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Multilevel and quasi-Monte Carlo methods for uncertainty quantification in particle travel times through random heterogeneous porous media

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Crevillén-García, D. and Power, H. (2017) Multilevel and quasi-Monte Carlo methods for uncertainty quantification in particle travel times through random heterogeneous porous media. Royal Society Open Science , 4 (8). 170203. doi:10.1098/rsos.170203 ISSN 2054-5703.

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Official URL: http://dx.doi.org/10.1098/rsos.170203

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Abstract

In this study, we apply four Monte Carlo simulation methods, namely, Monte Carlo, quasi-Monte Carlo, multilevel Monte Carlo and multilevel quasi-Monte Carlo to the problem of uncertainty quantification in the estimation of the average travel time during the transport of particles through random heterogeneous porous media. We apply the four methodologies to a model problem where the only input parameter, the hydraulic conductivity, is modelled as a log-Gaussian random field by using direct Karhunen–Loéve decompositions. The random terms in such expansions represent the coefficients in the equations. Numerical calculations demonstrating the effectiveness of each of the methods are presented. A comparison of the computational cost incurred by each of the methods for three different tolerances is provided. The accuracy of the approaches is quantified via the mean square error.

Item Type: Journal Article
Subjects: Q Science > QA Mathematics
T Technology > TA Engineering (General). Civil engineering (General)
Divisions: Faculty of Science, Engineering and Medicine > Engineering > Engineering
Library of Congress Subject Headings (LCSH): Porous materials -- Transport properties, Monte Carlo method, Measurement uncertainty (Statistics)
Journal or Publication Title: Royal Society Open Science
Publisher: The Royal Society Publishing
ISSN: 2054-5703
Official Date: 9 August 2017
Dates:
DateEvent
9 August 2017Published
15 June 2017Accepted
Volume: 4
Number: 8
Article Number: 170203
DOI: 10.1098/rsos.170203
Status: Peer Reviewed
Publication Status: Published
Access rights to Published version: Open Access (Creative Commons)
Date of first compliant deposit: 9 August 2017
Date of first compliant Open Access: 10 August 2017
Funder: Seventh Framework Programme (European Commission) (FP7), Engineering and Physical Sciences Research Council (EPSRC)
Grant number: 282900 (FP7), EP/L027682/1 (EPSRC)

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