Efficient fully-coupled solution techniques for two-phase flow in porous media. Parallel multigrid solution and large scale computations

Advances in Water Resources

Volumn 23, Issue 3, 1999, Pages 199-216

  Bastian, Peter ^a   Helmig, Rainer ^b  

^a UNIVERSITY OF STUTTGART   (Germany)

^b TECHNICAL UNIVERSITY OF BRAUNSCHWEIG   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

ALGEBRA; ALGORITHMS; CAPILLARY FLOW; COMPUTATIONAL GEOMETRY; CONVERGENCE OF NUMERICAL METHODS; LINEAR EQUATIONS; NONLINEAR EQUATIONS; OPTIMIZATION; POROUS MATERIALS; TWO PHASE FLOW;

KRYLOV-SPACE METHOD; NEWTON MULTIGRID ALGORITHM;

WATER RESOURCES;

POROUS MEDIUM; TWO-PHASE FLOW;

EID: 0033377831     PISSN: 03091708     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0309-1708(99)00014-7     Document Type: Article

References (24)

1. Alcouffe RE, Brandt A, Dendy JE, Painter JW. The multigrid method for the diffusion equation with strongly discontinuous coefficients. SIAM J. Sci. Stat. Comput. 1981;2:430-54.
2. Axelsson O, Barker VA. Finite element solution of boundary value problems. New York: Academic Press, 1984.
3. Bastian P. Parallele adaptive mehrgitterverfahren. Leipzig: Teubner (BSB) 1996.
4. Bastian P. Load balancing for adaptive multigrid methods. SIAM J. Sci. Stat. Comput. 1998;4:1305-28.
5. Bastian P, Birken K, Lang S, Johannsen K, Neuß N, Rentz-Reichert H, Wieners C. UG: A flexible software toolbox for solving partial differential equations. Computing and Visualization in Science 1997;1.
6. Braess D. Towards algebraic multigrid for elliptic problems of second order. Computing 1995;55:379-93.
7. Bramble JH, Pasciak JE, Wang J, Xu J. Convergence estimates for multigrid algorithms without regularity assumptions. Math. Comput. 1991;57:23-45.
8. Brenner SC, Scott LR. The mathematical theory of finite element methods. Berlin: Springer, 1994.
9. Chavent G, Jaffré J. Mathematical models and finite elements for reservoir simulation. Amsterdam: North-Holland, 1978.
10. Van der Vorst HA. BiCGSTAB: A fast and smoothly converging variant of Bi-CG for the solution of nonsymmetric linear systems. SIAM J. Sci. Stat. Comput. 1992;13:631-44.
11. Hackbusch W. Multigrid Methods and Applications. Berlin: Springer, 1985.
12. Hackbusch W. Iterative Solution of Large Sparse Systems of Linear Equations. Berlin: Springer, 1994.
13. Helmig R. Multiphase flow and transport processes in the Subsurface - A Contribution to the Modeling of Hydrosystems. Berlin: Springer, 1997.
14. Helmig R, Bastian P, Class J, Ewing R, Hinkelmann R, Huber H, Jakobs H, Sheta R. Architecture of the modular program system MUFTE-UG for simulating multiphase flow and transport processes in heterogeneous porous media. Mathematische Geologie 1998;2:123-31.
15. Kobus H. The role of large-scale experiments in groundwater and subsurface remediation research: The vegas concept and approach. In: Groundwater and Subsurface Remediation. Berlin: Springer, 1996.
16. McBryan OA, Frederickson PO, Linden J, Schüller A, Solchenbach K, Stüben K, Thole CA, Trottenberg U. Multigrid methods on parallel computers - A survey of recent developments. Impact of computing in science and engineering 1991;3:1-75.
17. Molenar J. Multigrid methods for fully implicit oil reservoir simulation. Technical report, TWI, Delft University of Technology, 1995.
18. Mulder WA, Gmelig Meyling RHJ. Numerical simulation of two- phase flow using locally refined grids in three space dimensions. SPE advanced technology series 1993;1(1):36-41.
19. Raw M. Robustness of coupled algebraic multigrid for the Navier-stokes equations. Technical report 96-0297, AIAA 1996.
20. Schöberl J. A rule-based tetrahedral mesh generator. Computing and Visualization in science 1997;1:1-26.
21. Vaněk P, Mandel J, Brezina M. Algebraic multigrid by smoothed aggregation for second and fourth order elliptic problems. Computing, to appear.
22. Washio T, Oosterlee CW. Experiences with robust parallel multilevel pre-conditioners for BiCGSTAB. Technical Report 949, Gesellschaft für Mathematik und Datenverarbeitung, 1995.
23. Wesseling P. An Introduction to Multigrid Methods. New York: Wiley, 1992.
24. Wittum G. On the robustness of ILU smoothing. SIAM J. Sci. Stat. Comput. 1989;10:699-717.