On iterative techniques for computing flow in large two-dimensional discrete fracture networks

Journal of Computational and Applied Mathematics

Volumn 236, Issue 18, 2012, Pages 4712-4724

  Parashar, Rishi ^a   Reeves, Donald M ^a  

^a DESERT RESEARCH INSTITUTE   (United States)

Author keywords

DFN methodology; Discrete fracture networks; Krylov subspace iterative methods; Sparse matrices

Indexed keywords

BOUNDED DOMAIN; COEFFICIENT MATRIX; COMPARATIVE STUDIES; COMPUTATIONAL EFFORT; COMPUTING FLOWS; CONVERGENCE BEHAVIORS; DFN METHODOLOGY; DISCRETE FRACTURE NETWORK; FRACTURE LENGTH; FRACTURE NETWORK; FRACTURE ORIENTATIONS; FRACTURE PARAMETER; HYDRAULIC HEADS; INTERSECTION POINTS; ITERATIVE TECHNIQUE; KRYLOV SUBSPACE ITERATIVE METHODS; LARGE SYSTEM; ORDERS OF MAGNITUDE; RATE OF CONVERGENCE; REGULAR STRUCTURE; SALIENT FEATURES; SPARSE MATRICES; SPARSITY PATTERNS; STATISTICAL PARAMETERS; SYSTEM OF LINEAR EQUATIONS; TRANSMISSIVITY;

APPROXIMATION THEORY; ITERATIVE METHODS;

FRACTURE;

EID: 84863983078     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cam.2012.02.038     Document Type: Conference Paper

References (37)

