Geodesic
Convergence analysis of macro spreading in 3D heterogeneous porous media
A. Beaudoin1 ; J.-R. de Dreuzy2 ; J. Erhel3 ; G. Pichot3
1University of Poitiers, UMR Pprime, Poitiers, France
2CNRS, UMR Géosciences, Rennes, France
3Inria, Rennes, France
ESAIM. Proceedings, Tome 41 (2013), pp. 59-76
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Models of hydrogeology must deal with both heterogeneity and lack of data. We consider in this paper a flow and transport model for an inert solute. The conductivity is a random field following a stationary log normal distribution with an exponential or Gaussian covariance function, with a very small correlation length. The quantities of interest studied here are the expectation of the spatial mean velocity, the equivalent permeability and the macro spreading. In particular, the asymptotic behavior of the plume is characterized, leading to large simulation times, consequently to large physical domains. Uncertainty is dealt with a classical Monte Carlo method, which turns out to be very efficient, thanks to the ergodicity of the conductivity field and to the very large domain. These large scale simulations are achieved by means of high performance computing algorithms and tools.
DOI : 10.1051/proc/201341003

A. Beaudoin  1   ; J.-R. de Dreuzy  2   ; J. Erhel  3   ; G. Pichot  3

1 University of Poitiers, UMR Pprime, Poitiers, France
2 CNRS, UMR Géosciences, Rennes, France
3 Inria, Rennes, France 
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     author = {A. Beaudoin and J.-R. de Dreuzy and J. Erhel and G. Pichot},
     title = {Convergence analysis of macro spreading in {3D} heterogeneous porous media},
     journal = {ESAIM. Proceedings},
     pages = {59--76},
     year = {2013},
     volume = {41},
     doi = {10.1051/proc/201341003},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/proc/201341003/}
}
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A. Beaudoin; J.-R. de Dreuzy; J. Erhel; G. Pichot. Convergence analysis of macro spreading in 3D heterogeneous porous media. ESAIM. Proceedings, Tome 41 (2013), pp. 59-76. doi: 10.1051/proc/201341003

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