Anisotropy favoring triangulation CVD(MPFA) finite-volume approximations

International Journal for Numerical Methods in Fluids

Volumn 67, Issue 10, 2011, Pages 1247-1263

  Pal, Mayur ^a   Edwards, Michael G ^b  

^a SHELL GLOBAL SOLUTIONS INTERNATIONAL B V   (United States)

^b SWANSEA UNIVERSITY   (United Kingdom)

Author keywords

CVD; Discrete maximum principle; Discretization; MPFA; Pressure; Reservoir; Unstructured

Indexed keywords

ANISOTROPY FIELD; ANISOTROPY RATIO; APPROXIMATION SCHEME; DISCONTINUOUS COEFFICIENTS; DISCRETE MAXIMUM PRINCIPLES; DISCRETIZATIONS; FINITE-VOLUME; MPFA; NUMERICAL CONVERGENCE; NUMERICAL SOLUTION; PRESSURE EQUATIONS; PRESSURE FIELD; RESERVOIR SIMULATION; SPURIOUS OSCILLATIONS; TEST EXAMPLES; TWO-DIMENSION; UNSTRUCTURED; UNSTRUCTURED GRID;

CONVERGENCE OF NUMERICAL METHODS; TENSORS; THREE DIMENSIONAL; TRIANGULATION;

ANISOTROPY;

EID: 79957920178     PISSN: 02712091     EISSN: 10970363     Source Type: Journal    
DOI: 10.1002/fld.2412     Document Type: Article

References (31)