1. E. Bonnet, O. Bour, N.E. Odling, P. Davy, I. Main, P. Cowie, and B. Berkowitz Scaling of fracture systems in geologic media Rev. Geophys. 39 3 2001 347 383 10.1029/1999RG000074
2. G. Kosakowski, B. Berkowitz, and H. Scher Analysis of field observations of tracer transport in a fractured till J. Contam. Hydrol. 47 2 2000 29 51
3. R. Mettier, G. Kosakowski, and O. Kolditz Influence of small-scale heterogeneities on contaminant transport in fractured crystalline rock Ground Water 44 5 2006 687 696 10.1111/j.1745-6584.2006.00236.x
4. J.-R. de Dreuzy, P. Davy, and O. Bour Hydraulic properties of two-dimensional random fracture networks following power law distributions of length and aperture Water Resour. Res. 38 12 2002 1276 10.1029/2001WR001009
5. S.D. Priest Discontinuity Analysis of Rock Engineering first ed. 1993 Chapman and Hall London
6. M. Sahimi Flow and Transport in Porous Media and Fractured Rocks first ed. 1995 VCH Weinheim
7. Y.W. Tsang Usage of equivalent apertures for rock fractures as derived from hydraulic and tracer tests Water Resour. Res. 28 5 1992 1451 1455
8. W. Dershowitz, S. Follin, T. Eiben, J. Anderson, SR 97-Alternative models project: discrete fracture network modeling for performance assessment of aberg, SKB Report R-99-43, Swedish Nuclear Fuel and Waste Management Co., Stockholm, Sweden, 1999.
9. C. Klimczak, R.A. Schultz, R. Parashar, and D.R. Reeves Cubic law with aperture-length correlation: implications for network scale fluid flow Hydrogeol. J. 18 2010 851 862 10.1007/s10040-009-0572-6
10. N.E. Odling Network properties of a two-dimensional natural fracture pattern Pure Appl. Geophys. 138 1 1992 95 114
11. N.E. Odling Scaling and connectivity of joint systems in sandstones from western Norway J. Struct. Geol. 19 10 1997 1251 1271
12. P. Davy On the frequency-length distribution of the San Andreas fault system J. Geophys. Res. 98 1993 12141 12151
13. R. Marrett Aggregate properties of fracture populations J. Struct. Geol. 18 2-3 1996 169 178
14. C.E. Renshaw Connectivity of joint networks with power law length distributions Water Resour. Res. 35 9 1999 2661 2670
15. A. Baghbanan, and L. Jing Hydraulic properties of fractured rock masses with correlated fracture length and aperture Int. J. Rock Mech. 44 2007 704 719
16. F.E. Botros, A.E. Hassan, D.M. Reeves, and G. Pohll On mapping fracture networks onto continuum Water Resour. Res. 44 2008 W08435 10.1029/2007WR006092
17. D.J. Best, and N.I. Fisher Efficient simulation of the von Mises distribution Appl. Stat. 28 2 1979 152 157
18. A. Niemi, K. Konito, A. Kuusela-Lahtinen, and A. Poteri Hydraulic characterization and upscaling of fracture networks based on multiple scale well test data Water Resour. Res. 36 12 2000 3481 3497
19. J. Ohman, and A. Niemi Upscaling of fracture hydraulics by means of an oriented correlated stochastic continuum model Water Resour. Res. 39 10 2003 1277 10.1029/2002WR001776
20. T.P. Wellman, A.M. Shapiro, and M.C. Hill Effects of simplifying fracture network representation on inert chemical migration in fracture-controlled aquifers Water Resour. Res. 45 2009 W01416 10.1029/2008WR007025
21. M. Karmi-Fard, B. Gong, and L.J. Durlofsky Generation of coarse-scale continuum flow models from detailed fracture characterizations Water Resour. Res. 42 2006 W10423 10.1029/2006WR005015
22. S. Painter, and V. Cvetkovic Upscaling discrete fracture network simulations: an alternative to continuum transport models Water Resour. Res. 41 2005 W02002 10.1029/2004WR003682
23. D.M. Reeves, D.A. Benson, and M.M. Meerschaert Transport of conservative solutes in simulated fracture networks: 1. Synthetic data generation Water Resour. Res. 44 2008 W05404 10.1029/2007WR006069
24. D. Roubinet, J.-R. de Dreuzy, and P. Davy Connectivity-consistent mapping method for 2-D discrete fracture networks Water Resour. Res. 46 2010 W07532 10.1029/2009WR008302
25. T.A. Davis Algorithm 832: UMFPACK V4.3-An unsymmetric-pattern multifrontal method ACM Trans. Math. Software 30 2 2004 196 199 10.1145/992200.992206
26. R.D. Falgout, J.E. Jones, and U.M. Yang Pursuing scalability for hypre's conceptual interfaces ACM Trans. Math. Software 31 3 2005 326 350 10.1145/1089014.1089018
27. J.-R. de Dreuzy, and J. Erhel Efficient algorithms for the determination of the connected fracture network and the solution to the steady-state flow equation in fracture networks Comput. Geosci. 29 1 2003 107 111 10.1016/S0098-3004(02)00081-X
28. Y. Saad Iterative methods for sparse linear systems second ed. 2003 SIAM Philadelphia
29. J.D.F. Cosgrove, J.C. Diaz, and A. Griewank Approximate inverse preconditioning for sparse linear systems Int. J. Comput. Math. 44 1992 91
30. M. Gorte, and T. Huckle Parallel preconditioning with sparse approximate inverses SIAM J. Sci. Comput. 18 1997 838
31. M. Benzi Preconditioning techniques for large linear systems: a survey J. Comput. Phys. 182 2002 418 477
32. B.N. Datta Numerical Linear Algebra and Applications 2010 SIAM Philadelphia, PA
33. A. Greenbaum Iterative Methods for Solving Linear Systems 1997 SIAM Philadelphia
34. V. Simoncini, and D.B. Szyld Recent computational developments in Krylov subspace methods for linear systems Numer. Linear Algebra Appl. 14 2007 1 59
35. C.C. Paige, and M.A. Saunders Solution of sparse indefinite systems of linear equations SIAM J. Numer. Anal. 12 1975 617 629
36. C.T. Kelley Iterative Methods for Linear and Nonlinear Equations 1995 SIAM Philadelphia, PA
37. N.M. Nachtigal, S.C. Reddy, and L.N. Trefethen How fast are nonsymmetric matrix Iterations? SIAM J. Matrix Anal. Appl. 13 1992 778 795