메뉴 건너뛰기




Volumn 21, Issue 6, 2009, Pages 779-789

Qualification of uncertainty for simulating solute transport in the heterogeneous media with sparse grid collocation method

Author keywords

collocation method; solute transport; stochastic partial differential equations; uncertainty

Indexed keywords

COLLOCATION METHOD; COLLOCATION POINTS; CONCENTRATION FIELDS; CONVERGENCE PROPERTIES; DETERMINISTIC EQUATIONS; FINITE ELEMENT CODES; HETEROGENEOUS MEDIA; KARHUNEN-LOEVE EXPANSION; LAGRANGE POLYNOMIALS; NUMERICAL COMPUTATIONS; NUMERICAL EXPERIMENTS; SPARSE GRID; STOCHASTIC COLLOCATION; STOCHASTIC PARTIAL DIFFERENTIAL EQUATION;

EID: 73149092130     PISSN: 10016058     EISSN: None     Source Type: Journal    
DOI: 10.1016/S1001-6058(08)60213-9     Document Type: Article
Times cited : (9)

References (29)
  • 3
    • 46049100371 scopus 로고    scopus 로고
    • Simulation of solute transport in a parallel single fracture with LBM/MMP mixed method[M]
    • TAN Y.-f., and ZHOU Z.-f. Simulation of solute transport in a parallel single fracture with LBM/MMP mixed method[M]. Journal of Hydrodynamics 20 3 (2008) 365-372
    • (2008) Journal of Hydrodynamics , vol.20 , Issue.3 , pp. 365-372
    • TAN, Y.-f.1    ZHOU, Z.-f.2
  • 5
    • 0030359245 scopus 로고    scopus 로고
    • Stochastic analyses of adsorbing solute transport in heterogeneous unsaturated soils[J]
    • YANG J.-z., ZHANG R.-d., and YE Z.-t. Stochastic analyses of adsorbing solute transport in heterogeneous unsaturated soils[J]. Journal of Hydrodynamics, Ser. B 8 3 (1996) 31-43
    • (1996) Journal of Hydrodynamics, Ser. B , vol.8 , Issue.3 , pp. 31-43
    • YANG, J.-z.1    ZHANG, R.-d.2    YE, Z.-t.3
  • 6
    • 73149123271 scopus 로고    scopus 로고
    • The basic equation and parameter structure for solute transport in unsaturated soils[J]
    • (in Chinese).
    • YANG J.-z., CAI S.-y., and YE Z.-t. The basic equation and parameter structure for solute transport in unsaturated soils[J]. Journal of Hydrodynamics, Ser. A 12 2 (1997) 209-216 (in Chinese).
    • (1997) Journal of Hydrodynamics, Ser. A , vol.12 , Issue.2 , pp. 209-216
    • YANG, J.-z.1    CAI, S.-y.2    YE, Z.-t.3
  • 7
    • 55149088861 scopus 로고    scopus 로고
    • Stochastic analysis of groundwater flow fubject to random boundary conditions[J]
    • SHI L.-s., YANG J.-z., CAI S.-y., et al. Stochastic analysis of groundwater flow fubject to random boundary conditions[J]. Journal of Hydrodynamics 20 5 (2008) 553-560
    • (2008) Journal of Hydrodynamics , vol.20 , Issue.5 , pp. 553-560
    • SHI, L.-s.1    YANG, J.-z.2    CAI, S.-y.3
  • 8
    • 0029799855 scopus 로고    scopus 로고
    • Effect of local dispersion on solute transport in randomly heterogeneous media[J]
    • ZHANG D., and NEUMAN S.P. Effect of local dispersion on solute transport in randomly heterogeneous media[J]. Water Resour. Res. 32 9 (1996) 2715-2723
    • (1996) Water Resour. Res. , vol.32 , Issue.9 , pp. 2715-2723
    • ZHANG, D.1    NEUMAN, S.P.2
  • 9
    • 33746357914 scopus 로고    scopus 로고
    • Non-local and localized analyses of non-reactive solute transport in bounded randomly heterogeneous porous media: Theoretical framework[J]
    • MORALES-CASIQUE E., NEUMAN S.P., and GUADAGNINI A. Non-local and localized analyses of non-reactive solute transport in bounded randomly heterogeneous porous media: Theoretical framework[J]. Adv. Water Resour. 29 8 (2006) 1238-1255
    • (2006) Adv. Water Resour. , vol.29 , Issue.8 , pp. 1238-1255
    • MORALES-CASIQUE, E.1    NEUMAN, S.P.2    GUADAGNINI, A.3
  • 10
    • 33746612848 scopus 로고    scopus 로고
    • Non-local and localized analyses of non-reactive solute transport in bounded randomly heterogeneous porous media: Computational analysis[J]
    • MORALES-CASIQUE E., NEUMAN S.P., and GUADAGNINI A. Non-local and localized analyses of non-reactive solute transport in bounded randomly heterogeneous porous media: Computational analysis[J]. Adv. Water Resour. 29 9 (2006) 1399-1418
    • (2006) Adv. Water Resour. , vol.29 , Issue.9 , pp. 1399-1418
    • MORALES-CASIQUE, E.1    NEUMAN, S.P.2    GUADAGNINI, A.3
  • 11
    • 9544247483 scopus 로고
