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Renormalization group methods in subsurface hydrology: Overview andapplications in hydraulic conductivity upscaling

D.T. Hristopulos

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URIhttp://purl.tuc.gr/dl/dias/5C4A0575-DAC2-45D0-BA3C-E2E6D51CBAA6-
Identifierhttps://doi.org/10.1016/S0309-1708(03)00103-9-
Languageen-
Extent29 pagesen
TitleRenormalization group methods in subsurface hydrology: Overview and applications in hydraulic conductivity upscalingen
CreatorD.T. Hristopulosen
Content SummaryThe renormalization group (RG) approach is a powerful theoretical framework, more suitable for upscaling strong heterogeneity than low-order perturbation expansions. Applications of RG methods in subsurface hydrology include the calculation of (1) macroscopic transport parameters such as effective and equivalent hydraulic conductivity and dispersion coefficients, and (2) anomalous exponents characterizing the dispersion of contaminants due to long-range conductivity correlations or broad (heavy-tailed) distributions of the groundwater velocity. First, we review the main ideas of RG methods and their hydrological applications. Then, we focus on the hydraulic conductivity in saturated porous media with isotropic lognormal heterogeneity, and we present an RG calculation based on the replica method. The RG analysis gives rigorous support to the exponential conjecture for the effective hydraulic conductivity [38]. Using numerical simulations in two dimensions with a bimodal conductivity distribution, we demonstrate that the exponential expression is not suitable for all types of heterogeneity. We also introduce an RG coarse-grained conductivity and investigate its applications in estimating the conductivity of blocks or flow domains with finite size. Finally, we define the fractional effective dimension, and we show that it justifies fractal exponents in the range 1−2 d ≤α <1 (where d is the actual medium dimension) in the geostatistical power average.el
Type of ItemPeer-Reviewed Journal Publicationen
Type of ItemΔημοσίευση σε Περιοδικό με Κριτέςel
Licensehttp://creativecommons.org/licenses/by/4.0/en
Date of Item2015-09-25-
Date of Publication2003-
SubjectProjects, Physicsen
Subjectphysics projectsen
Subjectprojects physicsen
Bibliographic CitationD.T. Hristopulos, "Renormalization group methods in subsurface hydrology: Overview and applications in hydraulic conductivity upscaling " , Adv. in Wat. Resour,vol. 26 ,no.12, pp.1279-1308,2003.doi:10.1016/S0309-1708(03)00103-9en

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