Nonlinear two-point flux approximations for simulating subsurface flows with full-tensor anisotropy

ECMOR 2006 - 10th European Conference on the Mathematics of Oil Recovery

Volumn , Issue , 2006, Pages

  Mallison, B T ^a   Chen, Y ^a   Durlofsky, L J ^b  

^a CHEVRON ENERGY TECHNOLOGY COMPANY   (United States)

^b STANFORD UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ITERATIVE METHODS;

ANISOTROPY EFFECT; DISCRETE SYSTEMS; LOCAL-GLOBAL UPSCALING; MULTIPOINT FLUX APPROXIMATIONS; NON-ORTHOGONALITY; PERMEABILITY ANISOTROPY; PERMEABILITY FIELDS; SUBSURFACE FLOW;

POTENTIAL FLOW;

EID: 84896296723     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (14)

1. Aavatsmark, I., "An introduction to multipoint flux approximations for quadrilateral grids," Computational Geosciences, 6, 405-432 (2002).
2. Aavatsmark, I., "Interpretation of a two-point flux stencil for skew parallelogram grids," Computational Geosciences, in review (2005).
3. Aavatsmark, I., Barkve, T., Mannseth, T., "Discretization on non-orthogonal, quadrilateral grids for inhomogeneous, anisotropic media," Journal of Computational Physics, 127, 2-14 (1996).
4. Chen, Y., Durlofsky, L.J., "Adaptive local-global upscaling for general flow scenarios in heterogeneous formations," Transport in Porous Media, 62, 157-85 (2006).
5. Chen, Y., Durlofsky, L.J., Gerritsen, M., Wen, X.H.: "A coupled local-global upscaling approach for simulating flow in highly heterogeneous formations," Advances in Water Resources, 26, 1041-1060 (2003).
6. Chen, Y., Mallison, B.T., Durlofsky, L.J.: "Nonlinear two-point flux approximation for modeling full-tensor effects in subsurface flow simulations," Computational Geosciences, in review (2006).
7. Edwards, M.G., Rogers, C.F., "Finite volume discretization with imposed flux continuity for the general tensor pressure equation," Computational Geosciences, 2, 259-290 (1998).
8. Eigestad, G.T., Aadland, T., Aavatsmark, I., Klausen, R.A, Nordbotten, J.M.: "Recent advances for MPFA methods," in: Proceedings of the 9th European Conference on Mathematics of Oil Recovery, Cannes, France, August 30-September 2. (2004).
9. Gerritsen, M.G., and Lambers, J.V., "A Specialized Upscaling Method for Adaptive Grids: Tight Integration of Local-Global Upscaling and Adaptivity Leads to Accurate Solution of Flow in Heterogeneous Formations," Computational Geosciences, in review (2006).
10. Holden, L., Nielsen, B.F.: "Global upscaling of permeability in heterogeneous reservoirs: the output least squares (OLS) method," Transport in Porous Media, 40, 115-143 (2000).
11. Lee, S.H., Tchelepi, H.A., Jenny, P., Dechant, L.J.: "Implementation of a flux-continuous finite-difference method for stratigraphic, hexahedron grids," SPE Journal, 7, 267-277 (2000).
12. Mlacnik, M.J., Durlofsky, L.J., "Unstructured grid optimization for improved monotonicity of discrete solutions of elliptic equations with highly anisotropic coefficients, Journal of Computational Physics, 216, 337-361 (2006).
13. Nordbotten, J.M., Aavatsmark, I., "Monotonicity conditions for control volume methods on uniform parallelogram grids in homogeneous media," Computational Geosciences, 9, 61-72 (2005).
14. Nordbotten, J.M., Aavatsmark, I., Eigestad, G.T., "Monotonicity of control volume methods," Numerische Mathematik, in review (2006).