1. Edwards MG, Rogers CF. Finite volume discretization with imposed flux continuity for the general tensor pressure equation. Computational Geosciences 1998; 2:259-290.
2. Edwards MG. Unstructured, control-volume distributed, full-tensor finite volume schemes with flow based grids. Computational Geosciences 2002; 6:433-452.
3. Pal M, Edwards MG, Lamb AR. Convergence study of a family of flux-continuous, finite-volume schemes for the general tensor pressure equation. International Journal for Numerical Methods in Fluids 2006; 51:1177-1203.
4. Pal M. Families of control-volume distributed multi-point flux approximation finite volume schems for the porous media pressure equation on structured and unstructured grids. Ph.D. Thesis, University of Swansea, U.K., 2007.
5. Pal M, Edwards MG. Quasi-monotonic Darcy-flux approximation for general 3-D grids of any element type. Paper SPE106486, SPE Reservoir Simulation Symposium, Houston, TX, February 2007.
6. Eigestad GT, Klausen RA. On the convergence of the multi-point flux approximation O-method: numerical experiments for the discontinuous permeability. Numerical Methods for Partial Differential Equations 2005; 21(6):1079-1098.
7. Aavatsmark I, Eigestad GT, Klausen RA. Numerical Convergence of the MPFA-O for General Quadrilateral Grids in Two and Three Dimension. Compatible Spatial Discretization. IMA, vol. 142. Springer: New York, 2006; 1-21.
8. Lee SH, Jenny P, Tchelepi HA. A finite-volume method with hexahedral multiblock grid for modeling flow in porous media. Computational Geosciences 2002; 6(3-4):353-379.
9. Wheeler MF, Yotov I. A multipoint flux mixed finite element method. SIAM 2006; 44:2082-2106.
10. Verma S. Flexible grids for reservoir simulation. Ph.D. Thesis, Stanford University, 1996.
11. Edwards MG. Higher-resolution hyperbolic-coupled-elliptic flux-continuous CVD schemes on structured and unstructured grids in 2-D. International Journal for Numerical Methods in Fluids 2006; 51:1059-1077.
12. Edwards MG. Higher-resolution hyperbolic-coupled-elliptic flux-continuous CVD schemes on structured and unstructured grids in 3-D. International Journal for Numerical Methods in Fluids 2006; 51(9-10):1079-1095.
13. Aavatsmark I, Eigestad GT. Numerical convergence of MPFA-O and U methods on general quadrilateral grids. International Journal for Numerical Methods in Fluids 2006; 51:939-961.
14. Friis HA, Edwards MG, Mykkeltveit J. Symmetric positive definite flux-continuous full-tensor finite-volume schemes on unstructured cell centered triangular grids. SISC 2008; 31:1192-1220.
15. Edwards MG. M-matrix flux splitting for general full tensor discretization operator on structured and unstructured grids. Journal of Computational Physics 2000; 160:1-28.
16. Edwards MG. Symmetric, Fux-continuous positive defnite approximation of elliptic full tensor pressure equation in local conservation form. SPE 291471, The 13th SPE Reservoir Simulation Symposium, San Antonio, TX, U.S.A., 1995; 553-562.
17. Edwards MG, Zheng H. A quasi-positive family of continuous Darcy-flux finite volume schemes with full pressure support. Journal of Computational Physics 2008; 227:9333-9364.
18. Pal M, Edwards MG. Flux-splitting Schemes for Improved Montonicity of Discrete Solution of Elliptic Equation with Highly Anisotropic Coefficients. Proceedings, ECOMASS CFD-2006 Conference. Egmond aan Zee: The Netherlands, 5-8 September 2006.
19. Pal M, Edwards MG. Family of flux-continuous finite-volume schemes with improved monotonicity. Proceedings of the 10th European Conference on the Mathematics of Oil Recovery, Amsterdam, The Netherlands, 4-7 September 2006.
20. Pal M, Edwards MG. Non-linear flux-splitting schemes with imposed discrete maximum principle for elliptic equations with highly anisotropic coefficients. International Journal for Numerical Methods in Fluids 2010; DOI: 10.1002/fld.2258.
21. Le Potier C. Schema volume finis pour des operator operateurs de diffusion fortement anisotropes sur des maillages de triangle nonstructures. Comptes Rendus de l'Académie des sciences 2005; 340(12):921-926.
22. Svyatskiy D, Lipnikov K, Sashkov M, Vassilevski Yu. Monotone finite volume schemes for diffusion equations on unstructured triangular and shape-regular polygonal meshes. Journal of Computational Physics 2008; 227:492-512.
23. Mlacnik MJ, Durlofsky LJ. Unstructured grid optimization for improved monotonicity of discrete solutions of elliptic equations with highly anisotropic coefficients. Journal of Computational Physics 2006; 216(1):337-361.
24. Edwards MG, Zheng H. Quasi-positive families of continuous Darcy-flux finite volume schemes on structured and unstructured grids. Journal of Computational and Applied Mathematics 2008; DOI: 10.1016/j.cam.2009.08.078.
25. Aavatsmark I, Eigestad GT, Mallison BT, Nordbotten JM. A compact multipoint flux approximation method with improved robustness. Numerical Methods for Partial Differential Equations 2008; 24:1329-1360.
26. Edwards MG, Zheng H. Double-families of quasi-positive darcy-flux approximations with highly anisotropic tensors on structured and unstructured grids. Journal of Computational Physics 2010; 229:594-625.
27. Zheng H, Edwards MG. Continuous Darcy-flux approximations with full pressure support for structured and unstructured grids in 3-D, Paper A01, European Conference on the Mathematics of Oil Recovery, Bergen, Norway, 7-11 September 2008.
28. Zheng H, Edwards MG. Quasi-positive multi-family continuous darcy-flux approximations with full pressure support on structured and unstructured grids in 3-D. Paper SPE119186, Proceedings of Reservoir Simulation Symposium, Houston, TX, U.S.A., February 2009.
29. Axelsson O. Iterative Solution Methods. Cambridge University Press: Cambridge, 1994.
30. Nordbotten JM, Aavatsmark I. Montonicity conditions for control volume methods on uniform parallelogram grids in homogeneous media. Computational Geosciences 2005; 9:61-72.
31. Edwards MG. Symmetric positive definite general tensor discretization operator on unstructured and flow based grids. The 8th European Conference on Mathematics of Oil Recovery, Freiberg, Germany, 2002.