Boundary condition sensitivity analysis of the stochastic flow equation

Advances in Water Resources

Volumn 19, Issue 2, 1996, Pages 109-120

  Oliver, L Dean ^a   Christakos, George ^a  

^a UNIVERSITY OF NORTH CAROLINA   (United States)

Author keywords

Boundary conditions; Effective conductivity; Groundwater flow moments; Stochastic hydrology

Indexed keywords

GROUND WATER;

BOUNDARY CONDITIONS; EFFECTIVE CONDUCTIVITY; GROUNDWATER FLOW; STOCHASTIC ANALYSIS;

CONDUCTANCE; MODEL; SENSITIVITY ANALYSIS;

BOUNDARY CONDITIONS; GROUNDWATER FLOW; HYDRAULICS; MATHEMATICAL MODELS; PERTURBATION TECHNIQUES; RANDOM PROCESSES; SENSITIVITY ANALYSIS;

BOUNDARY CONDITION SENSITIVITY ANALYSIS; CONSTANT GRADIENT BOUNDARIES; CONSTANT HEAD; EFFECTIVE CONDUCTIVITY; GROUNDWATER FLOW MOMENTS; STOCHASTIC FLOW EQUATION; STOCHASTIC HYDROLOGY; TWO DIMENSIONAL FLOW;

HYDROLOGY;

BOUNDARY FLOW; GROUNDWATER; STOCHASTIC METHODS;

EID: 0029735790     PISSN: 03091708     EISSN: None     Source Type: Journal    
DOI: 10.1016/0309-1708(95)00027-5     Document Type: Article

References (27)

1. Abramowitz, M. & Stegun, I. A., Handbook of Mathematical Functions. Dover Publications, New York, 1972.
2. Bakr, A. A., Gelhar, L. W., Gutjahr, A. L. & MacMillan, J. R., Stochastic analysis of spatial variability in subsurface flows. 1. Comparison of one-dimensional and three-dimensional flow. Water Resour. Res., 14 (1978) 263-71.
3. Cheng, A. H.-D. & Lafe, O. E., Boundary element solution for stochastic groundwater flow. Random boundary condition and recharge. Water Resour. Res., 27 (1991) 231-42.
4. Christakos, G., A Treatise on the Stochastic Interactive Perturbation Analysis of Groundwater Flow. Res. Notes no. SM/3.92, Dept. of Environ. Sci. and Engng, Univ. of North Carolina, Chapel Hill, 1992.
5. Christakos, G., Miller, C. T. & Oliver, D., Stochastic perturbation analysis of groundwater flow. Spatially variable soils, semi-infinite domains and large fluctuations. Stochastic Hydrol. Hydraul., 7 (1993) 213-39.
6. Cushman, J. H. (ed.), Comment on 'Three-dimensional stochastic analysis of macrodispersion in aquifers' by L. W. Gelhar & C. L. Axness. Water Resour. Res., 19 (1983) 1641-2.
7. Dagan, G., Stochastic analysis of groundwater flow by unconditional and conditional probabilities. 1. Conditional simulation and the direct problem. Water Resour. Res., 18 (1982) 813-34.
8. Dagan, G., Stochastic modeling of groundwater flow by unconditional and conditional probabilities: The inverse problem. Water Resour. Res., 21 (1985) 65-72.
9. Deutsch, C. V. & Journel, A. G., GSLIB: Geostatistical Software Library and User's Guide. Oxford University Press, New York, 1993.
10. Freeze, R. A., A stochastic-conceptual analysis of one-dimensional groundwater flow in nonuniform homogeneous media. Water Resour. Res., 11 (1975) 725-41.
11. Gelhar, L. W., Stochastic subsurface hydrology from theory to applications. Water Resour. Res., 22 (1986) 135S-45S.
12. Gutjahr, A. L. & Gelhar, L. W., Stochastic models of subsurface flow: Infinite vs finite domains and stationarity. Water Resour. Res., 17 (1981) 337-50.
13. Houyoux, M., An Evaluation of Decision Making for Aquifer Restoration. Master's Thesis, University of North Carolina, NC, USA, 1995.
14. Loaiciga, H. A. & Mariño, M. A., Error analysis and stochastic differentiability in subsurface flow modeling. Water Resour. Res., 26 (1990) 2897-902.
15. Mizell, S. A., Gutjahr, A. L. & Gelhar, L. W., Stochastic analysis of spatial variability in two-dimensional steady groundwater flow assuming stationary and nonstationary heads. Water Resour. Res., 22 (1982) 1053-67.
16. Naff, R. L. & Vecchia, A. V., Stochastic analysis of three-dimensional flow in a bounded domain. Water Resour. Res., 18 (1986) 695-704.
17. Oliver, L. D., Relationships Existing Between Green's Functions, Kriging Systems, and Finite Element Basis Functions: A Speculative Work. Research Notes PRN-050995, Department of Environmental Sciences and Engineering, University of North Carolina, NC, USA, 1995.
18. Oliver, L. D. & Christakos, G., Diagrammatic solutions for hydraulic head moments in 1-D and 2-D bounded domains. Stochastic Hydrol. Hydraul., in press.
19. Oliver, L. D., Christakos, G. & Hristopulos, D. T., Numerical implementation of a space transformation approach for solving the three-dimensional flow equation. SIAM J. Scientific Computing, in review.
20. Ronan, A. D., Velocity Uncertainty Estimation for Groundwater Transport Prediction. Ph.D. Dissertation, Stanford University, 1993.
21. Rubin, Y. & Dagan, G., Stochastic analysis of boundaries effects on head spatial variability in heterogeneous aquifers. 1. Constant head boundary. Water Resour. Res., 24 (1988) 1689-97.
22. Rubin, Y. & Dagan, G., Stochastic analysis of boundaries effects on head spatial variability in heterogeneous aquifers. 2. Impervious boundary. Water. Resour. Res., 25 (1989) 707-12.
23. Smith, L. & Freeze, R. A., Stochastic analysis of steady state groundwater flow in a bounded domain. 1. One-dimensional simulations. Water Resour. Res., 15 (1979a) 521-8.
24. Smith, L. & Freeze, R. A., Stochastic analysis of steady state groundwater flow in a bounded domain. 1. Two-dimensional simulations. Water Resour. Res., 15 (1979b) 1543-59.
25. Sudicky, E. A., A natural gradient experiment on solute transport in a sand aquifer: Spatial variability of hydraulic conductivity and its role in the dispersion process. Water Resour. Res., 22 (1986) 2069-82.
26. Tompson, A. F. B., Ababou, R. & Gelhar, L. W., Implementation of the three-dimensional turning bands random field generator. Water Resour. Res., 25 (1989) 2227-43.
27. Wolfram, S., Mathematica: A System for Doing Mathematics by Computer. Addison-Wesley, Redwood City, CA, 1991.