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Conditional Simulation of Flow in Heterogeneous Porous Media with the Probabilistic Collocation Method

Published online by Cambridge University Press:  03 June 2015

Heng Li
Heng Li*
Affiliation:
Department of Energy and Resources Engineering, College of Engineering, Peking University, Beijing 100871, China
*
*Corresponding author.Email:liheng@coe.pku.edu.cn
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Abstract

A stochastic approach to conditional simulation of flow in randomly heterogeneous media is proposed with the combination of the Karhunen-Loeve expansion and the probabilistic collocation method (PCM). The conditional log hydraulic conductivity field is represented with the Karhunen-Loeve expansion, in terms of some deterministic functions and a set of independent Gaussian random variables. The propagation of uncertainty in the flow simulations is carried out through the PCM, which relies on the efficient polynomial chaos expansion used to represent the flow responses such as the hydraulic head. With the PCM, existing flow simulators can be employed for uncertainty quantification of flow in heterogeneous porous media when direct measurements of hydraulic conductivity are taken into consideration. With illustration of several numerical examples of groundwater flow, this study reveals that the proposed approach is able to accurately quantify uncertainty of the flow responses conditioning on hydraulic conductivity data, while the computational efforts are significantly reduced in comparison to the Monte Carlo simulations.

Keywords

60H3565C5065M7076S05Conditional simulationprobabilistic collocation methodKarhunen-Loeve expansionpolynomial chaos expansion
Type
Research Article
Information
Communications in Computational Physics , Volume 16 , Issue 4 , October 2014 , pp. 1010 - 1030
Copyright
Copyright © Global Science Press Limited 2014

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