Coarsening of three-dimensional structured and unstructured grids for subsurface flow

Advances in Water Resources

Volumn 30, Issue 11, 2007, Pages 2177-2193

  Aarnes, Jørg Espen ^a   Hauge, Vera Louise ^a   Efendiev, Yalchin ^b  

^a SINTEF ICT   (Norway)

^b TEXAS A AND M UNIVERSITY   (United States)

Author keywords

Grid generation; Porous media; Two phase flow; Upscaling

Indexed keywords

ALGORITHMS; COMPUTER SIMULATION; FLOW OF WATER; POROUS MATERIALS;

COARSENING ALGORITHM; FLOW SIMULATION; GRID GENERATION; SUBSURFACE FLOW;

TWO PHASE FLOW;

ALGORITHMS; COMPUTER SIMULATION; FLOW OF WATER; POROUS MATERIALS; TWO PHASE FLOW;

ALGORITHM; FLOW MODELING; POROUS MEDIUM; SMOOTHING; SUBSURFACE FLOW; THREE-DIMENSIONAL FLOW; UPSCALING;

EID: 34548322704     PISSN: 03091708     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.advwatres.2007.04.007     Document Type: Article

References (19)

1. Aarnes J.E. On the use of a mixed multiscale finite element method for greater flexibility and increased speed or improved accuracy in reservoir simulation. Multiscale Model Simul. 2 3 (2004) 421-439
2. Aarnes J.E., Kippe V., and Lie K.-A. Mixed multiscale finite elements and streamline methods for reservoir simulation of large geomodels. Adv Water Resour 28 3 (2005) 257-271
3. Aarnes JE, Krogstad S, Lie K-A. Multiscale mixed/mimetic methods on corner-point grids. Comput Geosci, in press.
4. Aarnes JE, Krogstad S, Lie K-A, Laptev V. Multiscale mixed methods on corner-point grids: mimetic versus mixed subgrid solvers. Technical report, SINTEF, 2006.
5. Arbogast T. Numerical subgrid upscaling of two-phase flow in porous media. In: Chen Z, Ewing R, Shi Z-C, editors. Lecture Notes in Physics, Berlin: Springer-Verlag; 2000. pp. 35-49.
6. Arnold DN, Brezzi F. Mixed and nonconforming finite element methods: implementation, postprocessing and error estimates. RAIRO Modél Math Anal Numér 1985; 19(1): 7-32. MR 813687 (87g:65126).
7. Chen Z., and Hou T.Y. A mixed multiscale finite element method for elliptic problems with oscillating coefficients. Math Comp 72 (2003) 541-576
8. Chen Z., Huan G., and Li B. An improved impes method for two-phase flow in porous media. Trans Porous Media 54 (2004) 361-376
9. Christie M.A., and Blunt M.J. Tenth SPE comparative solution project: A comparison of upscaling techniques. SPE Reservoir Eval Eng. 4 (2001) 308-317
10. Durlofsky L.J., Jones R.C., and Milliken W.J. A nonuniform coarsening approach for the scale-up of displacement processes in heterogeneous porous media. Adv Water Resour 20 (1997) 335-347
11. Lipnikov K, Brezzi F, Shashkov M, Simoncini V. A new dicretization methodology for diffusion problems on generalized polyhedral meshes. LAUR-05-8717, Report, 2005.
12. Lipnikov K., Brezzi F., and Simoncini V. A family of mimetic finite difference methods on polygonal and polyhedral meshes. Math Models Methods Appl Sci 15 (2005) 1533-1553
13. He C., and Durlofksy L.J. Structured flow-based gridding and upscaling for modeling subsurface flow. Adv Water Resour 29 12 (2006) 1876-1892
14. Jenny P., Lee S.H., and Tchelepi H.A. Multi-scale finite-volume method for elliptic problems in subsurface flow simulation. J Comput Phys 187 (2003) 47-67
15. King MJ, Burn KS, Wang P, Muralidharan V, Alverado F, Ma X, et al. Optimal coarsening of 3d reservoir models for flow simulation, SPE 95759 (2005).
16. Kippe V, Aarnes JE, Lie K-A. A comparison of multiscale methods for elliptic problems in porous media flow. Comp Geosci, in press.
17. Ponting DK. Corner point geometry in reservoir simulation. In: King PR, editor. Proceedings of the first European Conference on Mathematics of Oil Recovery, Cambridge, 1989 (Oxford), Clarendon Press; July 25-27 1989. pp. 45-65.
18. Raviart P.A., and Thomas J.M. A mixed finite element method for second order elliptic equations. In: Galligani I., and Magenes E. (Eds). Mathematical Aspects of Finite Element Methods (1977), Springer-Verlag, Berlin, Heidelberg, New York 292-315
19. Wen X.-H., and Gómez-Hernández J.J. Upscaling hydraulic conductivities in heterogeneous media: an overview. J Hydrol 183 (1996) ix-xxxii