Face-centered and volume-centered discrete analogs of the exterior differential equations governing porous medium flow I: Theory

Transport in Porous Media

Volumn 60, Issue 1, 2005, Pages 109-122

  Zijl, Wouter ^a  

^a TNO   (Netherlands)

Author keywords

Discrete analogs; Dual operator; Exterior differential forms; Face centered finite element methods; Volume centered methods

Indexed keywords

ANISOTROPY; APPROXIMATION THEORY; CONTINUUM MECHANICS; DECOMPOSITION; DIFFERENTIAL EQUATIONS; FINITE ELEMENT METHOD; FINITE VOLUME METHOD; FLOW OF FLUIDS; MATRIX ALGEBRA;

CONTINUUM EQUATIONS; DOMAIN DECOMPOSITION TECHNIQUE; FACE-CENETERED APPROXIMATION; VOLUME-CENTRED APPROXIMATION;

POROUS MATERIALS;

FLOW MODELING; POROUS MEDIUM;

EID: 15044348206     PISSN: 01693913     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11242-004-4044-0     Document Type: Article

References (36)

1. I. Aavatsmark 2002 An introduction to multipoint flux approximations for quadrilateral grids Comput. Geosci. 6 405-432
2. M. P. Anderson W.W. Woessner 2002 Applied Groundwater Modeling: Simulation of Flow and Advective Transport. Academic Press San Diego
3. K. Aziz A. Settari 1979 Petroleum Reservoir Simulation Applied Science Publishers, Ltd. London
4. M. Bai D. Elsworth 2000 Coupled Processes in Subsurface Deformation, Flow and Transport ASCE Press Reston, VA
5. J. Bear 1998 Dynamics of Fluids in Porous Media Dover Publications New York
6. A. Bossavit 1998 Computational Electromagnetism: Variational Formulations, Complementarity, Edge Elements Academic Press San Diego
7. A. Bossavit 1999a Computational electromagnetism and geometry: Building a finite-dimensional "Maxwell's house" J. Jpn. Soc. Appl. Electromagn. Mech. 7 150-159
8. A. Bossavit 1999b Computational electromagnetism and geometry: Network constitutive laws J. Jpn. Soc. Appl. Electromagn. Mech. 7 294-301
9. A. Bossavit 1999c Computational electromagnetism and geometry: convergence J. Jpn. Soc. Appl. Electromagn. Mech. 7 401-408
10. A. Bossavit 2000a Computational electromagnetism and geometry: From degrees of freedom to fields J. Jpn. Soc. Appl. Electromagn. Mech. 8 102-109
11. A. Bossavit 2000b Computational electromagnetism and geometry: The "Galerkin Hodge" J. Jpn. Soc. Appl. Electromagn. Mech. 8 203-209
12. A. Bossavit 2000c Computational electromagnetism and geometry: Some questions and answers J. Jpn. Soc. Appl. Electromagn. Mech. 8 372-377
13. A. Bossavit 2001 Generalized finite differences in computational electromagnetism Progress Electromag. Res 32 45-64
14. A. Bossavit 2003 Mixed-hybrid methods in magnetostatics: Complementarity in one stroke IEEE Trans. Magn 39 3 1099-1102
15. Bossavit, A.: 2004, Private communication.
16. W. L. Burke 1997 Applied Differential Geometry Cambridge University Press Cambridge
17. G. Chavent J. Jaffré 1986 Mathematical Models and Finite Elements for Reservoir Simulation North Holland Amsterdam
18. T. Frankel 2001 The Geometry of Physics Cambridge University Press Cambridge
19. E. Isaacson H. B. Keller 1967 Analysis of Numerical Methods Wiley New York
20. E. F. Kaasschieter A. J. M. Huijben 1992 Mixed-hybrid finite elements and streamline computations for the potential flow problem Numer. Meth. PDEs 8 221-266
21. J.-L. Mallet 2002 Geomodeling Oxford University Press New York
22. C. W. Misner K. S. Thorne J. A. Wheeler 1973 Gravitation Freeman and Co. San Francisco
23. R. W. Parsons 1996 Permeability of idealized fractured rock J. Soc. Petrol. Eng 6 126-136
24. Post, E. J.: 1984, The metric dependence of four-dimensional formulations of electromagnetism, J. Math. Phys. 25(3).
25. R. D. Richtmyer K. W Morton 1967 Difference Methods for Initial Value Problems Interscience Publishers New York
26. G. Strang G. J. Fix 1973 An Analysis of the Finite Element Method Prentice-Hall Englewood Cliffs
27. T. Tarhasaari L. Kettunen 1999 Some realizations of a discrete Hodge operator: A reinterpretation of finite element techniques IEEE Trans. on Magn 35 3 1494-1497
28. A. Trykozko W. Zijl A. Bossavit 2001 Nodal and mixed finite elements for the numerical homogenization of 3D permeability Comput. Geosci 5 61-84
29. J. S. Welij van 1985 Calculations of eddy currents in terms of hexahedra IEEE Trans. Magn 21 6 2239-2241
30. S. H. Weintraub 1997 Differential Forms: A Complement to Vector Calculus Academic Press San Diego
31. S. Whitaker 1999 The Method of Volume Averaging Kluwer Academic Publishers Dordrecht
32. O. C. Zienkewicz R. L. Taylor 1989 The Finite Element Method, Volume 1: Basic Formulation and Linear Problems McGraw-Hill Book Company London
33. W. Zijl 2004 A direct method for the identification of the permeability field based on flux assimilation by a discrete analog of Darcy's law Transport in Porous Media 56 1 87-112
34. Zijl, W.: 2005, Face-centered and volume-centered discrete analogs of the exterior differential equations governing porous medium flow II: Examples, Transport in Porous Media, accepted.
35. W. Zijl M. Nawalany 2004 The edge-based face element method for three-dimensional stream function and flux calculations in porous media flow Transport in Porous Media 55 3 361-382
36. Zijl, W. and Trykozko, A.: 2001, Numerical homogenization of the absolute permeability tensor around wells, SPEJ 399-408