Numerical error in groundwater flow and solute transport simulation

Water Resources Research

Volumn 39, Issue 6, 2003, Pages

  Woods, Juliette A ^a,b   Teubner, Michael D ^a   Simmons, Craig T ^c   Narayan, Kumar A ^d  

^a UNIVERSITY OF ADELAIDE   (Australia)

^b UNIVERSITY OF TEXAS AT AUSTIN   (United States)

^c FLINDERS UNIVERSITY   (Australia)

^d CSIRO   (Australia)

Author keywords

Benchmarking; Contaminant transport; Elder problem; Salinity; Variable density

Indexed keywords

COMPUTER SIMULATION; CONVERGENCE OF NUMERICAL METHODS; NUMERICAL ANALYSIS; PROBLEM SOLVING;

ELDER PROBLEM; NUMERICAL ERRORS;

GROUNDWATER FLOW;

ERROR; GROUNDWATER; POLLUTANT TRANSPORT; POROUS MEDIUM; SALINITY; SOLUTE TRANSPORT;

ERROR ANALYSIS; GROUNDWATER FLOW; POLLUTANT TRANSPORT; SALINITY; SOLUTE TRANSPORT;

SAMBUCUS NIGRA CANADENSIS;

EID: 1542441753     PISSN: 00431397     EISSN: None     Source Type: Journal    
DOI: 10.1029/2001WR000586     Document Type: Article

References (46)

