Effects of first-order approximations on head and specific discharge covariances in high-contrast log conductivity

Water Resources Research

Volumn 32, Issue 5, 1996, Pages 1197-1207

  Van Lent, Thomas ^a   Kitanidis, Peter K ^b  

^a South Dakota State University   (United States)

^b Stanford University   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

GROUNDWATER; POROUS MEDIA-FLOW THROUGH; STOCHASTIC METHODS;

DISCHARGE; FLUID FLOW; GROUNDWATER; HYDRAULIC HEAD; HYDROGEOLOGY; PERTURBATION APPROXIMATION; POROUS MEDIUM;

EID: 0029656857     PISSN: 00431397     EISSN: None     Source Type: Journal    
DOI: 10.1029/96WR00196     Document Type: Article

References (41)

1. Ababou, R., L. W. Gelhar, and D. McLaughlin, Three dimensional flow in random porous media. Tech. Rep. 318, Ralph M. Parsons Lab., Mass. Inst. of Technol., Cambridge, Mass., 1988.
2. Ababou, R., D. McLaughlin, and A. Tompson, Numerical simulation of three-dimensional saturated flow in randomly heterogeneous porous media, Trans. Porous Media, 4, 549-565, 1989
3. Bakr, A. A., L. W. Gelhar, A. L Gutjahr, and J. R. MacMillan. Stochastic analysis of spatial variability in subsurface flows, 1, Comparison of one- and three-dimensional flows, Water Resour. Res., 14(2), 263-271, 1978.
4. Beckie, R., A. Aldama, and E. Wood, The universal structure of the groundwater flow equations. Water Resour. Res., 30(5), 1407-1419, 1994.
5. Bellin, A., P. Salandin, and A. Rinaldo, Simulation of dispersion in heterogeneous porous formations: Statistics, first-order theories, convergence of computations, Water Resour. Res , 28(9), 2211-2277, 1992.
6. Bellin, A., Y. Rubin, and A. Rinaldo, Eulcrian-Lagrangian approach for modeling flow and transport in heterogeneous geological formations, Water Resour. Res., 30(11), 2913-2924, 1994.
7. Chin, D., and T. Wang, An investigation of the validity of first-order stochastic dispersion theories in isotropic porous media, Water Resour. Res., 28(6), 1531-1542, 1992.
8. Dagan, G., Stochastic modeling of groundwater flow by unconditional and conditional properties, 1, Conditional simulation and the direct problem, Water Resour. Res., 18(4), 813-833, 1982a.
9. Dagan, G., Analysis of flow through heterogeneous random aquifers, 2, Unsteady flow in confined aquifers, Water Resour. Res., 18(5), 1571-1585, 1982b.
10. Dagan, G., A note on higher-order corrections of the head covariances in steady aquifer flow, Water Resour. Res., 21(4), 573-578, 1985.
11. Dagan, G., Theory of solute transport by groundwater, Annu. Rev. Fluid Mech., 19, 183-215, 1987.
12. Dagan, G., Time-dependent macrodispersion for solute transport in anisotropic heterogeneous aquifers, Water Resour. Res., 24(9), 1491-1500, 1988.
13. Dagan, G., Flow and Transport in Porous Formations, 465 pp., Springer-Verlag, New York, 1989.
14. Dagan, G., and S. Neuman, Nonasymptotic behavior of a common Eulerian approximation for transport in random velocity fields, Water Resour. Res., 27(12), 3249-3256, 1991.
15. Dettinger, M., and J. L., Wilson, First order analysis of uncertainty in numerical models of groundwater flow, 1, Mathematical development, Water Resour. Res., 17(1), 149-161, 1981.
16. Dikow, E., Stochastic analysis of groundwater flow in a bounded domain by spectral methods, Trans. Porous Media, 3, 173-184, 1988.
17. Dykaar, B., and P. K. Kitanidis, Determination of effective hydraulic conductivity for heterogeneous porous media using a numerical spectral approach, 1, Method, Water Resour. Res., 28(4), 1155-1166, 1992.
18. Fiorotto. V., and A. Giorgini, Stochastic analysis of groundwater flow by spectral analysis, in Proceedings of the Sixth IAHR International Symposium on Stochastic Hydrology, edited by J. Kuo and G. Lin, pp. 517-524, Water Resour. Publ., Fort Collins, Colo., 1992.