    • Statistical properties of steady state 3-D Eulerian and Lagrangian velocity fields[J]
    • LEVIN O., ZHANG D., and NEUMAN S.P. Statistical properties of steady state 3-D Eulerian and Lagrangian velocity fields[J]. Eos Trans. AGU 73 43 (1992) 214
    • (1992) Eos Trans. AGU , vol.73 , Issue.43 , pp. 214
    • LEVIN, O.1    ZHANG, D.2    NEUMAN, S.P.3
  • 12
    • 33646577797 scopus 로고    scopus 로고
    • High-order collocation methods for differential equations with random inputs[J]
    • XIU D., and HESTHAVEN J. High-order collocation methods for differential equations with random inputs[J]. SIAM J. Sci. Comput. 27 3 (2005) 1118-1139
    • (2005) SIAM J. Sci. Comput. , vol.27 , Issue.3 , pp. 1118-1139
    • XIU, D.1    HESTHAVEN, J.2
  • 13
    • 34547591758 scopus 로고    scopus 로고
    • Stochastic simulation of riser-sections with uncertain measured pressure loads and/or uncertain material properties[J]
    • 10.1016/j.cma.2007.04.005
    • FOO J., YOSIBASH Z., and KARNIADAKIS G.E. Stochastic simulation of riser-sections with uncertain measured pressure loads and/or uncertain material properties[J]. Comput. Methods Appl. Mech. Enggrg. (2007) 10.1016/j.cma.2007.04.005
    • (2007) Comput. Methods Appl. Mech. Enggrg.
    • FOO, J.1    YOSIBASH, Z.2    KARNIADAKIS, G.E.3
  • 14
    • 40249116821 scopus 로고    scopus 로고
    • A seamless approach towards stochastic modeling: Sparse grid collocation and data driven input models[J]
    • 10.1016/j.finel.2007.11.015
    • GANAPATHYSUBRAMANIAN B., and ZABARAS N. A seamless approach towards stochastic modeling: Sparse grid collocation and data driven input models[J]. Finite Elem. Anal. Des. (2007) 10.1016/j.finel.2007.11.015
    • (2007) Finite Elem. Anal. Des.
    • GANAPATHYSUBRAMANIAN, B.1    ZABARAS, N.2
  • 15
    • 73149096168 scopus 로고    scopus 로고
    • SIMUNEK J, VOGEL T. and Van GENUCHTEN M. The SWMS_2D code for simulating water flow and solute transport in two-dimensional variably saturated media[R, Version 1.1, Research Report No. 126. US Salinity Lab, 1992
    • SIMUNEK J., VOGEL T. and Van GENUCHTEN M. The SWMS_2D code for simulating water flow and solute transport in two-dimensional variably saturated media[R]. Version 1.1, Research Report No. 126. US Salinity Lab., 1992.
  • 16
    • 0023327820 scopus 로고
    • An alternating direction Galerkin technique for simulation of groundwater contaminant transport in three dimensions: 2 Dimensionality effects[J]
    • BURNETT R.D., and FRIND E.O. An alternating direction Galerkin technique for simulation of groundwater contaminant transport in three dimensions: 2 Dimensionality effects[J]. Water Resour. Res. 23 4 (1987) 695-705
    • (1987) Water Resour. Res. , vol.23 , Issue.4 , pp. 695-705
    • BURNETT, R.D.1    FRIND, E.O.2
  • 18
    • 1442307688 scopus 로고    scopus 로고
    • An efficient, highorder perturbation approach for flow in random porous media via Karhunen-Loeve and polynomial expansion[J]
    • ZHANG D.-x., and LU Z.-m. An efficient, highorder perturbation approach for flow in random porous media via Karhunen-Loeve and polynomial expansion[J]. J. Comput. Phys. 194 2 (2004) 773-794
    • (2004) J. Comput. Phys. , vol.194 , Issue.2 , pp. 773-794
    • ZHANG, D.-x.1    LU, Z.-m.2
  • 19
    • 46449084805 scopus 로고
    • Explicit cost bounds of algorithms for multivariate tensor product problems[J]
    • WASILKOWSKI G.W., and WOZNIAKOWSKI H. Explicit cost bounds of algorithms for multivariate tensor product problems[J]. Journal of Complexity 11 1 (1995) 1-56
    • (1995) Journal of Complexity , vol.11 , Issue.1 , pp. 1-56
    • WASILKOWSKI, G.W.1    WOZNIAKOWSKI, H.2
  • 20
    • 0242389714 scopus 로고    scopus 로고
    • Smolyak cubature of given polynomial degree with few nodes for increasing dimension[J]
    • PETRAS K. Smolyak cubature of given polynomial degree with few nodes for increasing dimension[J]. Numer. Math. 93 (2003) 729-753
    • (2003) Numer. Math. , vol.93 , pp. 729-753
    • PETRAS, K.1
  • 21
    • 33750371348 scopus 로고    scopus 로고
    • Stochastic uncertainty analysis for unconfined flow systems[J]
    • doi: 10.1029/2005WR004766
