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Volumn 294, Issue 1-3, 2004, Pages 18-38

Stochastic analysis of saturated-unsaturated flow in heterogeneous media by combining Karhunen-Loeve expansion and perturbation method

Author keywords

Karhunen Loeve expansion; Numerical analysis; Perturbation method; Saturated unsaturated flow; Stochastic modeling; Vadose zone

Indexed keywords

HYDRAULIC CONDUCTIVITY; MATHEMATICAL MODELS; PARTIAL DIFFERENTIAL EQUATIONS; PERTURBATION TECHNIQUES; RANDOM PROCESSES;

EID: 3042595850     PISSN: 00221694     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jhydrol.2003.10.023     Document Type: Article
Times cited : (52)

References (45)
  • 1
    • 0019728155 scopus 로고
    • Convective and pore scale dispersive solute transport in unsaturated heterogeneous fields
    • Bresler E., Dagan G. Convective and pore scale dispersive solute transport in unsaturated heterogeneous fields. Water Resour. Res. 17:(6):1981;1683-1693
    • (1981) Water Resour. Res. , vol.17 , Issue.6 , pp. 1683-1693
    • Bresler, E.1    Dagan, G.2
  • 3
    • 0000148817 scopus 로고
    • The orthogonal development of nonlinear functionals in series of Fourier-Hermite functionals
    • Cameron R.H., Martin W.T. The orthogonal development of nonlinear functionals in series of Fourier-Hermite functionals. Ann. Math. 48:1947;385-392
    • (1947) Ann. Math. , vol.48 , pp. 385-392
    • Cameron, R.H.1    Martin, W.T.2
  • 4
    • 0021470157 scopus 로고
    • Solute transport in heterogenous porous formations
    • Dagan G. Solute transport in heterogenous porous formations. J. Fluid Mech. 145:1984;151-177
    • (1984) J. Fluid Mech. , vol.145 , pp. 151-177
    • Dagan, G.1
  • 6
    • 0018654679 scopus 로고
    • Solute dispersion in unsaturated heterogeneous soil at field scale I
    • Dagan G., Bresler E. Solute dispersion in unsaturated heterogeneous soil at field scale I. Theory Soil Sci. Soc. Am. J. 43:1979;461-467
    • (1979) Theory Soil Sci. Soc. Am. J. , vol.43 , pp. 461-467
    • Dagan, G.1    Bresler, E.2
  • 7
    • 38249004291 scopus 로고
    • Stochastic FEM sensitivity analysis of nonlinear dynamic problems
    • Deodatis G. Stochastic FEM sensitivity analysis of nonlinear dynamic problems. ASCE J. Eng. Mech. 4:(3):1989;135-141
    • (1989) ASCE J. Eng. Mech. , vol.4 , Issue.3 , pp. 135-141
    • Deodatis, G.1
  • 8
    • 33845514960 scopus 로고
    • Some steady state solutions of unsaturated moisture flow equations with application to evaporation from a water table
    • Gardner W.R. Some steady state solutions of unsaturated moisture flow equations with application to evaporation from a water table. Soil Sci. 85:1958;228-232
    • (1958) Soil Sci. , vol.85 , pp. 228-232
    • Gardner, W.R.1
  • 9
    • 0020971569 scopus 로고
    • Three-dimensional stochastic analysis of macrodispersion in aquifers
    • Gelhar L.W., Axness C.L. Three-dimensional stochastic analysis of macrodispersion in aquifers. Water Resour. Res. 19:(1):1983;161-180
    • (1983) Water Resour. Res. , vol.19 , Issue.1 , pp. 161-180
    • Gelhar, L.W.1    Axness, C.L.2
  • 10
    • 0019057216 scopus 로고
    • A closed-form equation for predicting the hydraulic conductivity of unsaturated soils
    • van Genuchten M.T. A closed-form equation for predicting the hydraulic conductivity of unsaturated soils. Soil Sci. Soc. Am. J. 44:1980;892-898
    • (1980) Soil Sci. Soc. Am. J. , vol.44 , pp. 892-898
    • Van Genuchten, M.T.1
  • 11
    • 0032496593 scopus 로고    scopus 로고
    • Probabilistic characterization of transport in heterogeneous media
    • Ghanem R.G. Probabilistic characterization of transport in heterogeneous media. Comp. Meth. Appl. Mech. Eng. 158:1998;199-220
    • (1998) Comp. Meth. Appl. Mech. Eng. , vol.158 , pp. 199-220
    • Ghanem, R.G.1
  • 12
    • 0033528038 scopus 로고    scopus 로고
    • Ingredients for a general purpose stochastic finite elements implementation
