Linearization of the Travel Time Functional in Porous Media Flows

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

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 18, 2022
• Journal: SIAM Journal on Scientific Computing
• Print ISSN: 1064-8275
• Electronic ISSN: 1095-7197
• Publisher: Society for Industrial and Applied Mathematics
• 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