19. Gelhar, L. W., Effects of hydraulic conductivity variations on groundwater flow, in Hydraulic Problems Solved by Stochastic Methods, edited by P. Hjorth, L. Jönsson, and P. Larson, pp. 409-431, Water Resour. Publ., Fort Collins, Colo., 1977.
20. Gelhar, L. W., Stochastic Subsurface Hydrology, 390 pp., Prentice-Hall, Englewood Cliffs, N. J., 1993.
21. Gelhar, L. W., and C. L. Axness, Three-dimensional stochastic analysis of macrodispersion in aquifers, Water Resour. Res., 19(1), 161-180, 1983.
22. Graham, W., and D. McLaughlin, Stochastic analysis of nonstationary solute transport, 1, Unconditional moments. Water Resour. Res., 25(2), 215-232, 1989.
23. Gutjahr, A., Fast Fourier transform for random field generation, technical report project report, contract 4-RS of Los Alamos National Laboratory, N. M. Inst. of Min. and Technol., Socorro, N. M., 1989.
24. Gutjahr, A., L. W. Gelhar, A. A Bakr, and J. R. MacMillan, Stochastic analysis of spatial variability in subsurface flows, 2 , Estimation and application, Water Resour. Res., 14(5), 953-959, 1978.
25. Jones, L., Some results comparing Monte Carlo simulations and first order Taylor series approximations for steady groundwater flow, Stochastic Hydrol. Hydraul., 3(3), 179-190, 1989.
26. Li, S.-H., and D. McLaughlin, A nonstationary spectral method for solving stochastic groundwater problems: Unconditional analysis, Water Resour. Res., 27(7), 1589-1605, 1991.
27. Li, S.-H., and D. McLaughlin, Using the nonstationary spectral method to analyze flow through heterogeneous trending media, Water Resour. Res., 31(3), 541-552, 1995.
28. Mizell, S. A., A. L. Gutjahr, and L W, Gelhar, Stochastic analysis of spatial variability in two-dimensional steady groundwater flow assuming stationary and nonstationary fields. Water Resour. Res., 18(4), 1053-1067, 1982.
29. Neuman, S. P., C. L. Winter, and C. M. Newman, Stochastic theory of field-scale Fickian dispersion in anisotropic porous media, Water Resour. Res., 23(3), 453-466, 1987.
30. Priestley, M. B., Spectral Analysis and Time Series, 890 pp., Academic, San Diego, Calif., 1981.
31. Robin, M., A. Gutjahr, E. Sudicky, and J. Wilson, Cross-correlated random field generation with the direct Fourier transform method, Water Resour. Res., 29(7), 2385-2397, 1993.
32. Rubin, Y., Stochastic modeling of macrodispersion in heterogeneous porous media, Water Resour. Res., 26(1), 133-141, 1990.
33. Rubin, Y., and G. Dagan, Stochastic analysis of boundaries effects on head spatial variability in heterogeneous aquifers, 1, Constant head boundary. Water Resour. Res., 24(10), 1689-1697, 1988.
34. Rubin, Y., and G. Dagan, Stochastic analysis of boundaries effects on head spatial variability in heterogeneous aquifers, 2, Impervious boundary, Water Resour. Res., 25(4), 707-712, 1989.
35. Sagar, B., Galerkin finite element procedure for analyzing flow through random media, Water Resour. Res., 14(6), 1035-1044, 1978.
36. Smith, L., and R. A Freeze, Stochastic analysis of steady state groundwater flow in a bounded domain, 1, One-dimensional simulations, Water Resour. Res., 15(3), 521-528, 1979a.
37. Smith, L., and R. A. Freeze, Stochastic analysis of steady state groundwater flow in a bounded domain, 2, Two-dimensional simulations, Water Resour. Res., 15(6), 1543-1559, 1979b.
38. Smith, L., and F. W. Schwartz, Mass transport, 1, A stochastic analysis of macroscopic dispersion, Waler Resour. Res., 16(2), 303-313, 1980.
39. Smith, L., and F. W. Schwartz, Mass transport, 2, Analysis of uncertainty in prediction, Water Resour. Res., 17(2), 352-369, 1981.
40. Van Lent, T., Numerical spectral methods applied to flow in highly heterogeneous aquifers, Ph.D. thesis, Stanford Univ., Stanford, Calif., 1992.
41. Van Lent, T., and P. K. Kitanidis, A numerical spectral approach for the derivation of piezometric head covariance functions, Water Resour. Res., 25(11), 2287-2298, 1989.