Coupled groundwater flow and transport: 2. Thermohaline and 3D convection systems

Advances in Water Resources

Volumn 21, Issue 5, 1998, Pages 401-425

  Diersch, H J G ^a   Kolditz, O ^b  

^a WASY Inst Water Rsrc Plan S   (Germany)

^b LEIBNIZ UNIVERSITY HANNOVER   (Germany)

Author keywords

Double diffusive convection; Finite element method; Porous media; Thermohaline convection; Three dimensional B nard convection; Variable density flow

Indexed keywords

APPROXIMATION THEORY; BUOYANCY; COMPUTER SIMULATION; COMPUTER SOFTWARE; DENSITY OF LIQUIDS; FINITE ELEMENT METHOD; HEAT CONDUCTION; POROUS MATERIALS; PROBLEM SOLVING;

BENARD CONVECTION; BUOSSINESQ APPROXIMATION; DISCRETIZATION TECHNIQUES; ELDER PROBLEM; THERMOHALINE ELDER SYSTEM;

GROUNDWATER FLOW;

CONVECTION; FLOW; GROUNDWATER; POROUS MEDIUM;

CONVECTION; FINITE ELEMENT METHOD; FINITE-ELEMENT METHOD; GROUNDWATER FLOW; POROUS MEDIUM; THERMOHALINE;

EID: 0032053255     PISSN: 03091708     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0309-1708(97)00003-1     Document Type: Article

References (79)

