A hybrid finite-element finite-volume method with embedded discontinuities for solute transport in heterogeneous media

Vadose Zone Journal

Volumn 10, Issue 1, 2011, Pages 299-312

  Nick, H M ^a,b   Matthai S K ^c  

^a IMPERIAL COLLEGE LONDON   (United Kingdom)

^b UTRECHT UNIVERSITY   (Netherlands)

^c UNIVERSITY OF LEOBEN   (Austria)

Author keywords

[No Author keywords available]

Indexed keywords

COARSER MESHES; CONTINUOUS METHODS; CONTINUUM MODEL; DEPENDENT VARIABLES; DISCRETIZATIONS; EMBEDDED DISCONTINUITY; FINITE-ELEMENT; FINITE-VOLUME; FIRST-ORDER DEPENDENCE; HETEROGENEOUS MEDIA; HETEROGENEOUS POROUS MEDIA; HIGHER ORDER; INTERFACE NODE; MATERIAL INTERFACES; MESH REFINEMENT; NODAL CONCENTRATIONS; POTENTIAL DISCONTINUITY; TRANSPORT MODELS;

CONTINUUM MECHANICS; FINITE VOLUME METHOD; INTERFACES (MATERIALS); MULTIPHASE FLOW; NUMERICAL METHODS; POROUS MATERIALS; SOLUTE TRANSPORT;

FINITE ELEMENT METHOD;

FINITE ELEMENT METHOD; FINITE VOLUME METHOD; FLOW MODELING; HETEROGENEOUS MEDIUM; MULTIPHASE FLOW; NUMERICAL MODEL; POROUS MEDIUM; SATURATION; SOLUTE TRANSPORT;

EID: 79960191068     PISSN: None     EISSN: 15391663     Source Type: Journal    
DOI: 10.2136/vzj2010.0015     Document Type: Article

References (41)

