Coarse Graining for Upscaling of Flow in Heterogeneous Porous Media

Eberhard, Jens P.; Attinger, Sabine; Wittum, Gabriel

doi:10.1137/030600497

Cited by 30 publications

(27 citation statements)

References 24 publications

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“…Multiscale approaches can be also used to define the permeability of saturated or unsaturated porous media [47][48][49][50][51]. These works show that the fluid movement can be supposed Newtonian in small pores and satisfied Navier-Stokes equations.…”

Section: The Non-linear Hydraulic Behaviourmentioning

confidence: 99%

Micromechanical contributions to the behaviour of cement-based materials: Two-scale modelling of cement paste and concrete in tension at high temperatures

Grondin

Dumontet

Hamida

et al. 2011

Cement and Concrete Composites

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Section: The Non-linear Hydraulic Behaviourmentioning

confidence: 99%

Micromechanical contributions to the behaviour of cement-based materials: Two-scale modelling of cement paste and concrete in tension at high temperatures

Grondin

Dumontet

Hamida

et al. 2011

Cement and Concrete Composites

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“…The methodology has already been presented in section 2, as some of the methods included in this group also allow obtaining effective parameters. Depending on the filtering methods used to truncate the series in the spectral space, different methods are available in the literature, all of them highly demanding in numerical terms [ Hristopulos and Christakos , 1999; Eberhard et al , 2004].…”

Section: Mean Parallel Flow: Equivalent Parametersmentioning

confidence: 99%

Representative hydraulic conductivities in saturated groundwater flow

Sánchez-Vila

Guadagnini

Carrera

2006

Reviews of Geophysics

271

209

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Heterogeneity is the single most salient feature of hydrogeology. An enormous amount of work has been devoted during the last 30 years to addressing this issue. Our objective is to synthesize and to offer a critical appraisal of results related to the problem of finding representative hydraulic conductivities. By representative hydraulic conductivity we mean a parameter controlling the average behavior of groundwater flow within an aquifer at a given scale. Three related concepts are defined: effective hydraulic conductivity, which relates the ensemble averages of flux and head gradient; equivalent conductivity, which relates the spatial averages of flux and head gradient within a given volume of an aquifer; and interpreted conductivity, which is the one derived from interpretation of field data. Most theoretical results are related to effective conductivity, and their application to real world scenarios relies on ergodic assumptions. Fortunately, a number of results are available suggesting that conventional hydraulic test interpretations yield (interpreted) hydraulic conductivity values that can be closely linked to equivalent and/or effective hydraulic conductivities. Complex spatial distributions of geologic hydrofacies and flow conditions have a strong impact upon the existence and the actual values of representative parameters. Therefore it is not surprising that a large body of literature provides particular solutions for simplified boundary conditions and geological settings, which are, nevertheless, useful for many practical applications. Still, frequent observations of scale effects imply that efforts should be directed at characterizing well-connected stochastic random fields and at evaluating the corresponding representative hydraulic conductivities

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“…A further approximation has to be introduced similar as in the case of upscaling of flow in heterogeneous media, see [13]. The idea is that SðÁ; ÁÞ acts locally as a smoother when it is folded with a function with compact support.…”

Section: Approximation Of Dm Eff In Real Spacementioning

confidence: 99%

“…[7,17,20]. The stochastic modelling combined with the Coarse Graining method yields an upscaled model equation along with a variable scale for the upscaling without the restrictions for the periodicity and the regularity of function spaces as in the homogenization method [2,11,13].…”

Section: Stochastic Modellingmentioning

confidence: 99%