Diagrammatic theory of effective hydraulic conductivity |
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| Authors: | Dionissios T Hristopulos and George Christakos |
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| Institution: | (1) Department of Environmental Sciences and Engineering, CB #7400, University of North Carolina, 27599-7400 Chapel Hill, NC, USA |
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| Abstract: | This work presents a stochastic diagrammatic theory for the calculation of the effective hydraulic conductivity of heterogeneous
media. The theory is based on the mean-flux series expansion of a log-normal hydraulic conductivity medium in terms of diagrammatic
representations and leads to certain general results for the effective hydraulic conductivity of three-dimensional media.
A selective summation technique is used to improve low-order perturbation analysis by evaluating an infinite set of diagrammatic
terms with a specific topological structure that dominates the perturbation series. For stochastically isotropic media the
selective summation yeilds the anticipated exponential expression for the effective hydraulic conductivity. This expression
is extended to stochastically anisotropic media. It is also shown that in the case of non homogeneous media the uniform effective
hydraulic conductivity is replaced by a non-local tensor kernel, for which general diagrammatic expressions are obtained.
The non-local kernel leads to the standard exponential behavior for the effective hydraulic conductivity at the homogeneous
limit. |
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| Keywords: | Random fields diagrams perturbation non-local effective conductivity |
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