Modeling the large-scale dynamics of saturated groundwater flow using spatial-filtering theory: 1. Theoretical development

Water Resources Research

Volumn 32, Issue 5, 1996, Pages 1269-1280

  Beckie, Roger ^a   Aldama, Alvaro A ^b   Wood, Eric F ^c  

^a UNIVERSITY OF BRITISH COLUMBIA   (Canada)

^b INSTITUTO MEXICANO DE TECNOLOGÍA DEL AGUA   (Mexico)

^c Princeton University   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

DYNAMICS; FLUID FLOW; GROUNDWATER; LARGE EDDY SIMULATION; POROUS MEDIUM;

DYNAMICS; GROUNDWATER; LARGE EDDY; SATURATED; SIMULATION;

EID: 0029656849     PISSN: 00431397     EISSN: None     Source Type: Journal    
DOI: 10.1029/96WR00276     Document Type: Review

References (37)

1. Aldama, A. A., Filtering Techniques for Turbulent Flow Simulation, Lecture Notes in Engineering, vol. 56, Springer-Verlag, New York, 1990.
2. Aldama, A. A., A subgrid scale theory for physical processes with quadratic nonlinearities: An a priori test for Burgers' flow, in Computational Methods in Water Resources IX, edited by T. Russell, R. Ewing, C. Brebbia, W. Gray, and G. Pinder, pp. 91-98, Elsevier. New York, 1992.
3. Aldama, A. A., and D. R F. Harleman, The approximation of non-linearities in the filtered Navier-Stokes equations, Adv. Water Resour., 14(1), 15-30, 1991.
4. Baveye, P., and G. Sposito, The operational significance of the continuum hypothesis in the theory of water movement through soils and aquifers, Water Resour. Res., 20(5), 521-530, 1984.
5. Beckie, R., Measurement scale, network sampling scale, and groundwater model parameters, Water Resour. Res., 32, 65-76, 1996.
6. Beckie, R., A. A. Aldama, and E. F. Wood, The universal structure of the groundwater flow equations, Water Resour. Res., 30(5), 1407-1419, 1994.
7. Beckie, R., A. A. Aldama, and E. F. Wood, Modeling the large-scale dynamics of a saturated groundwater flow using spatial filtering theory, 2, Numerical evaluation, Water Resour. Res., this issue.
8. Beven, K., Changing ideas in hydrology - the case for physically-based models, J. Hydrol., 105, 157-172, 1989.
9. Bracewell, R., The Fourier Transform and Its Applications, Electrical and Electronic Engineering Series, McGraw-Hill, New York, 1965.
10. Champeney, D. C., A Handbook of Fourier Theorems, Cambridge Univ. Press, New York, 1987.
11. Clark, R. A., J. H. Ferziger, and W. C. Reynolds, Evaluation of subgrid-scale turbulence models using a fully simulated turbulent flow, Rep. TF-9, Dep. Mech. of Eng., Stanford Univ., Nov. 1977.
12. Cushman, J. H., On unifying the concepts of scale, instrumentation, and stochastics in the development of multiphase transport theory, Water Resour. Res., 20(11), 1668-1676, 1984.
13. Dagan, G., Flow and Transport in Porous Formations, Springer-Verlag, New York, 1989.
14. Desbarats, A J., and R. Dimitrakopoulos, Geostatistical modeling of transmissivity for 2D reservoir studies, J. Soc. Petrol. Eng. Form. Eval., 5(4), 437-443, 1990.
15. Durlofsky, L. J., Numerical calculation of equivalent grid block permeability tensors for heterogeneous porous media. Water Resour. Res., 27(5), 699-708, 1991.
16. Dykaar, B. B., and P. K. Kitanidis, Determination of the effective hydraulic conductivity for heterogeneous porous media using a numerical spectral approach, 1, Method, Water Resour. Res., 28(4), 1155-1166, 1992.
17. Folland, G. B., Introduction to Partial Differential Equations, Princeton Univ. Press, Princeton, N. J., 1976.
18. Frisch, U., and S. A. Orszag, Turbulence: Challenges for theory and experimentation, Phys. Today, 43(1), 24-32, 1990.
19. Germano, M., Turbulence: The filtering approach, J. Fluid Mech., 238, 325-336, 1992.
20. Gutjahr, A. L., L. W. Gelhar, A. A. Bakr, and J. R. MacMillan, Stochastic analysis of spatial variability in subsurface flows, 2, Evaluation and application, Water Resour. Res., 34(5), 953-959, 1978.
21. Indelman, P., and G. Dagan, Upscaling of permeability of anisotropic heterogeneous formations, 1, General framework, Water Resour. Res., 29(4), 917-923, 1993.
22. Leonard, A., Energy cascade in large-eddy simulations of turbulent fluid flows, Adv. Geophys., 18A, 237-248, 1974.
23. Leslie, D. C., and G. L. Quarini, The application of turbulence theory to the formulation of subgrid modelling procedures, J. fluid Mech., 91, 65-91, 1979.
24. McLaughlin, D. B., and E. F. Wood, A distributed parameter approach for evaluating the accuracy of groundwater model predictions, 1, Theory, Water Resour. Res., 24(7), 1037-1047, 1988.
25. Milne, R. D., Applied Functional Analysis: An Introductory Treatment, Pitman, London, 1980.
26. Nayfeh, A. H., Introduction to Perturbation Techniques, John Wiley, New York, 1981.
27. Nitsche, L. C., and H. Brenner, Eulerian kinematics of flow through spatially periodic models of porous media, Arch. Ration. Mech. Anal., 107(3), 225-292, 1991.
28. Rajaram, H., and L. W. Gelhar, Plume scale-dependent dispersion in heterogeneous aquifers, 1, Lagrangian analysis in a stratified aquifer, Water Resour. Res., 29(9), 3249-3260, 1993.
29. Rajaram, H., and D. B. McLaughlin, Identification of large-scale spatial trends in hydrologic data, Water Resour. Res., 20(10), 2411-2424, 1990.
30. Rogallo, R. S., and P. Moin, Numerical simulation of turbulent flows, Annu. Rev. Fluid Mech., 16, 99-137, 1984.
31. Rose, H. A., Eddy diffusivity, eddy noise, and subgrid-scale modclling, J. Fluid Mech., 81, 719-734, 1977.
32. Rubin, Y., and J. J. Gómez-Hernández, A stochastic approach to the problem of upscaling of conductivity in disordered media: Theory and unconditional numerical simulations, Water Resour. Res., 20(4), 691-702, 1990.
33. Russo, D., and W. A. Jury, A theoretical study of the estimation of the correlation scale in spatially variable fields, 2, Nonstationary fields, Water Resour. Res., 23(7), 1269-1279, 1987.
34. Sánchez-Vila, X., J. P. Girardi, and J. Carrera, A synthesis of approaches to upscaling of hydraulic conductivities, Water Resour. Res., 31(4), 867-882, 1995.
35. Warren, J. E., and H. S. Price, Flow in heterogeneous porous media, Soc. Pet. Eng. J., 1, 153-169, 1961.
36. Yakhot, V., and S. A. Orszag, Reriormalization group analysis of turbulence, I, Basic theory, J Sci. Comput., 1(1), 3-51, 1986.
37. Zemanian, A. H., Distribution Theory and Transform Analysis, Dover, Mineola, N. Y., 1987.