    • Ghanem R.G. Ingredients for a general purpose stochastic finite elements implementation. Comp. Meth. Appl. Mech. Eng. 168:1999;19-34
    • (1999) Comp. Meth. Appl. Mech. Eng. , vol.168 , pp. 19-34
    • Ghanem, R.G.1
  • 13
    • 0033293545 scopus 로고    scopus 로고
    • The nonlinear gaussian spectrum of log-normal stochastic processes and variables
    • Ghanem R.G. The nonlinear gaussian spectrum of log-normal stochastic processes and variables. J. Appl. Mech., ASME. 66:1999;964-973
    • (1999) J. Appl. Mech., ASME , vol.66 , pp. 964-973
    • Ghanem, R.G.1
  • 14
    • 0033008165 scopus 로고    scopus 로고
    • Stochastic finite elements with multiple random non-Gaussian properties
    • Ghanem R.G. Stochastic finite elements with multiple random non-Gaussian properties. J. Eng. Mech. ASCE. 125:(1):1999;26-40
    • (1999) J. Eng. Mech. ASCE , vol.125 , Issue.1 , pp. 26-40
    • Ghanem, R.G.1
  • 15
    • 0029776146 scopus 로고    scopus 로고
    • Numerical solution of spectral stochastic finite element systems
    • Ghanem R.G., Kruger R. Numerical solution of spectral stochastic finite element systems. Comp. Meth. Appl. Mech. Eng. 129:(3):1996;289-303
    • (1996) Comp. Meth. Appl. Mech. Eng. , vol.129 , Issue.3 , pp. 289-303
    • Ghanem, R.G.1    Kruger, R.2
  • 16
    • 0032173318 scopus 로고    scopus 로고
    • Stochastic finite element analysis for multiphase flow in heterogeneous media
    • Ghanem R.G., Dham S. Stochastic finite element analysis for multiphase flow in heterogeneous media. Transp Porous Media. 32:1998;239-262
    • (1998) Transp Porous Media , vol.32 , pp. 239-262
    • Ghanem, R.G.1    Dham, S.2
  • 17
    • 0026238497 scopus 로고
    • Spectral stochastic finite-element formulation for reliability analysis
    • Ghanem R.G., Spanos P.D. Spectral stochastic finite-element formulation for reliability analysis. J. Eng. Mech. 117:(10):1991;2351-2372
    • (1991) J. Eng. Mech. , vol.117 , Issue.10 , pp. 2351-2372
    • Ghanem, R.G.1    Spanos, P.D.2
  • 19
    • 0020354689 scopus 로고
    • Simulation of solute transport using a transfer function model
    • Jury W.A. Simulation of solute transport using a transfer function model. Water Resour. Res. 18:1982;363-368
    • (1982) Water Resour. Res. , vol.18 , pp. 363-368
    • Jury, W.A.1
  • 20
    • 0032550609 scopus 로고    scopus 로고
    • Sensitivity and moment analyses of head in variably saturated regimes
    • Li B., Yeh T.-C.J. Sensitivity and moment analyses of head in variably saturated regimes. Adv. Water Resour. 21:1998;477-485
    • (1998) Adv. Water Resour. , vol.21 , pp. 477-485
    • Li, B.1    Yeh, T.-C.J.2
  • 21
    • 0028669377 scopus 로고
    • A conceptual perturbation model of water movement in stochastically heterogeneous soils
    • Liedl R. A conceptual perturbation model of water movement in stochastically heterogeneous soils. Adv. Water Resour. 17:1994;171-179
    • (1994) Adv. Water Resour. , vol.17 , pp. 171-179
    • Liedl, R.1
  • 23
    • 1542629531 scopus 로고    scopus 로고
    • Stochastic analysis of transient flow in heterogeneous, variably saturated porous media: The van Genuchten-Mualem constitutive model
    • Lu Z., Zhang D. Stochastic analysis of transient flow in heterogeneous, variably saturated porous media: the van Genuchten-Mualem constitutive model. Vadose Zone J. 1:2002;137-149
    • (2002) Vadose Zone J. , vol.1 , pp. 137-149
    • Lu, Z.1    Zhang, D.2
  • 24
    • 0026438856 scopus 로고
    • A theoretical approach for modeling unsaturated flow in spatially variable soils: Effective flow models in finite domains and nonstationarity
    • Mantoglou A. A theoretical approach for modeling unsaturated flow in spatially variable soils: effective flow models in finite domains and nonstationarity. Water Resour. Res. 28:(1):1992;251-267
    • (1992) Water Resour. Res. , vol.28 , Issue.1 , pp. 251-267
    • Mantoglou, A.1
  • 25
    • 0023524206 scopus 로고
    • Stochastic modeling of large-scale transient unsaturated flow systems
    • Mantoglou A., Gelhar, L.W. Stochastic modeling of large-scale transient unsaturated flow systems. Water Resour. Res. 23:1987;37-46