1. Ackerer, P., Mosé, R., Siegel, P. & Chavent, G., Reply to contribution of reference 11. Water Resour. Res., 32 (1996) 1911-1913.
2. Angisara, D. & Scrinivasan, J., Natural convection flows due to the combined buoyancy of heat and mass diffusion in a thermally stratified medium. J. Heat Transfer, 111 (1989) 657-663.
3. Axelsson, O., Iterative Solution Methods, Cambridge University Press, 1994.
4. Beauwens, R., Modified incomplete factorization strategies. In: Preconditioned Conjugate Gradient Methods, Lecture Notes in Mathematics, 1457, ed. O. Axelsson & L. Kolotilina, Springer, New York, 1990, 1-16.
5. Behie, A. & Vinsome, P. K. W., Block iterative methods for fully implicit reservoir simulation. SPEJ Soc. Pet. Eng. J., (October 1981) 658-668.
6. Beukema, K. J. & Bruin, S., Three-dimensional natural convection in a confined porous medium with internal heat generation. Int. J. Heat Mass Transfer, 26 (1983) 451-458.
7. Bixler, N. E., An improved time integrator for finite element analysis. Communications in Applied Numerical Methods, 5 (1989) 69-78.
8. Brandt, A. & Fernando, H. J. S. (Eds), Double-diffusive Convection, Geophysical Monograph Vol. 94, American Geophysical Union, Washington, D.C., 1995.
9. Caltagirone, J. P., Meyer, G. & Mojtabi, A., Structurations thermoconvectives tridimensionelles dans une couche poreuse horizontale. J. Mécanique, 20 (1981) 219-232.
10. Chan, Y. T. & Banerjee, S., Analysis of transient three-dimensional natural convection in porous media. ASME J. Heat Transfer, 103 (1981) 242-248.
11. Cordes, Ch. & Kinzelbach, W., Comment on contribution of reference 51. Water Resour. Res., 32 (1996) 1905-1909.
12. Croucher, A. E. & O'Sullivan, M. J., The Henry problem for saltwater intrusion. Water Resour. Res., 31 (1995) 1809-1814.
13. Diersch, H.-J., Primitive variables finite element solutions of free convection flows in porous media. Zeitschr. Angew. Math. Mech. (ZAMM), 61 (1981) 325-337.
14. Diersch, H.-J., Study of free convective flows in porous media and effects of mechanical dispersion using finite element methods. Gerlands Beiträge zur Geophysik, 90 (1981) 489-506.
15. Diersch, H.-J., On finite element upwinding and its numerical performance in simulating coupled convective transport processes. Zeitschr. Angew. Math. Mech. (ZAMM), 63 (1983) 479-488.
16. Diersch, H.-J., Prochnow, D. & Thiele, M., Finite element analysis of dispersion-affected saltwater upconing below a pumping well. Appl. Math. Modelling, 8 (1984) 305-312.
17. Diersch, H.-J., Finite element modelling of recirculating density-driven saltwater intrusion processes in groundwater. Adv. Water Resour., 11 (1988) 25-43.
18. Diersch, H.-J. G., Computational aspects in developing an interactive 3D groundwater transport simulator using FEM and GIS. Groundwater Quality Management (Proceedings of the GQM 93 Conference held at Tallinn, September 1993). IAHS Publ. no. 220, 1994, 313-326.
19. Diersch, H.-J., Albert, H., Schreyer, J. & Richter, J., Three-dimensional modeling of flow and contaminant transport processes arising in flooding the Königstein uranium pit. In: Proc. Intern. Conf. Uranium-Mining and Hydrogeology, eds. B. Merkel et al. Verlag Sven von Loga, Köln, 1995, 121-130.
20. Diersch, H.-J. G., Interactive, graphics-based finite-element simulation system FEFLOW for modeling groundwater flow, contaminant mass and heat transport processes, User's Manual Version 4.5, April 1996, WASY Institute for Water Resources Planning and Systems Research Ltd, Berlin.
21. Diersch, H.-J. G. & Kolditz, O., On finite-element analysis of spatio-temporal buoyancy-driven convection processes in porous media. Calibration and Reliability in Groundwater Modelling (Proceedings of the ModelCARE 96 Conference held at Golden, Colorado, September 1996), IAHS Publ. no. 237, 1996, 407-415.
22. Diersch, H.-J. G., FEFLOW - Physical basis of modeling, WASY Ltd., Berlin, November 1996, 82p.
23. Elder, J. W., Transient convection in a porous medium. J. Fluid Mech., 27, Part 3 (1967) 609-623.
24. Evans, G. E. & Nunn, J. A., Free thermohaline convection in sediments surrounding a salt column. J. Geophys. Res., 94 (1989) 12413-12422.
25. Fan, Y. & Kahawita, R., A numerical study of variable density flow and mixing in porous media. Water Resour. Res., 30 (1994) 2707-2716.
26. Frind, E. O., Simulation of long-term transient density-dependent transport in groundwater. Adv. Water Resour., 5 (1982) 73-88.
27. Galeati, G., Gambolati, G. & Neuman, S. P., Coupled and partially coupled Eulerian-Lagrangian model of freshwater-seawater mixing. Water Resour. Res., 28 (1992) 149-165.