1. Ackerer, P., A. Younes, and R. Mosé, Modeling variable density flow and solute transport in porous medium: 1. Numerical model and verification, Transp. Porous Media, 35, 345-373, 1999.
2. Bear, J., Dynamics of Fluids in Porous Media, Elsevier Sci., New York, 1972.
3. Bear, J., A. H.-D. Cheng, S. Sorek, D. Ouazar, and I. Herrera, Seawater Intrusion in Coastal Aquifers: Concepts, Methods, and Practices, Theory Appl. Transp. Porous Media, vol. 15, Kluwer Acad. Press, Norwell, Mass., 1999.
4. Becker, E. B., G. F. Carey, and J. Tinsley, Finite Elements, vol. 6, Fluid Mechanics, Prentice-Hall, Old Tappan, N. J., 1986.
5. Benson, D. A., A. E. Carey, and S. W. Wheatcraft, Numerical advective flux in highly variable velocity fields exemplified by saltwater intrusion, J. Contam. Hydrol., 34, 207-233, 1998.
6. Boufadel, M., M. Suidan, and A. Venosa, Numerical modeling of water flow below dry salt lakes: Effect of capillarity and viscosity, J. Hydrol., 221, 55-74, 1999.
7. Croucher, A., and M. O'Sullivan, The Henry problem for saltwater intrusion, Water Resour. Res., 31, 1809-1814, 1995.
8. Diersch, H.-J., Interactive, graphics-based finite-element simulation system FEFLOW for modeling groundwater flow, contaminant mass and heat transport processes, FEFLOW user's manual version 4.5., WASY Ltd., Berlin, 1996.
9. Elder, J., Transient convection in a porous medium, J. Fluid Mech., 27, 609-623, 1967.
10. Ferziger, J. H., and M. Perić, Computational Methods for Fluid Dynamics, Springer-Verlag, New York, 1999.
11. Frolkovič, P., and H. D. Schepper, Numerical modelling of convection dominated transport coupled with density driven flow in porous media, Adv. Water Resour., 24, 63-72, 2000.
12. Gresho, P. M., and R. Sani, Incompressible Flow and the Finite Element Method: Advection-Diffusion and Isothermal Laminar Flow, John Wiley, 1998.
13. Henry, H., Effects of dispersion on salt encroachment in coastal aquifers, U. S. Geol. Surv. Water Supply Pap., 1613-C, 1964.
14. Hindmarsh, A., P. Gresho, and D. Griffiths, The stability of explicit Euler time-integration for certain finite difference approximations of the multi-dimensional advection-diffusion equation, Int. J. Numer. Methods Fluids, 4, 853-897, 1984.
15. Holzbecher, E., Modeling Density-Driven Flow in Porous Media: Principles, Numerics, Software, Springer-Verlag, New York, 1998.
16. Javandel, I., C. Doughty, and C. Tsang, Groundwater Transport: Handbook of Mathematical Models, Water Resour. Monogr., vol. 10, AGU, Washington, D. C., 1984.
17. Koch, M., and G. Zhang, Numerical simulation of the effects of variable density in a contaminant plume, Ground Water, 30, 731-742, 1992.
18. Kolditz, O., R. Ratke, H.-J. Diersch, and W. Zielke, Coupled groundwater flow and transport 1. Verification of variable density flow and transport models, Adv. Water Resour., 21, 27-46, 1997.
19. Konikow, L., W. Sanford, and P. Campbell, Constant-concentration boundary conditions: Lessons from the HYDROCOIN variable-density groundwater benchmark problem, Water Resour. Res., 33, 2253-2261, 1997.
20. Lal, A. W., Numerical errors in groundwater and overland flow models, Water Resour. Res., 36, 1237-1247, 2000.
21. Leonard, B., and B. J. Noye, Second and third order two-level implicit FDMs for unsteady one-dimensional convection-diffusion equation, in Computational Techniques and Applications: CTAC-89, edited by H. Hogarth and B. J. Noye, pp. 311-317, Taylor and Francis, Philadelphia, Pa., 1990.
22. May, R., and B. J. Noye, The numerical solution of ordinary differential equations: Initial value problems, in Computational Techniques for Differential Equations, edited by B. J. Noye, pp. 1 -94, North-Holland, New York, 1984.
23. Narayan, K. A., and D. Armstrong, Simulation of groundwater interception at Lake Ranfurly, Victoria, incorporating variable density flow and solute transport, J. Hydrol., 165, 161-184, 1995.
24. Nield, D. A., and A. Bejan, Convection in Porous Media, Springer-Verlag, New York, 1992.
25. Noye, B. J., Finite difference techniques, in Numerical Simulation of Fluid Motion, edited by B. J. Noye, pp. 1-112, North-Holland, New York, 1978.
26. Noye, B. J., A new third-order finite-difference method for transient one-dimensional advection-diffusion, Comput. Appl. Numer. Methods, 6, 279-288, 1990.
27. Noye, B. J., A compact unconditionally-stable finite-difference method for transient one-dimensional advection-diffusion, Comm. App. Numer. Meth. Eng., 7, 501-512, 1991.
28. Noye, B., Explicit finite difference methods for variable velocity advection in the presence of a source, Comput. Fluids, 29, 385-399, 2000.
29. Noye, B. J., and K. Hayman, Accurate finite difference methods for solving the advection-diffusion equation, in Computational Techniques and Applications: CTAC-85, edited by B. J. Noye and R. May, pp. 137-157, North-Holland, New York, 1985.
30. Noye, B. J., and K. Hayman, Explicit two-level finite-difference methods for the two-dimensional diffusion equation, Int. J. Comput. Math., 42, 223-236, 1992.
31. Noye, B. J., and A. von Trojan, An explicit finite-difference method for variable velocity advection, in Computational Techniques and Applications: CTAC-97, edited by B. J. Noye, M. D. Teubner, and A. W. Gill, pp. 513-520, World Sci., River Edge, N. J., 1998.
32. Oldenburg, C. M., and K. Pruess, Dispersive transport dynamics in a strongly coupled groundwater-brine flow system, Water Resour. Res., 31, 289-302, 1995.
33. Oltean, C., and M. A. Buès, Coupled groundwater flow and transport in porous media: A conservative or non-conservative form?, Transp. Porous Media, 44, 219-246, 2001.
34. Prasad, A., Density-driven groundwater flow and solute transport in heterogeneous porous media, M.S. thesis, Flinders Univ. of South Australia, Adelaide, 2000.
35. Prickett, T. A., T. G. Naymik, and C. G. Lonnquist, A "random-walk" solute transport model for selected groundwater quality evaluation, technical report, Ill. Dep. of Energy and Nat. Resour., Champaign, 1981.
36. Schincariol, R. A., F. W. Schwartz, and C. A. Mendoza, On the generation of instabilities in variable density flow, Water Resour. Res., 30, 913-927, 1994.
37. Simmons, C. T., Density-induced groundwater flow and solute transport beneath saline disposal basins, Ph.D. thesis, Flinders Univ. of South Australia, Adelaide, 1997.
38. Simmons, C. T., K. A. Narayan, and R. A. Wooding, On a test case for density-dependent groundwater flow and solute transport models: The salt lake problem, Water Resour. Res., 35, 3607-3620, 1999.
39. van Duijn, C., and R. Schotting, Brine transport in porous media: On the use of Von Mises and similarity transformations, Modell. Anal. Simulation Rep. MAS-R9724, Cent. voor Wiskundeen Inf., Amsterdam, 1997.
40. Voss, C. I., SUTRA: A finite-element simulation model for saturated-unsaturated fluid-density-dependent ground-water flow with energy transport or chemically-reactive single-species solute transport, U.S. Geol. Surv. Water Resour. Invest. Rep., 84-4369, 1984.
41. Voss, C. I., and W. R. Souza, Variable density flow and solute transport simulation of regional aquifers containing a narrow freshwater-saltwater transition zone, Water Resour. Res., 23, 1851-1866, 1987.
42. Warming, R., and B. Hyett, The modified equation approach to the stability and accuracy analysis of finite difference methods, J. Comput. Phys., 14, 159-179, 1974.
43. Watson, S. J., and D. A. Barry, Numerical analysis of stable brine displacements for evaluation of density-dependent flow theory, Phys Chem. Earth, Part B, Hydrol. Oceans Atmos., 26, 325-331, 2001.
44. Woods, J., C. T. Simmons, and K. A. Narayan, Verification of black box groundwater models, in Proceedings of the Third Biennial Engineering Mathematics and Applications Conference: EMAC98, edited by E. Tuck and J. Stott, pp. 523-526, Inst. of Eng., Barton, Australia, 1998.
45. Woods, J., M. D. Teubner, C. T. Simmons, and K. A. Narayan, Numerical inaccuracy in groundwater modelling: diagnosis and pathology, in Water 99 Joint Congress: 25th Hydrology and Water Resources Symposium, 2nd International Conference on Water Resources and Environment Research: Handbook and Proceedings, pp. 532-538, Inst. of Eng. Aust., Brisbane, 1999.
46. Zoppou, C., and S. Roberts, Behaviour of finite difference schemes for advection diffusion equations, Tech. Rep. Math. Res. Rep. MRR 062-96, Aust. Natl. Univ., Canberra, 1996.