Journal ArticleDOI
Boundary element solution for stochastic groundwater flow: Random boundary condition and recharge
Alexander H.-D. Cheng,O. E. Lafe +1 more
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In this paper, an integral equation technique for solving stochastic boundary value problems in groundwater flow is presented, where the mean and covariance of head and flux are derived using the distribution of fictitious sources and dipoles.Abstract:
This paper presents an integral equation technique for solving stochastic boundary value problems in groundwater flow The aquifer considered has deterministic hydraulic conductivity but is subject to random boundary condition and domain recharge Using the distribution of fictitious sources and dipoles, stochastic integral equations for the mean and covariance of head and flux are derived An iterative boundary element technique is applied for numerical solution Two one-dimensional examples are examined and compared with exact solution A two-dimensional problem is then presentedread more
Citations
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Prediction of steady state flow in nonuniform geologic media by conditional moments: Exact nonlocal formalism, effective conductivities, and weak approximation
Shlomo P. Neuman,Shlomo Orr +1 more
TL;DR: In this paper, the effect of measuring randomly varying local hydraulic conductivities K(x) on one's ability to predict steady state flow within a bounded domain, driven by random source and boundary functions, was considered.
Journal ArticleDOI
A computationally practical approach for modeling complex mean flows in mildly heterogeneous media
TL;DR: In this article, the non-stationary spectral method of Li and McLaughlin (1991, 1995) was reformulated for non-uniform mean flows in heterogeneous porous media.
Journal ArticleDOI
Solution of Poisson's equation by iterative DRBEM using compactly supported, positive definite radial basis function
TL;DR: In this article, an iterative dual reciprocity boundary element method (DRBEM) is developed to solve Poisson's equation without the need of assembling a matrix, which requires that the right hand side of Poisson equation be approximated by a radial basis function interpolation.
Journal ArticleDOI
BEM solution of stochastic seawater intrusion problems
TL;DR: In this article, the stochastic saltwater-freshwater interface location in coastal aquifer is sought, subject to the uncertainty of input parameters such as hydraulic conductivity, freshwater outflow, and pumping rate.
Journal ArticleDOI
Generalized stochastic perturbation technique in engineering computations
TL;DR: In this paper, a generalized stochastic perturbation technique based on the classical Taylor expansion with a single random variable is presented. But the main problem discussed below is an application of this expansion to the solution of various partial differential equations with random coefficients by the fundamental numerical methods, i.e. Boundary Element Method, Finite Element Method as well as the Finite Difference Method.
References
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Journal ArticleDOI
A Stochastic-Conceptual Analysis of One-Dimensional Groundwater Flow in Nonuniform Homogeneous Media
TL;DR: In this paper, the effects of stochastic parameter distributions on predicted hydraulic heads are analyzed with the aid of a set of Monte Carlo solutions to the pertinent boundary value problems, and the results show that the standard deviations of the input hydrogeologic parameters, particularly σy and σc, are important index properties; changes in their values lead to different responses for even when the means μy, μc, and μn are fixed.
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Statistical Theory of Groundwater Flow and Transport: Pore to Laboratory, Laboratory to Formation, and Formation to Regional Scale
TL;DR: In this article, the authors proposed a unified statistical approach to groundwater flow and transport problems at three fundamental scales: the pore scale, the log hydraulic conductivity, and the log transmissivity integral scales.