Transport in Porous Media

, Volume 43, Issue 1, pp 65–86 | Cite as

On the Reliability of Numerical Solutions of Brine Transport in Groundwater: Analysis of Infiltration from a Salt Lake

  • Annamaria Mazzia
  • Luca Bergamaschi
  • Mario Putti
Article

Abstract

The density dependent flow and transport problem in groundwater is solved numerically by means of a mixed finite element scheme for the flow equation and a mixed finite element-finite volume time-splitting based technique for the transport equation. The proposed approach, spatially second order accurate, is used to address the issue of grid convergence by solving on successively refined grids the salt lake problem, a physically unstable downward convection with formation of fingers. Numerical results indicate that achievement of grid convergence is problematic due to ill-conditioning arising from the strong nonlinearities of the mathematical model.

mixed finite elements finite volumes operator splitting brine transport 

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References

  1. Bear, J.: 1979, Hydraulics of Groundwater, New York: McGraw-Hill.Google Scholar
  2. Bergamaschi, L. and M. Putti: 1999, Mixed finite elements and Newton-like linearization for the solution of Richard's equation, Int. J. Numer. Methods Engng 45(8), 1025-1046.Google Scholar
  3. Diersch, H.-J. G. and Kolditz, O.: 1998, Coupled groundwater flow and transport: 2. Thermohaline and 3D convection systems, Adv. Water Resour. 21, 401-425.Google Scholar
  4. van Duijn, C. J., Peletier, L. A. and Schotting, R. J.: 1996, Brine transport in porous media: Selfsimilar solutions, Report AM-R9616, CWI.Google Scholar
  5. Durlofsky, L. J.: 1993, A triangle based mixed finite element-finite volume technique for modeling two phase flow through porous media, J. Comp. Phys. 105, 252-266.Google Scholar
  6. Durlofsky, L. J., Engquist, B. and Osher, S.: 1992, Triangle based adaptive stencils for the solution of hyperbolic conservation laws, J. Comp. Phys. 98, 64-73.Google Scholar
  7. Gambolati, G., Putti, M. and Paniconi, C.: 1999, Three-dimensional model of coupled densitydependent flow and miscible salt transport in groundwater, In: J. Bear, A. H.-D. Cheng, S. Sorek, D. Ouazar and I. Herrera (eds), Seawater Intrusion in Coastal Aquifers; Concepts, Methods and Practices, Dordrecth, The Netherlands: Kluwer Academic Publ., Chapt. 10, pp. 315-362.Google Scholar
  8. Hassanizadeh, S. M.: 1986, Derivation of basic equations of mass transport in porous media, Part 2.Generalized darcy's and Fick's laws. Adv. Water Resour. 9, 207-222.Google Scholar
  9. Hassanizadeh, S. M. and Leijnse, T.: 1988, On the modeling of brine transport in porous media, Water Resour. Res. 24(3), 321-330.Google Scholar
  10. Hassanizadeh, S. M. and Leijnse, T.: 1995, A non-linear theory of high-concentration-gradient dispersion in porous media, Adv. Water Resour. 18(4), 203-215.Google Scholar
  11. Kolditz, O., Ratke, R., Diersch, H. J. G. and Zielke, W.: 1998, Coupled groundwater flow and transport: 1. Verification of variable density flow and transport models, Adv. Water Resour. 21(1), 27-46.Google Scholar
  12. Liu, X.-D.: 1993, A maximum principle satisfying modification of triangle based adaptive stencils for the solution of scalar hyperbolic conservation laws, SIAM J. Num. Anal. 30(3), 701-716.Google Scholar
  13. Mazzia, A.: 1999, Mixed finite elements and finite volumes for the solution of density dependent flow and transport of radioactive contaminants in porous media, Ph.D. thesis, UniversitÀ di Padova.Google Scholar
  14. Mazzia, A., Bergamaschi, L. and Putti, M.: 2000a, A time-splitting technique for advectiondispersion equation in groundwater, J. Comp. Phys. 157(1), 181-198.Google Scholar
  15. Mazzia, A., Bergamaschi, L. and Putti, M.: 2000b, Triangular finite volume-mixed finite element discretization for the advection-diffusion equation, In: M. Griebel, S. Margenov and P. Yalamov (eds), Large Scale Scientific Computations of Engineering and Environmental Sciences, pp. 371-378.Google Scholar
  16. Putti, M. and Paniconi, C.: 1995a, Finite element modeling of saltwater intrusion problems with an application to an Italian coastal aquifer, In: G. Gambolati and G. Verri (eds): Advanced Methods for Groundwater Pollution Control, Wien, New York, pp. 65-84.Google Scholar
  17. Putti, M. and Paniconi, C.: 1995b, Picard and Newton linearization for the coupled model of saltwater intrusion in aquifers, Adv. Water Resour. 18(3), 159-170.Google Scholar
  18. Putti, M., Yeh, W. W.-G. and Mulder, W. A.: 1990, A triangular finite volume approach with high resolution upwind terms for the solution of groundwater transport equations, Water Resour. Res. 26(12), 2865-2880.Google Scholar
  19. Schotting, R. J., Moser, H. and Hassanizadeh, S. M.: 1999, High-concentration-gradient dispersion in porous media: Experiments, analysis and approximations, Adv. Water Resour. 22(7), 665-680.Google Scholar
  20. Simmons, C. T., Narayan, K. A. and Wooding, R. A.: 1999, On a test case for density-dependent groundwater flow and solute transport model: The salt lake problem, Water Resour. Res. 35(12), 3607-3620.Google Scholar
  21. Straka, J. M., Wilhelmson, R. B., Wicker, L. J., Anderson, J. R. and Droegemeier, K. K.: 1993, Numerical solutions of a non-linear density current: A Benchmark' solution and comparison, Int. J. Num. Meth. Fluids 17, 1-22.Google Scholar
  22. Sweby, P. K.: 1985, High Resolution TVD schemes using flux limiters, Lectures Appl. Math. 22, 289-309.Google Scholar
  23. Voss, C. I. and Souza, W. R.: 1987, Variable density flow and solute transport simulation of regional aquifers containing a narrow freshwater-saltwater transition zone, Water Resour. Res. 23(10), 1851-1866.Google Scholar
  24. Wooding, R. A., Tyler, S.W. and White, I.: 1997a, Convection in groundwater below an evaporating salt lake, 1, Onset of instability, Water Resour. Res. 33(6), 1199-1217.Google Scholar
  25. Wooding, R. A., Tyler, S.W., White, I. and Anderson, P. A.: 1997b, Convection in groundwater below an evaporating salt lake, 2, Evolution of fingers or plumes, Water Resour. Res. 33(6), 1219-1228.Google Scholar

Copyright information

© Kluwer Academic Publishers 2001

Authors and Affiliations

  • Annamaria Mazzia
    • 1
  • Luca Bergamaschi
    • 1
  • Mario Putti
    • 1
  1. 1.Department of Mathematical Methods and Models for Scientific ApplicationsUniversity of PaduaItaly

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