    • (1987) Water Resour. Res. , vol.23 , pp. 37-46
    • Mantoglou, A.1    Gelhar W, L.2
  • 26
    • 0031333532 scopus 로고    scopus 로고
    • Uncertainties in probabilistic numerical analysis of structures and solids-stochastic finite elements
    • Matthies H.G., Brenner C.E., Bucher C.G., Soares C.G. Uncertainties in probabilistic numerical analysis of structures and solids-stochastic finite elements. Struct. Safety. 19:(3):1997;283-336
    • (1997) Struct. Safety , vol.19 , Issue.3 , pp. 283-336
    • Matthies, H.G.1    Brenner, C.E.2    Bucher, C.G.3    Soares, C.G.4
  • 27
    • 0023105729 scopus 로고
    • Stochastic theory of field-scale Fickian dispersion in anisotropic porous media
    • Neuman S.P., Winter C.L., Newman C.M. Stochastic theory of field-scale Fickian dispersion in anisotropic porous media. Water Resour. Res. 23:1987;453-466
    • (1987) Water Resour. Res. , vol.23 , pp. 453-466
    • Neuman, S.P.1    Winter, C.L.2    Newman, C.M.3
  • 28
    • 0031123106 scopus 로고    scopus 로고
    • Probabilistic analysis of flow in random porous media by stochastic boundary element
    • Roy R.V., Grilli S.T. Probabilistic analysis of flow in random porous media by stochastic boundary element. Eng. Anal. Boundary Elem. 19:1997;239-255
    • (1997) Eng. Anal. Boundary Elem. , vol.19 , pp. 239-255
    • Roy, R.V.1    Grilli, S.T.2
  • 29
    • 0023794195 scopus 로고
    • Determining soil hydraulic properties by parameter estimation: On the selection of a model for the hydraulic properties
    • Russo D. Determining soil hydraulic properties by parameter estimation: On the selection of a model for the hydraulic properties. Water Resour. Res. 24:(3):1988;453-459
    • (1988) Water Resour. Res. , vol.24 , Issue.3 , pp. 453-459
    • Russo, D.1
  • 30
    • 0027385856 scopus 로고
    • Stochastic modeling of macrodispersion for solute transport in a heterogeneous unsaturated porous formation
    • Russo D. Stochastic modeling of macrodispersion for solute transport in a heterogeneous unsaturated porous formation. Water Resour. Res. 29:1993;383-397
    • (1993) Water Resour. Res. , vol.29 , pp. 383-397
    • Russo, D.1
  • 31
    • 0028975045 scopus 로고
    • On the velocity covariance and transport modeling in heterogeneous anisotropic porous formations, 2, unsaturated flow
    • Russo D. On the velocity covariance and transport modeling in heterogeneous anisotropic porous formations, 2, unsaturated flow. Water Resour. Res. 31:(1):1995;139-145
    • (1995) Water Resour. Res. , vol.31 , Issue.1 , pp. 139-145
    • Russo, D.1
  • 32
    • 0000786435 scopus 로고
    • The homogeneous chaos
    • Wiener N. The homogeneous chaos. Am. J. Math. 60:1938;897-936
    • (1938) Am. J. Math. , vol.60 , pp. 897-936
    • Wiener, N.1
  • 33
    • 0021408616 scopus 로고
    • A perturbation expansion for diffusion in a random velocity field
    • Winter C.L., Newman C.M., Neuman S.P. A perturbation expansion for diffusion in a random velocity field. SIAM J. Appl. Math. 44:(2):1984;411-424
    • (1984) SIAM J. Appl. Math. , vol.44 , Issue.2 , pp. 411-424
    • Winter, C.L.1    Newman, C.M.2    Neuman, S.P.3
  • 34
    • 0029777247 scopus 로고    scopus 로고
    • A analytical solution of macrodispersivity for adsorbing solute transport in unsaturated soils
    • Yang J., Zhang R., Wu J. A analytical solution of macrodispersivity for adsorbing solute transport in unsaturated soils. Water Resour. Res. 32:1996;355-362
    • (1996) Water Resour. Res. , vol.32 , pp. 355-362
    • Yang, J.1    Zhang, R.2    Wu, J.3
  • 35
    • 0030835512 scopus 로고    scopus 로고
    • Stochastic analysis of adsorbing solute transport in three-dimensional heterogeneous unsaturated soils
    • Yang J., Zhang R., Wu J. Stochastic analysis of adsorbing solute transport in three-dimensional heterogeneous unsaturated soils. Water Resour. Res. 33:1997;1947-1956
    • (1997) Water Resour. Res. , vol.33 , pp. 1947-1956
