Convergence study of a family of flux-continuous, finite volume schemes for the general tensor pressure equation

International Journal for Numerical Methods in Fluids

Volumn 51, Issue 9-10, 2006, Pages 1177-1203

  Pal, Mayur ^a   Edwards, Michael G ^a   Lamb, Anthony R ^a  

^a SWANSEA UNIVERSITY   (United Kingdom)

Author keywords

Convergence; Discontinuous coefficients; Flux continuous; Quadrature and pressure equation

Indexed keywords

CONVERGENCE OF NUMERICAL METHODS; FINITE VOLUME METHOD; MATHEMATICAL MODELS; TENSORS;

GENERAL TENSOR PRESSURE EQUATION; QUADRATURE PARAMETERIZATION; SUBSURFACE FLOW MODELLING;

COMPUTATIONAL FLUID DYNAMICS;

COMPUTATIONAL FLUID DYNAMICS; CONVERGENCE OF NUMERICAL METHODS; FINITE VOLUME METHOD; MATHEMATICAL MODELS; TENSORS;

EID: 33746174150     PISSN: 02712091     EISSN: 10970363     Source Type: Journal    
DOI: 10.1002/fld.1211     Document Type: Article

References (25)

1. Edwards MG, Rogers CF. Finite volume discretization with imposed flux continuity for the general tensor pressure equation. Computers and Geosciences 1998; 2:259-290.
2. Edwards MG. Unstructured, control-volume distributed, full-tensor finite volume schemes with flow based grids. Computers and Geosciences 2002; 6:433-452.
3. Edwards MG. Simulation with a full-tensor coefficient velocity field recovered from a diagonal tensor solution. SPE Journal 2000; 5:387-393.
4. Edwards MG. M-matrix flux splitting for general full tensor discretization operators on structured and unstructured grids. Journal of Computational Physics 2000; 160:1-28.
5. Edwards MG. Superconvergent renormalization and tensor approximation. Paper Presented at the 5th ECMOR, Leoben, Austria, 3-6 September 1996.
6. Edwards MG. Symmetric Positive Definite General Tensor Discretization Operator on Unstructured and Flow Based Grids. 8th European Conference on Mathematics of Oil Recovery, Freiberg, Germany, 3-6 September 2002.
7. Edwards MG. Control-volume distributed sub-cell flux schemes for unstructured and flow based grids. SPE Reservoir Simulation Symposium, Houston, Texas, U.S.A., 3-5 February 2003.
8. Lamb AR. Convergence study of a family of nine-point flux continuous, finite volume schemes for the general tensor pressure equation. MSc Thesis, University of Wales, Swansea, 2004.
9. Aavatsmark I, Barkve T, Bøe Ø, Mannseth T. Discretization on non-orthogonal, quadrilateral grids for inhomogeneous, anisotropic media. Journal of Computational Physics 1996; 127:2-14.
10. Aavatsmark I, Barkve T, Bøe Ø, Mannseth T. Discretization on unstructured grids for inhomogeneous, anisotropic media. Part I: Derivation of the methods. SIAM Journal on Scientific Computing 1998; 19:1700-1716.
11. Aavatsmark I, Barkve T, Bøe Ø, Mannseth T. Discretization on unstructured grids for inhomogeneous, anisotropic media. Part II: Discussion and numerical results. SIAM Journal on Scientific Computing 1998; 19:1717-1736.
12. Aavatsmark I. Introduction to multipoint flux approximation for quadrilateral grids. Computers and Geosciences 2002; 6:405-432.
13. Eigestad GT, Aadland T, Asvatsmark I, Klausen RA, Nordbotten JM. Recent advances in MPFA methods. 9th European Conference on the Mathematics of Oil Recovery-Cannes, France, 30 August-2 September 2004.
14. Eigestad GT, Klausen RA. On the convergence of the multi-point flux approximation O-method: numerical experiments for discontinuous permeability. Numerical Methods for Partial Differential Equations 2005; 21(6):1079-1098.
15. Lee SH, Jenny P, Tchelepi HA. A finite-volume method with hexahedral multiblock grids for modeling flow in porous media. Computers and Geosciences 2002; 6:353-379.
16. Verma S. Flexible grids for reservoir simulation. Ph. D Thesis, Stanford University, June 1996.
17. Russell TF. Relationships among some conservative discretization methods. In Numerical Treatment of Multiphase Flows in Porous Media, Chen Z et al. (eds), Lecture Notes in Physics, vol. 552. Springer: Heidelberg, 2000; 267-282.
18. Arbogast T, Wheeler MF, Yotov I. Mixed finite elements for elliptic problems with tensor coefficients as cell centered finite differences. SIAM Journal on Numerical Analysis 1997; 34(2):828-852.
19. Russell TF, Wheeler WF. Finite element and finite difference methods for continuous flows in porous media. In Mathematics of Reservoir Simulation (Chapter 2), Ewing RE (ed.), Frontiers in Applied Mathematics. SIAM: Philadelphia, PA, 1983; 35-106.
20. Durlofsky LJ. A triangle based mixed finite element finite volume technique for modeling two phase flow through porous media. Journal of Computational Physics 1993; 252-266.
21. Riviere B, Wheeler MF, Banas K. Discontinuous Galerkin method applied to a single phase flow in porous media. Computers and Geosciences 2000; 49:337-341.
22. Edwards MG. Cross flow tenser and finite volume approximation with by deferred Correction. Computer Methods in Applied Mechanics and Engineering 1998; 151:143-161.
23. Aziz K, Settari A. Petroleum Reservoir Simulation. Applied Science Publishers: London, 1979.
24. Edwards MG, Pal M. Symmetric positive definite pressure equation discretization and a family of sub-cell flux-continuous CVD schemes on cell centred quadrilateral grids. IJNMF, submitted.
25. Riviere B. Discontinuous Galerkin method for solving the miscible displacement problem in porous media. Ph.D. Thesis, The University of Texas at Austin, 2000.