Deterministic solution of stochastic groundwater flow equations by nonlocal finite elements

A. Guadagnini, Shlomo P Neuman

Research output: Chapter in Book/Report/Conference proceedingConference contribution

6 Citations (Scopus)

Abstract

We consider the effect of measuring randomly varying hydraulic conductivities K(x) on the prediction of groundwater flow in a bounded porous domain under uncertainty. Hydraulic head is governed by a stochastic Poisson equation subject to random source and boundary terms. We present a system of exact nonlocal deterministic equations for optimum unbiased predictors of these quantities and for measures of corresponding prediction errors. We then develop recursive approximations for these equations and solve them to leading order in the variance of ln K(x) by nonlocal Galerkin finite elements. Our results compare well with Monte Carlo simulations of mean uniform and convergent flows in media with large variance and arbitrary correlation.

Original languageEnglish (US)
Title of host publicationInternational Conference on Computational Methods in Water Resources, CMWR
EditorsV.N. Burganos, G.P. Karatzas, A.C. Payatakes, C.A. Brebbia, W.G. Gray, G.F. Pinder
PublisherComputational Mechanics Publ
Pages347-354
Number of pages8
Volume1
StatePublished - 1998
Externally publishedYes
EventProceedings of the 1998 12th International Conference on Computational Methods in Water Resources, CMWR XII'98. Part 1 (of 2) - Crete, Greece
Duration: Jun 1 1998Jun 1 1998

Other

OtherProceedings of the 1998 12th International Conference on Computational Methods in Water Resources, CMWR XII'98. Part 1 (of 2)
CityCrete, Greece
Period6/1/986/1/98

Fingerprint

Groundwater flow
Poisson equation
Hydraulic conductivity
Hydraulics
Uncertainty
Monte Carlo simulation

ASJC Scopus subject areas

  • Engineering(all)

Cite this

Guadagnini, A., & Neuman, S. P. (1998). Deterministic solution of stochastic groundwater flow equations by nonlocal finite elements. In V. N. Burganos, G. P. Karatzas, A. C. Payatakes, C. A. Brebbia, W. G. Gray, & G. F. Pinder (Eds.), International Conference on Computational Methods in Water Resources, CMWR (Vol. 1, pp. 347-354). Computational Mechanics Publ.

Deterministic solution of stochastic groundwater flow equations by nonlocal finite elements. / Guadagnini, A.; Neuman, Shlomo P.

International Conference on Computational Methods in Water Resources, CMWR. ed. / V.N. Burganos; G.P. Karatzas; A.C. Payatakes; C.A. Brebbia; W.G. Gray; G.F. Pinder. Vol. 1 Computational Mechanics Publ, 1998. p. 347-354.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Guadagnini, A & Neuman, SP 1998, Deterministic solution of stochastic groundwater flow equations by nonlocal finite elements. in VN Burganos, GP Karatzas, AC Payatakes, CA Brebbia, WG Gray & GF Pinder (eds), International Conference on Computational Methods in Water Resources, CMWR. vol. 1, Computational Mechanics Publ, pp. 347-354, Proceedings of the 1998 12th International Conference on Computational Methods in Water Resources, CMWR XII'98. Part 1 (of 2), Crete, Greece, 6/1/98.
Guadagnini A, Neuman SP. Deterministic solution of stochastic groundwater flow equations by nonlocal finite elements. In Burganos VN, Karatzas GP, Payatakes AC, Brebbia CA, Gray WG, Pinder GF, editors, International Conference on Computational Methods in Water Resources, CMWR. Vol. 1. Computational Mechanics Publ. 1998. p. 347-354
Guadagnini, A. ; Neuman, Shlomo P. / Deterministic solution of stochastic groundwater flow equations by nonlocal finite elements. International Conference on Computational Methods in Water Resources, CMWR. editor / V.N. Burganos ; G.P. Karatzas ; A.C. Payatakes ; C.A. Brebbia ; W.G. Gray ; G.F. Pinder. Vol. 1 Computational Mechanics Publ, 1998. pp. 347-354
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