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Linearization of the Travel Time Functional in Porous Media Flows

Rourke, Connor J.; Houston, Paul; Rourke, Connor; van der Zee, Kristoffer G.

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Authors

Connor J. Rourke

PAUL HOUSTON PAUL.HOUSTON@NOTTINGHAM.AC.UK
Professor of Computational and Applied Maths

Connor Rourke

KRISTOFFER VAN DER ZEE KG.VANDERZEE@NOTTINGHAM.AC.UK
Professor of Numerical Analysis &computational Applied Mathematics



Abstract

The travel time functional measures the time taken for a particle trajectory to travel from a given initial position to the boundary of the domain. Such evaluation is paramount in the postclosure safety assessment of deep geological storage facilities for radioactive waste where leaked, nonsorbing solutes can be transported to the surface of the site by the surrounding groundwater. The accurate simulation of this transport can be attained using standard dual-weighted-residual techniques to derive goal-oriented a posteriori error bounds. This work provides a key aspect in obtaining a suitable error estimate for the travel time functional: the evaluation of its G\^ ateaux derivative. A mixed finite element method is implemented to approximate Darcy's equations, and numerical experiments are presented to test the performance of the proposed error estimator. In particular, we consider a test case inspired by the Sellafield site located in Cumbria, UK.

Citation

Rourke, C. J., Houston, P., Rourke, C., & van der Zee, K. G. (2022). Linearization of the Travel Time Functional in Porous Media Flows. SIAM Journal on Scientific Computing, 44(3), B531-B557. https://doi.org/10.1137/21M1451105

Journal Article Type Article
Acceptance Date Feb 14, 2022
Online Publication Date May 23, 2022
Publication Date 2022-06
Deposit Date Mar 10, 2022
Publicly Available Date Mar 28, 2024
Journal SIAM Journal on Scientific Computing
Print ISSN 1064-8275
Electronic ISSN 1095-7197
Publisher Society for Industrial & Applied Mathematics (SIAM)
Peer Reviewed Peer Reviewed
Volume 44
Issue 3
Pages B531-B557
DOI https://doi.org/10.1137/21M1451105
Keywords Applied Mathematics; Computational Mathematics
Public URL https://nottingham-repository.worktribe.com/output/7569141
Publisher URL https://epubs.siam.org/doi/10.1137/21M1451105
Additional Information Linearization of the Travel Time Functional in Porous Media Flows Paul Houston, Connor J. Rourke, and Kristoffer G. van der Zee SIAM Journal on Scientific Computing 2022 44:3, B531-B557

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