Performance of a flux splitting scheme when solving the single-phase pressure equation discretized by MPFA

Computational Geosciences

Volumn 8, Issue 4, 2004, Pages 325-340

  Aadland, Torbjorn ^a   Aavatsmark, Ivar ^a   Dahle, Helge K ^a  

^a UNIVERSITY OF BERGEN   (Norway)

Author keywords

Convergence; Flux splitting; Iteration method; MPFA

Indexed keywords

MATHEMATICAL ANALYSIS;

EID: 22144479025     PISSN: 14200597     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10596-004-3774-y     Document Type: Article

References (19)

1. I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids, Comput. Geosci. 6 (2002) 405-432. 10.1023/ A:1021291114475
2. I. Aavatsmark, T. Barkve, Ø. Bøe and T. Mannseth, Discretization on non-orthogonal, curvilinear grids for multi-phase flow, in: Proc. of the 4th European Conf. on the Mathematics of Oil Recovery, Røros, Norway (1994) Vol. D, 17 pp.
3. I. Aavatsmark, T. Barkve, Ø. Bøe and T. Mannseth, Discretization on non-orthogonal, quadrilateral grids for inhomogeneous, anisotropic media, J. Comput. Phys. 127 (1996) 2-14. 10.1006/ jcph.1996.0154
4. I. Aavatsmark, T. Barkve, Ø. Bøe and T. Mannseth, A class of discretization methods for structured and unstructured grids in anisotropic, inhomogeneous media, in: Proc. of the 5th European Conf. on the Mathematics of Oil Recovery, eds. Z.E. Heinemann and M. Kriebernegg, Leoben, Austria (1996) pp. 157-166.
5. I. Aavatsmark, T. Barkve, Ø. Bøe and T. Mannseth, Discretization on unstructured grids for inhomogeneous, anisotropic media. Part I: Derivation of the methods, SIAM J. Sci. Comput. 19 (1998) 1700-1716.
6. I. Aavatsmark, T. Barkve and T. Mannseth, Control-volume discretization methods for 3D quadrilateral grids in inhomogeneous, anisotropic reservoirs, SPE J. 3 (1998) 146-154.
7. M.G. Edwards, Cross flow tensors and finite volume approximation with deferred correction, Comput. Methods Appl. Mech. Engrg. 151 (1998) 143-161. 10.1016/S0045-7825(97)00109-6
8. M.G. Edwards, Simulation with a full-tensor coefficient velocity field recovered from a diagonal-tensor solution, SPE J. 5 (2000) 387-393.
9. M.G. Edwards, M-matrix flux splitting for general full tensor discretization operators on structured and unstructured grids, J. Comput. Phys. 160 (2000) 1-28. 10.1006/jcph.2000.6418
10. M.G. Edwards, Split full tensor operators coupled with quasi K-orthogonal grids, SPE 51903, in: Proc. of 1999 SPE Reservoir Simulation Symposium, Houston (2001) pp. 243-252.
11. M.G. Edwards, Split full tensor discretization operators for structured and unstructured grids in three dimensions, SPE 66358, in: Proc. of 2001 SPE Reservoir Simulation Symposium, Houston (2001) 12 pp.
12. M.G. Edwards and C.F. Rogers, A flux continuous scheme for the full tensor pressure equation, in: Proc. of the 4th European Conf. on the Mathematics of Oil Recovery, Røros, Norway (1994) Vol. D, 12 pp.
13. M.G. Edwards and C.F. Rogers, Finite volume discretization with imposed flux continuity for the general tensor pressure equation, Comput. Geosci. 2 (1998) 259-290. 10.1023/A:1011510505406
14. R.E. Ewing 1983 Problems arising in modeling of processes for hydrocarbon recovery, R.E. Ewing The Mathematics of Reservoir Simulation SIAM Philadelphia, PA 3-34
15. W. Hackbusch 1986 Theorie und Numerik elliptischer Differentialgleichungen Teubner Studienbücher Stuttgart
16. S.H. Lee, L.J. Durlofsky, M.F. Lough and W.H. Chen, Finite difference simulation of geologically complex reservoirs with tensor permeabilities, SPE Resevoir Evaluation Engrg. 1 (1998) 567-574. 1:CAS:528:DyaK1MXisVyhug%3D%3D
17. S.H. Lee, H. Tchelepi and L.F. DeChant, Implementation of a flux-continuous finite difference method for stratigraphic, hexahedron grids, SPE 51901, in: Proc. of 1999 SPE Reservoir Simulation Symposium, Houston (1999) pp. 231-241.
18. S. Verma and K. Aziz, A control volume scheme for flexible grids in reservoir simulation, SPE 37999, in: Proc. of 1997 SPE Reservoir Simulation Symposium, Dallas (1997) pp. 215-227.
19. A.F. Ware, A.K. Parrott and C. Rogers, A finite difference discretization for porous media flows governed by non-diagonal permeability tensors, in: Proc. of CFD'95, eds. P.A. Thibault and D.M. Bergeron, Banff, Canada (1995) pp. 357-364.