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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
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Official URL: http://dx.doi.org/10.1098/rsos.170203
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 | ||||||
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| Subjects: | Q Science > QA Mathematics T Technology > TA Engineering (General). Civil engineering (General) |
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| Divisions: | Faculty of Science > 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: |
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| 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 | ||||||
| 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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