Discontinuous Galerkin methods for advective transport in single-continuum models of fractured media

Advances in Water Resources

Volumn 32, Issue 4, 2009, Pages 493-506

  Eikemo, Birgitte ^a   Lie, Knut Andreas ^a,b   Eigestad, Geir Terje ^a   Dahle, Helge K ^a  

^a UNIVERSITY OF BERGEN   (Norway)

^b SINTEF ICT   (Norway)

Author keywords

Directed asyclic graphs; Discontinuous Galerkin discretization; Fractured media; Linear solvers; Time of flight; Transport in porous media; Unstructured grids

Indexed keywords

COMPUTATIONAL FLUID DYNAMICS; CONTINUUM MECHANICS; FLOW SIMULATION; FRACTURE; LINEAR SYSTEMS; NEGATIVE IONS; POROUS MATERIALS; ROCKS;

DIRECTED ASYCLIC GRAPHS; DISCONTINUOUS GALERKIN DISCRETIZATION; FRACTURED MEDIA; LINEAR SOLVERS; TIME-OF-FLIGHT; TRANSPORT IN POROUS MEDIA; UNSTRUCTURED GRIDS;

GALERKIN METHODS;

ADVECTION; COMPUTER SIMULATION; FRACTURE ZONE; FRACTURED MEDIUM; GALERKIN METHOD; MATRIX; NUMERICAL MODEL; PERMEABILITY; POROSITY; SHEAR ZONE;

EID: 62349087086     PISSN: 03091708     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.advwatres.2008.12.010     Document Type: Article

References (18)

1. Dietrich P., Helmig R., Sauter M., Hötzl H., Köngeter J., and Teutsch G. Flow and transport in fractured porous media (2005), Springer
2. Reichenberger V, Helmig R, Jakobs H, Bastian P, Niessner J. Complex gas-water processes in discrete fracture-matrix systems: upscaling, mass-conservative discretization and efficient multilevel solution, Institut für Wasserbau, Universität Stuttgart; 2004.
3. In: Council N.R. (Ed). Rock fractures and fluid flow (1996), National Academy Press
4. Neunhäuserer L, Hemminger A, Helmig R. Influence of fracture-matrix-interaction on flow and transport processes and the resulting effective parameters in fractured porous systems. In: Hydraulic engineering for sustainable water resources management at the turn of the millennium, XXVIII IAHR congress, Graz, Austria; 1999.
5. Datta-Gupta A., and King M.J. Streamline simulation: theory and practice. SPE textbook series vol. 11 (2007), Society of Petroleum Engineers
6. Eikemo B, Berre I, Dahle HK, Lie K-A, Natvig JR, A discontinuous Galerkin method for computing time-of-flight in discrete-fracture models. In: Binning PJ, Engesgaard PK, Dahle HK, Pinder GF, Gray WG, editors. Proceedings of the XVI international conference on computational methods in water resources, Copenhagen, Denmark. ; 2006.
7. Natvig J.R., and Lie K.-A. Fast computation of multiphase flow in porous media by implicit discontinuous Galerkin schemes with optimal ordering of elements. J Comput Phys 227 24 (2008) 10108-10124 doi:10.1016/j.jcp.2008.08.02
8. Natvig JR, Lie K-A. On efficient implicit upwind schemes. In: ECMOR XI, 11th European conference on the mathematics of oil recovery, EAGE. ; 2008.
9. Hoteit H, Firoozabadi A. Multicomponent fluid flow by discontinuous Galerkin and mixed methods in unfractured and fractured media. Water Resour Res 41 (W11412), doi:10.1029/2005WR004339.
10. Qian J., Zhang Y.-T., and Zhao H.-K. Fast sweeping methods for eikonal equations on triangular meshes. SIAM J Numer Anal 45 1 (2007) 83-107 [electronic]
11. Li F., Shu C.-W., Zhang Y.-T., and Zhao H. A second order discontinuous Galerkin fast sweeping method for eikonal equations. J Comput Phys 227 17 (2008) 8191-8208 doi:10.1016/j.jcp.2008.05.018
12. Zhang Y.-T., Zhao H.-K., and Qian J. High order fast sweeping methods for static Hamilton-Jacobi equations. J Sci Comput 29 1 (2006) 25-56
13. Kao C.-Y., Osher S., and Qian J. Legendre-transform-based fast sweeping methods for static Hamilton-Jacobi equations on triangulated meshes. J Comput Phys 227 24 (2008) 10209-10225 10.1016/j.jcp.2008.08.016
14. Natvig J.R., Lie K.-A., Eikemo B., and Berre I. An efficient discontinuous Galerkin method for advective transport in porous media. Adv Water Resour 30 12 (2007) 2424-2438
15. Natvig JR, Lie K-A, Eikemo B. Fast solvers for flow in porous media based on discontinuous Galerkin methods and optimal reordering. In: Binning PJ, Engesgaard PK, Dahle HK, Pinder GF, Gray WG, editors. Proceedings of the XVI international conference on computational methods in water resources, Copenhagen, Denmark. ; 2006.
16. Klausen R., and Winther R. Robust convergence of multi point flux approximation on rough grids. Numer Math 104 (2006) 317-337 10.1007/s00211-006-0023-4
17. Aavatsmark I., Eigestad G., Klausen R., Wheeler M., and Yotov I. Convergence of a symmetric MPFA method on quadrilateral grids. Comput Geosci 11 (2007) 333-345 10.1007/s10596-007-9056-8
18. Christie MA, Blunt MJ. Tenth SPE comparative solution project: a comparison of upscaling techniques, SPE Reserv Eval Eng 2001;4(4):308-17. .