Adaptive finite volume methods for displacement problems in porous media

Computing and Visualization in Science

Volumn 5, Issue 2, 2002, Pages 95-106

  Bürkle, David ^a   Ohlberger, Mario ^a  

^a UNIVERSITY OF FREIBURG   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION ALGORITHMS; FINITE VOLUME METHOD; TWO PHASE FLOW;

A-POSTERIORI ERROR ESTIMATES; ADAPTIVE FINITE VOLUME METHOD; CONCENTRATION EQUATIONS; IMMISCIBLE DISPLACEMENT; OPERATOR SPLITTING TECHNIQUE; RAVIART-THOMAS MIXED FINITE ELEMENTS; SINGLE- AND TWO-PHASE FLOW; VERTEX-CENTERED FINITE VOLUME METHOD;

POROUS MATERIALS;

EID: 84900545736     PISSN: 14329360     EISSN: 14330369     Source Type: Journal    
DOI: 10.1007/s00791-002-0091-7     Document Type: Article

References (28)

1. Angermann, L., Knabner, P., Thiele, K.: An error estimate for a finite volume discretization of density driven flow in porous media. Appl. Numer. Math. 26, 179-191 (1998)
2. Bear, J.: Dynamics of Fluids in Porous Media. New York: American Elsevier 1972
3. Bürkle, D.: Kombinierte Finite Volumen-Finite Elemente Verfahren zur Diskretisierung von dichtegetriebenen Grundwasserströmungen. Diplomarbeit, Institut für Angewandte Mathematik, Universität Freiburg, Mai, 1999
4. Bürkle, D.: Combined Finite Volume-Finite Element Method for the Discretization of Density Driven Groundwater Flow. Proceedings of NMICM 2000, Prag, 2000
5. Chavent, G.: A new formulation of diphasic incompressible flows in porous media. Lecture Notes in Mathematics, Vol. 503, pp. 292-315. Berlin, Heidelberg, New York: Springer 1976
6. Chavent, G., Jaffre, J.: Mathematical models and finite elements for reservoir simulation. New York: Elsevier 1986
7. Cockburn, B., Gau, H.: A posteriori error estimates for general numerical methods for scalar conservation laws. Comput. Appl. Math. 14, 37-47 (1995)
8. Douglas, J., Ewing, R.E., Wheeler, M.F.: The approximation of the pressure by a mixed method in the simulation of miscible displacement. R.A.I.R.O. Numer. Anal. 17, 17-33 (1983)
9. Droniou, J., Eymard, R., Hilhorst, D., Zhou, D.: Convergence of a finite volume-mixed finite element method for reservoir simulation. In preparation, ENS Lyon, 2002
10. Durlofsky, L.J.: A triangle based mixed finite element-finite volume technique for modelling two phase flow through porous media. J. Comput. Phys. 105, 252-266 (1993)
11. Eymard, R., Herbin, R., Michel, A.: Mathematical study of a petroleum engineering scheme. In preparation, CMI Marseille, 2002
12. Helmig, R.: Multiphase Flow and Transport Processes in the Subsurface: A contribution to the modeling of hydrosystems. Berlin, Heidelberg, New York: Springer 1997
13. Johannsen, K., Kinzelbach, W., Oswald, S., Wittum, G.: The saltpool benchmark problem -numerical simulation of saltwater upconing in a porous medium. Advances in Water Research 25(3), 335-348 (2002)
14. Knabner, P., Angermann, L.: Numerik partieller Differentialgleichungen. Berlin, Heidelberg, New York: Springer 2000
15. Kröner, D.: Numerical schemes for conservation laws. Stuttgart: Wiley-Teubner 1997
16. Kröner, D., Ohlberger, M.: A-posteriori error estimates for upwind finite volume schemes for nonlinear conservation laws in multi dimensions. Math. Comput. 69, 25-39 (2000)
17. Ohlberger, M.: Convergence of a Mixed Finite Element-Finite Volume Method for the Two Phase Flow in Porous Media. East-West J. Numer. Math. 5, 183-210 (1997)
18. Ohlberger, M.: Mixed Finite Element-Finite Volume Methods for Two Phase Flow in Porous Media. In Proceedings of the 4th International Conference on NUMERICAL METHODS and APPLICATIONS, Sofia (1998), pp. 461-469. Signapore, New Jersy, London, Hong Kong: World Scientific Publishing Co. Pte. Ltd. 1999
19. Ohlberger, M.: A posteriori error estimates for finite volume approximations to singularly perturbed nonlinear convection-diffusion equations. Numer. Math. 87(4), 737-761 (2001)
20. Ohlberger, M.: A posteriori error estimates for vertex centered finite volume approximations of convection-diffusion-reaction equations. M2AN Math. Model. Numer. Anal. 35(2), 355-387 (2001)
21. Ohlberger, M., Rohde, C.: Adaptive finite volume approximations for weakly coupled convection dominated parabolic systems. IMA J. Numer. Anal. 22(2), 253-280 (2002)
22. Putti, M., Yeh, W.W.-G., Mulder, W.A.: A triangular finite volume approach with high-resolution upwind terms for the solution of groundwater transport equations. Water Resources Research 26, 2865-2880 (1990)
23. Raviart, P.A., Thomas, J.M.: A mixed finite element method for 2-nd order elliptic problems. Lecture Notes in Mathematics, Vol. 606, pp. 292-315. Berlin: Springer 1977
24. Schneider, A., Fein, E.: d3 f -Ein Programm zur Modellierung von Dichteströmungen. Abschlußbericht, Gesellschaft für Analgen-und Reaktorsicherheit (GRS) mbH, Braunschweig, Dezember, 1999
25. Starke, G.: Least-squares mixed finite element solution of unsaturatedsaturated subsurface flow problems. Preprint, Fachbereich Mathematik, Universität-GH Essen, 1999
26. Wagner, C., Kinzelbach, W., Wittum, G.: Schur-complement multigrid. A robust method for groundwater flow and transport problems. Numer. Math. 75(4), 523-545 (1997)
27. Wohlmuth, B., Hoppe, R.H.W.: A comparison of a posteriori error estimators for mixed finite element discretizations by Raviart-Thomas elements. Math. Comput. 68(228), 1347-1378 (1999)
28. Zielke, W.: Coupled groundwater flow and transport verification of density variable flow and transport models. Preprint, Institut für Strömungsmechanik, Hanover, 1996