    • Yang, J.1    Zhang, R.2    Wu, J.3
  • 36
    • 0022266398 scopus 로고
    • Stochastic analysis of unsaturated flow in heterogeneous soils, 1, statistically isotropic media
    • Yeh T.-C., Gelhar L.W., Gutjahr A.L. Stochastic analysis of unsaturated flow in heterogeneous soils, 1, statistically isotropic media. Water Resour. Res. 21:(4):1985;447-456
    • (1985) Water Resour. Res. , vol.21 , Issue.4 , pp. 447-456
    • Yeh, T.-C.1    Gelhar, L.W.2    Gutjahr, A.L.3
  • 37
    • 0022266399 scopus 로고
    • Stochastic analysis of unsaturated flow in heterogeneous soils, 2, statistically anisotropic media with variable a
    • Yeh T.-C., Gelhar L.W., Gutjahr A.L. Stochastic analysis of unsaturated flow in heterogeneous soils, 2, statistically anisotropic media with variable a. Water Resour. Res. 21:(4):1985;457-464
    • (1985) Water Resour. Res. , vol.21 , Issue.4 , pp. 457-464
    • Yeh, T.-C.1    Gelhar, L.W.2    Gutjahr, A.L.3
  • 38
    • 0022266404 scopus 로고
    • Stochastic analysis of unsaturated flow in heterogeneous soils, 3, observation and Application
    • Yeh T.-C., Gelhar L.W., Gutjahr A.L. Stochastic analysis of unsaturated flow in heterogeneous soils, 3, observation and Application. Water Resour. Res. 21:(4):1985;465-471
    • (1985) Water Resour. Res. , vol.21 , Issue.4 , pp. 465-471
    • Yeh, T.-C.1    Gelhar, L.W.2    Gutjahr, A.L.3
  • 39
    • 0031931834 scopus 로고    scopus 로고
    • Numerical solutions to statistical moment equations of groundwater flow in nonstationary, bounded heterogeneous media
    • Zhang D. Numerical solutions to statistical moment equations of groundwater flow in nonstationary, bounded heterogeneous media. Water Resour. Res. 34:(3):1998;529-538
    • (1998) Water Resour. Res. , vol.34 , Issue.3 , pp. 529-538
    • Zhang, D.1
  • 40
    • 0032634748 scopus 로고    scopus 로고
    • Nonstationary stochastic analysis of transient unsaturated flow in randomly heterogeneous media
    • Zhang D. Nonstationary stochastic analysis of transient unsaturated flow in randomly heterogeneous media. Water Resour. Res. 35:(4):1999;1127-1141
    • (1999) Water Resour. Res. , vol.35 , Issue.4 , pp. 1127-1141
    • Zhang, D.1
  • 42
    • 0036219809 scopus 로고    scopus 로고
    • Stochastic analysis of flow in a heterogeneous unsaturated-saturated system
    • Zhang D., Lu Z. Stochastic analysis of flow in a heterogeneous unsaturated-saturated system. Water Resour. Res. 38:(2):2002;101029
    • (2002) Water Resour. Res. , vol.38 , Issue.2 , pp. 101029
    • Zhang, D.1    Lu, Z.2
  • 43
    • 1442307688 scopus 로고    scopus 로고
    • An efficient, higher-order perturbation approach for flow in randomly heterogeneous porous media via Karhunen-Loeve decomposition
    • Zhang D., Lu Z. An efficient, higher-order perturbation approach for flow in randomly heterogeneous porous media via Karhunen-Loeve decomposition. J. Comput. Phys. 194:(2):2004;773-794
    • (2004) J. Comput. Phys. , vol.194 , Issue.2 , pp. 773-794
    • Zhang, D.1    Lu, Z.2
  • 44
    • 0031960693 scopus 로고    scopus 로고
    • Nonstationary stochastic analysis of steady state flow through variably saturated, heterogeneous media
    • Zhang D., Winter C.L. Nonstationary stochastic analysis of steady state flow through variably saturated, heterogeneous media. Water Resour. Res. 34:1998;1091-1100
    • (1998) Water Resour. Res. , vol.34 , pp. 1091-1100
    • Zhang, D.1    Winter, C.L.2
  • 45
    • 0031778764 scopus 로고    scopus 로고
    • Stochastic analysis of steady state unsaturated flow in heterogeneous media: Comparison of the Brooks-Corey and Gardner-Russo models
    • Zhang D., Wallstrom T.C., Winter C.L. Stochastic analysis of steady state unsaturated flow in heterogeneous media: comparison of the Brooks-Corey and Gardner-Russo models. Water Resour. Res. 34:(6):1998;1437-1449
    • (1998) Water Resour. Res. , vol.34 , Issue.6 , pp. 1437-1449
    • Zhang, D.1    Wallstrom, T.C.2    Winter, C.L.3


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