28. Gartling, D. K. & Hickox, C. E., Numerical study of the application of the Boussinesq approximation for a fluid-saturated porous medium. Int. J. Numer. Methods Fluids, 5 (1985) 995-1013.
29. Gresho, P. M., Lee, R. L., Chan, S. T. & Leone Jr., J. M., A new finite element for Boussinesq fluids. Pre-print UCRL-82842, Lawrence Livermore Laboratory, University of California, 1979, 12p.
30. Gresho, P. M., Lee, R. L. & Sani, R. L., On the time-dependent solution of the incompressible Navier-Stokes equations in two and three dimensions. Preprint UCRL-83282, Lawrence Livermore Laboratory, University of California, 1979, 53p.
31. Hassanizadeh, M. S. & Leijnse, A., On the modeling of brine transport in porous media. Water Resour. Res., 24 (1988) 321-330.
32. Herbert, A. W., Jackson, C. P. & Lever, D. A., Coupled groundwater flow and solute transport with fluid density strongly dependent upon concentration. Water Resour. Res., 24 (1988) 1781-1795.
33. Hestenes, M. R. & Stiefel, E., Methods of conjugate gradients for solving linear systems. J. Res. Natl. Bur. Stand. Sect. B, 49 (1952) 409-436.
34. Holst, P. H. & Aziz, K., Transient three-dimensional natural convection in confined porous media. Int. J. Heat Mass Transfer., 15 (1972) 73-90.
35. Horne, R. N. & O'Sullivan, M. J., Oscillatory convection in a porous medium heated from below. J. Fluid Mech., 66 (1974) 339-352.
36. Horne, R. N., Three-dimensional natural convection in a confined porous medium heated from below. J. Fluid Mech., 92 (1979) Part 4, 751-766.
37. Horne, R. N. & Caltagirone, J. P., On the evaluation of thermal disturbances during natural convection in a porous medium. J. Fluid Mech., 100 (1980) 385-395.
38. Huyakorn, P. S. & Taylor, C., Finite element models for coupled groundwater and convective dispersion. Proc. 1st Int. Conf. Finite Elements in Water Resources, ed. Gray, W. G. et al. Princeton University, July 1976, Pentech Press, London, 1977, 1.131-1.151.
39. Huyakorn, P. S., Anderson, P. F., Mercer, J. W. & White, Jr., H. O., Saltwater intrusion in aquifers: development and testing of a three-dimensional finite element model. Water Resour. Res., 23 (1987) 293-312.
40. Kakinuma, T., Kishi, Y. & Inouchi, K., The behaviour of groundwater with dispersion in coastal aquifers. J. Hydrology, 98 (1988) 225-248.
41. Knaber, P. & Frolkovic, P., Consistent velocity approximation for finite volume or element discretization of density driven flow in porous media. Proc. XI. Int. Conf. Computational Methods in Water Resources held in Cancun, México, July 1996, Comp. Mech. Publ., Vol. 1, ed. Aldama et al. Southampton, 1996, 93-100.
42. Kolditz, O., Benchmarks for numerical groundwater simulations, In: FEFLOW User's Manual, Chapter 5, H.-J. G. Diersch, WASY Ltd, Berlin, 1996.
43. Kolditz, O., Ratke, R., Diersch, H.-J. G. & Zielke, W., Coupled groundwater flow and transport: 1, Verification of variable-density flow and transport models. Adv. Water Resour., 21 (1998) 27-46.
44. Konikow, L. F., Campbell, P. J. & Sanford, W. E., Modelling brine transport in a porous medium: a re-evaluation of the HYDROCOIN Level 1, Case 5 problem. Calibration and Reliability in Groundwater Modelling (Proceedings of the ModelCARE 96 Conference held at Golden, Colorado, September 1996), IAHS Publ. no. 237, 1996, 363-372.
45. Lee, R. L., Gresho, P. M. & Sani, R. L., Numerical smoothing techniques applied to some finite element solutions of the Navier-Stokes equations. Proc. 1st Int. Conf. Finite Elements in Water Resources, ed. Gray, W. G. et al. Princeton University, July 1976, Pentech Press, London, 1977, 4.127-4.145.
46. Leijnse, A., Three-dimensional modeling of coupled flow and transport in porous media. Dissertation, University of Notre Dame, Indiana (USA), 1992.
47. Letniowski, F. W., An overview of preconditioned iterative methods for sparse matrix equations. Research Report CS-89-26, Faculty of Mathematics, University of Waterloo, Canada, 1989, 32p.
48. Lever, D. A. & Jackson, C. P., On the equations for the flow of concentrated salt solution through a porous medium. U.K. DOE Report No. DOE/RW/85.100, 1985.
49. Meijerink, J. A. & Van der Vorst, H. A., Guidelines for the usage of incomplete decomposition in solving sets of linear systems as they occur in practical problems. J. Comput. Physics., 44 (1981) 134-155.
50. Mercer, J. W. & Pinder, G. F., Finite element analysis of hydrothermal systems. Finite Element Methods in Flow Problems (Proc. 1st Symp., Swansea, 1974), ed. Oden, J. T. et al. University of Alabama Press, 1974, 401-414.
