| Issue |
ESAIM: Proc.
Volume 41, December 2013
CANUM 2012, 41e Congrès National d'Analyse Numérique
|
|
|---|---|---|
| Page(s) | 59 - 76 | |
| DOI | https://doi.org/10.1051/proc/201341003 | |
| Published online | 09 December 2013 | |
Convergence analysis of macro spreading in 3D heterogeneous porous media*,**
1 University of Poitiers, UMR
Pprime, Poitiers,
France
2 CNRS, UMR Géosciences,
Rennes,
France
3 Inria, Rennes,
France
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.
© EDP Sciences, SMAI 2013
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