    • LIU G.S., ZHANG D. X. and LU Z. M. Stochastic uncertainty analysis for unconfined flow systems[J]. Water Resour. Res., 42: W09412, doi: 10.1029/2005WR004766.
    • Water Resour. Res , vol.42
    • LIU, G.S.1    ZHANG, D.X.2    LU, Z.M.3
  • 22
    • 46249104705 scopus 로고    scopus 로고
    • A new numerical method for groundwater fiow and solute transport using velocity field[J]
    • ZHANG Q.-f., LAN S.-q., WANG Y.-m., et al. A new numerical method for groundwater fiow and solute transport using velocity field[J]. Journal of Hydrodynamics 20 3 (2008) 356-364
    • (2008) Journal of Hydrodynamics , vol.20 , Issue.3 , pp. 356-364
    • ZHANG, Q.-f.1    LAN, S.-q.2    WANG, Y.-m.3
  • 23
    • 33845885890 scopus 로고    scopus 로고
    • Numerical modeling of wastewater transport and degradation in soil aquifer[J]
    • YIN H.-l., XU Z.-x., LI H.-z., et al. Numerical modeling of wastewater transport and degradation in soil aquifer[J]. Journal of Hydrodynamics, Ser. B 18 5 (2006) 597-605
    • (2006) Journal of Hydrodynamics, Ser. B , vol.18 , Issue.5 , pp. 597-605
    • YIN, H.-l.1    XU, Z.-x.2    LI, H.-z.3
  • 24
    • 0026291617 scopus 로고
    • Large-scale natural gradient tracer test in sand and gravel, Cape Cod, Massachusetts: 1. Experimental design and observed tracer movement[J]
    • LEBLANC D.R., GARABEDIAN S.P., HESS K.M., et al. Large-scale natural gradient tracer test in sand and gravel, Cape Cod, Massachusetts: 1. Experimental design and observed tracer movement[J]. Water Resour. Res. 27 5 (1991) 895-910
    • (1991) Water Resour. Res. , vol.27 , Issue.5 , pp. 895-910
    • LEBLANC, D.R.1    GARABEDIAN, S.P.2    HESS, K.M.3
  • 25
    • 0027098993 scopus 로고
    • Large-scale natural gradient tracer test in sand and gravel, Cape Cod, Massachusetts, 3. Hydraulic conductivity variability and calculated macrodispersivities[J]
    • HESS K.M., WOLF S.H., and CELIA M.A. Large-scale natural gradient tracer test in sand and gravel, Cape Cod, Massachusetts, 3. Hydraulic conductivity variability and calculated macrodispersivities[J]. Water Resour. Res. 28 8 (1992) 201I-2027
    • (1992) Water Resour. Res. , vol.28 , Issue.8
    • HESS, K.M.1    WOLF, S.H.2    CELIA, M.A.3
  • 26
    • 0029657356 scopus 로고    scopus 로고
    • Uncertainty in deterministic groundwater transport models due to the assumption of macrodispersive mixing: Evidence from Cape Cod (Massachusetts, U.S.A. and Borden (Ontario, Canada) tracer tests[J]
    • FITTS C.R. Uncertainty in deterministic groundwater transport models due to the assumption of macrodispersive mixing: Evidence from Cape Cod (Massachusetts, U.S.A. and Borden (Ontario, Canada) tracer tests[J]. J. Contam. Hydrol. 23 (1996) 69-84
    • (1996) J. Contam. Hydrol. , vol.23 , pp. 69-84
    • FITTS, C.R.1
  • 27
    • 34848820544 scopus 로고    scopus 로고
    • Probability density function of non-reactive solute concentration in heterogeneous porous formations[J]
    • BELLIN A., and TONINA D. Probability density function of non-reactive solute concentration in heterogeneous porous formations[J]. Journal of Contaminant Hydrology 94 (2007) 109-125
    • (2007) Journal of Contaminant Hydrology , vol.94 , pp. 109-125
    • BELLIN, A.1    TONINA, D.2
  • 28
    • 0026279724 scopus 로고
    • Sampling design for groundwater solute transport: Tests of methods and analysis of Cape Cod tracer test data[J]
    • KNOPMAN D.S., GARABEDIAN S.P., and VOSS C.I. Sampling design for groundwater solute transport: Tests of methods and analysis of Cape Cod tracer test data[J]. Water Resour. Res. 27 5 (1991) 925-949
    • (1991) Water Resour. Res. , vol.27 , Issue.5 , pp. 925-949
    • KNOPMAN, D.S.1    GARABEDIAN, S.P.2    VOSS, C.I.3
  • 29
    • 67649498294 scopus 로고    scopus 로고
    • On rates of convergence for stochastic optimization problems under non-independent and identically distributed sampling[J]
    • HOMEM-DE-MELLO T. On rates of convergence for stochastic optimization problems under non-independent and identically distributed sampling[J]. SIAM Journal on Optimization 19 2 (2008) 524-551
    • (2008) SIAM Journal on Optimization , vol.19 , Issue.2 , pp. 524-551
    • HOMEM-DE-MELLO, T.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.