer-Verlag, Berlin (1970)
21. Neuss-Radu, M.: Some extensions of two-scale convergence. C. R. Acad. Sci., Sér. 1 Math. 322, 899-904 (1996)
22. Nguetseng, G.: A general convergence result for a functional related to the theory of homogenization. SIAM J. Math. Anal. 20, 608-623 (1989)
23. Peaceman, D.W.: Fundamentals of Numerical Reservoir Simulation. Elsevier, Amsterdam (1977)
24. Saffman, P.G.: On the boundary condition at the interface of a porous medium. Stud. Appl. Math. 1, 93-101 (1971)
25. Salinger, A.G., Aris, R., Derby, J.J.: Finite element formulations for large-scale, coupled flows in adjacent porous and open fluid domains. Int. J. Numer. Methods Fluids 18, 1185-1209 (1994)
26. Sanchez-Palencia, E.: Non-homogeneous Media and Vibration Theory, no. 127 in Lecture Notes in Physics. Springer-Verlag, New York (1980)
27. Tartar, L.: Incompressible fluid flow in a porous medium-convergence of the homogenization process. In: Non-homogeneous Media and Vibration Theory, E. Sanchez-Palencia, Lecture Notes in Physics 127, pp. 368-377. Springer-Verlag, Berlin (1980)
28. Temam, R.: Navier-Stokes Equations, Theory and Numerical Analysis, 2nd ed. North-Holland, Amsterdam (1979)
29. Whitaker, S.: Flow in porous media I: A theoretical derivation of Darcy's law. Transp. Porous Media 1, 3-25 (1986)