1. Abriola, L, and G. Pinder. 1985. A multiphase approach to the modeling of porous media contamination by organic compounds: 1. Equation developments. Water Resour. Res. 21:11-18.
2. Bassi, F., and S. Rebay. 1996. High-order accurate discontinuous finite element solution of the 2D Euler equations. J. Comput. Phys. 138:251-285.
3. Bear, J. 1988. Dynamics of fluids in porous media. Dover Publ., New York.
4. Berkowitz, B., A. Corn's, I. Dror, and H. Scher. 2009. Laboratory experiments on dispersive transport across interfaces: The role of flow direction. Water Resour. Res. 45:W02201, doi:10.1029/2008WR007342.
5. Carrera, J., X. Sanchez-Vila, I. Benet, A. Medina, G. Galarza, and J. Guimera. 1998. On matrix diffusion: Formulations, solution methods and qualitative effects. Hydrogeol. J. 6:178-190.
6. Carslaw, H., and J. Jaeger. 1963. Operational methods in applied mathematics. Dover Publ., New York.
7. Chen, Z., and R. Ewing (ed.). 2001. Fluid flow and transport in porous media: Mathematical and numerical treatment. Proc. AMS-IMS-SIAM Joint Summer Res. Conf, South Hadley, MA. 17-21 June 2001. Am. Math. Soc, Providence, RI.
8. Chen, Z., H. Steeb, and S. Diebels. 2008. A space-time discontinuous Galer-kin method applied to single-phase flow in porous media. Comput. Geos-ci. 12:525-539.
9. Cockburn, B. 2003. Discontinuous Galerkin methods. Z. Angew. Math. Mech. 83:731-754.
10. Cordes, C, and W. Kinzelbach. 1992. Continuous groundwater velocity fields and path lines in linear, bilinear, and trilinear finite elements. Water Resour. Res. 28:2903-2911.
11. Dagan, G. 1989. Flow and transport in porous formations. Springer-Verlag, Berlin.
12. Dawe, R., and C. Grattoni. 2008. Experimental displacement patterns in a 2 × 2 quadrant block with permeability and wettability heterogeneities: Problems for numerical modelling. Transp. Porous Media 71:5-22.
13. Dawe, R., M. Wheat, and M. Bidner. 1992. Experimental investigation of capillary pressure effects on immiscible displacement in lensed and layered porous media. Transp. Porous Media 9:83-101.
14. Epshteyn, Y, and B. Riviere. 2007. Fully implicit discontinuous finite element methods for two-phase flow. Appl. Numer. Math. 57:383-401.
15. Geiger, S., S. Roberts, S. Matthäi, C. Zoppou, and A. Burri. 2004. Combining finite element and finite volume methods for efficient multiphase flow simulations in highly heterogeneous and structurally complex geologic media. Geofluids 4:284-299.
16. Gerke, H. 2006. Preferential flow descriptions for structured soils. J. Plant Nutr. Soil Sci. 169:382-400.
17. Gerritsen, M., and J. Durlofsky. 2005. Modeling fluid flow in oil reservoirs. Annu. Rev. Fluid Mech. 37:211-238.
18. Gray, W.G., and C.T Miller. 2005. Thermodynamically constrained averaging theory approach for modeling flow and transport phenomena in porous medium systems: 1. Motivation and overview. Adv. Water Resour. 28:161-180.
19. Harten, A. 1983. High resolution schemes for hyperbolic conservation laws. Comput. Phys. 59:357-393.
20. Hassanizadeh, S., and W. Gray. 1989. Boundary and interface conditions in porous media. Water Resour. Res. 25:1705-1715.
21. Helmig, R. 1997. Multiphase flow and transport processes in the subsurface: A contribution to the modeling of hydrosystems. Springer-Verlag, Berlin.
22. Hoteit, H., and A. Firoozabadi. 2008. Numerical modeling of two-phase flow in heterogeneous permeable media with different capillarity pressures. Adv. Water Resour. 31:56-73.
23. Huber, R., and R. Helmig. 2000. Node-centered finite volume discretizations for the numerical simulation of multiphase flow in heterogeneous porous media. Comput. Geosci. 4:141-164.
24. Landman, A.J. 2005. Analysis of physical mechanisms underlying density-dependent transport in porous media. Ph.D. diss. Utrecht Univ., Utrecht, the Netherlands.
25. Leij, F., and M.Th. van Genuchten. 1994. Approximate analytical solutions for solute transport in two-layer porous media. Transp. Porous Media 18:65-85.
26. LeVeque, R. 2002. Finite volume methods for hyperbolic problems. Cambridge Univ. Press, Cambridge, UK.
27. Manzini, G., and A. Russo. 2008. A finite volume method for advection-diffusion problems in convection-dominated regimes. Comput. Methods Appl. Mech. Eng. 197:1242-1261.
28. Marseguerra, M., and A. Zoia. 2006. Normal and anomalous transport across an interface: Monte Carlo and analytical approach. Ann. Nucl. Energy 33:1396-1407.
29. Matthäi, S.K., S. Geiger, and S.G. Roberts. 2004. The Complex Systems Platform CSP5.0: User's guide. ETH, Zurich, Switzerland.
30. Matthäi, S.K., S. Geiger, S.G. Roberts, A. Paluszny, M. Belayneh, A. Burri, A. Mezentsev, H. Lu, D. Coumou, T. Driesner, and C.A. Heinrich. 2007a. Numerical simulation of multi-phase fluid flow in structurally complex reservoirs. p. 405-429. In S.J. Jolley et al. (ed.) Structurally complex reservoirs. Spec. Publ. 292. Geol. Soc. London, London.
31. Matthäi, S., A. Mezentsev, and M. Belayneh. 2007b. Finite element node-centered finite volume two-phase flow experiments with fractured rock represented by unstructured hybrid element meshes. SPE Reservoir Eval. Eng. 10:740-756.
32. Matthäi, S.K., and H. Nick. 2009. Upscaling two phase flow in naturally fractured reservoirs. AAPG Bull. 93:1621-1632.
33. Matthäi, S.K., H. Nick, C. Pain, and I. Neuweiler. 2009. Simulation of solute transport through fractured rock: A higher-order accurate finite-element finite-volume method permitting large time steps. Transp. Porous Media 83:289-318.
34. Nick, H., R. Schotting, M. Gutierrez-Neri, and K. Johannsen. 2009. Modeling transverse dispersion and variable density flow in porous media. Transp. Porous Media 78:11-35.
35. Paluszny, A., S. Matthäi, and M. Hohmeyer. 2007. Hybrid finite element finite volume discretization of complex geologic structures and a new simulation workflow demonstrated on fractured rocks. Geofluids 7:186-208.
36. Reichenberger, V., H. Jakobs, P. Bastian, and R. Helmig. 2006. A mixed-dimensional finite volume method for two-phase flow in fractured porous media. Adv. Water Resour. 29:1020-1036.
37. Scheidegger, A. 1961. General theory of dispersion in porous media. J. Geo-phys. Res. 66:3273-3278.
38. Segerlind, L. 1984. Applied fi nite element analysis. 2nd ed. John Wiley & Sons, New York.
39. Shewchuk, J. 1996. Triangle: Engineering a 2D quality mesh generator and Delaunay triangulator. Lect. Notes Comput. Sci. 1148:203-222.
40. Stuben, K. 1999. Algebraic multigrid (AMG): An introduction with applications. Forschungszentrum Informationstechnik GmbH, Sankt Augustin, Germany.
41. Sweby, J. 1984. High resolution schemes using flux limiter for hyperbolic conservation laws. SIAM Numer. Anal. 995-1011.