51. Mosé, R., Siegel, P., Ackerer, P. & Chavent, G., Application of the mixed hybrid finite element approximation in a groundwater flow model: Luxury or necessity? Water Resour. Res., 30 (1994) 3001-3012.
52. Murray, B. T. & Chen, C. F., Double-diffusive convection on a porous medium. J. Fluid Mech., 201 (1989) 147-166.
53. Nield, D. A., Onset of thermohaline convection in a porous medium. Water Resour. Res., 11 (1968) 553-560.
54. Nield, D. A. & Bejan, A., Convection in Porous Media, Springer Verlag, Berlin, 1992.
55. Oldenburg, C. M. & Pruess, K., Dispersive transport dynamics in a strongly coupled groundwater-brine system. Water Resour. Res., 31 (1995) 289-302.
56. Perrochet, P., Personal communication. EPFL Lausanne, GEOLEP Laboratoire de géologie, Lausanne (Switzerland), 1996.
57. Pinder, G. F. & Cooper, H. H., A numerical technique for calculating the transient position of the saltwater front. Water Resour. Res., 6 (1970) 875-832.
58. Riley, D. S. & Winters, K. H., Time-periodic convection in porous media: the evolution of Hopf bifurcations with aspect ratio. J. Fluid Mech., 223 (1991) 457-474.
59. Rubin, H., Onset of thermohaline convection in a cavernous aquifer. Water Resour. Res., 12 (1976) 141-147.
60. Rubin, H. & Roth, C., Thermohaline convection in flowing groundwater. Adv. Water Resour., 6 (1983) 146-156.
61. Saad, Y. & Schultz, M. H., GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM J. Sci. Stat. Comp., 7 (1986) 856-869.
62. Sauter, F. J. & Beusen, A. H. W., Streamline calculations using continuous and discontinuous velocity fields and several time integration methods. Groundwater Quality Management (Proc. of the GQM 93 Conf. held at Tallinn, Sept. 1993). IAHS Publ. no. 220, 1994, 347-355.
63. Schincariol, R. A., Schwartz, F. W. & Mendoza, C. A., On the generation of instabilities in variable density flow. Water Resour. Res., 30 (1994) 913-927.
64. Schubert, G. & Straus, J. M., Three-dimensional and multicellular steady and unsteady convection in fluid-saturated porous media at high Rayleigh numbers. J. Fluid Mech., 94 (1979) Part 1, 25-38.
65. Schubert, G. & Straus, J. M., Transitions in time-dependent thermal convection in fluid-saturated porous media. J. Fluid Mech., 121 (1982) 301-303.
66. Segol, G., Pinder, G. F. & Gray, W. G., A Galerkin finite element technique for calculating the transient position of the saltwater front. Water Resour. Res., 11 (1975) 343-347.
67. Shen, C. Y., The evolution of the double-diffusive instabilities: salt fingers. Phys. Fluids, A1 (1989) 5.
68. Sonneveld, P., CGS, a fast Lanczos-type solver for nonsymmetric linear systems. SIAM J. Sci. Stat. Comp., 10 (1989) 36-52.
69. Straus, J. M. & Schubert, G., Three-dimensional convection in a cubic box of fluid-saturated porous material. J. Fluid Mech., 91 (1979) Part 1, 155-165.
70. Straus, J. M. & Schubert, G., Modes of finite-amplitude three-dimensional convection in rectangular boxes of fluid-saturated material;. J. Fluid Mech., 103 (1981) 23-32.
71. Tong, C. H., A comparative study of preconditioned Lanczos methods for nonsymmetric linear systems. Sandia Report SAND91-8240, Sandia National Lab., Albuquerque, Sept. 1992, 118p.
72. Trevisan, O. V. and Bejan, A., Natural convection with combined heat and mass transfer buoyancy effects in a porous medium. Int. J. Heat Mass Transfer, 28 (1985) 1597-1611.
73. Tyvand, P. A., Thermohaline instability in anisotropic porous media. Water Resour. Res., 16 (1980) 325-330.
74. Van der Vorst, H. A., Bi-CGSTAB: A fast and smoothly convergent variant of BiCG for the solution of nonsymmetric linear systems. SIAM J. Sci. Stat. Comp., 13 (1992) 631-644.
75. Voss, C. I. & Souza, W. R., Variable density flow and solute transport simulation of regional aquifers containing a narrow freshwater-saltwater transition zone. Water Resour. Res., 26 (1987) 2097-2106.
76. Xue, Y., Xie, C., Wu, J., Liu, P., Wang, J. & Jiang, Q. A three-dimensional miscible transport model for seawater intrusion in China. Water Resour. Res., 31 (1995) 903-912.
77. Yeh, G. T., On the computation of Darcian velocity and mass balance in the finite element modeling of groundwater flow. Water Resour. Res., 17 (1981) 1529-1534.
78. Zebib, A. & Kassoy, D. R., Three-dimensional natural convection motion in a confined medium. Phys. Fluids, 21 (1978) 1-3.
79. Zhang, H. & Schwartz, F. W., Multispecies contaminant plumes in variable density flow systems. Water Resour. Res., 31 (1995) 837-847.