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Cite Details

D. M. Tartakovsky and D. Xiu, "Uncertainty quantification for flow in highly heterogeneous porous media", in Proceedings of the XV International Conference "Computational Methods in Water Resources (CMWR 2004)", (Chapel Hill, North Carolina), pp. 695-704, Jun 2004


Natural porous media are highly heterogeneous and characterized by parameters that are often uncertain due to the lack of sufficient data. This uncertainty (randomness) occurs on a multiplicity of scales. We focus on geologic formations with the two dominant scales of uncertainty: a large-scale uncertainty in the spatial arrangement of geologic facies and a small-scale uncertainty in the parameters within each facies. We propose an approach that combines random domain decompositions (RDD) and polynomial chaos expansions (PCE) to account for the large- and small-scales of uncertainty, respectively. We present a general framework and use a one-dimensional flow example to demonstrate that our combined approach provides robust, non-perturbative approximations for the statistics of the system states.

BibTeX Entry

author = {D. M. Tartakovsky and D. Xiu},
title = {Uncertainty quantification for flow in highly heterogeneous porous media},
year = {2004},
month = Jun,
urlpdf = {http://math.lanl.gov/~dmt/papers/CMWR2004_rdd.pdf},
booktitle = {Proceedings of the XV {I}nternational {C}onference "{C}omputational {M}ethods in {W}ater {R}esources ({CMWR} 2004)"},
address = {Chapel Hill, North Carolina},
pages = {695-704}