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    Solution of the 3D density-driven groundwater flow problem with uncertain porosity and permeability

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    Type
    Article
    Authors
    Litvinenko, Alexander cc
    Logashenko, Dmitry
    Tempone, Raul cc
    Wittum, Gabriel
    Keyes, David E. cc
    KAUST Department
    Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
    Applied Mathematics and Computational Science Program
    Extreme Computing Research Center
    Office of the President
    Date
    2020-03-02
    Preprint Posting Date
    2019-05-31
    Online Publication Date
    2020-03-02
    Print Publication Date
    2020-12
    Embargo End Date
    2021-03-02
    Submitted Date
    2019-05-23
    Permanent link to this record
    http://hdl.handle.net/10754/655509
    
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    Abstract
    The pollution of groundwater, essential for supporting populations and agriculture, can have catastrophic consequences. Thus, accurate modeling of water pollution at the surface and in groundwater aquifers is vital. Here, we consider a density-driven groundwater flow problem with uncertain porosity and permeability. Addressing this problem is relevant for geothermal reservoir simulations, natural saline-disposal basins, modeling of contaminant plumes and subsurface flow predictions. This strongly nonlinear time-dependent problem describes the convection of a two-phase flow, whereby a liquid flows and propagates into groundwater reservoirs under the force of gravity to form so-called “fingers”. To achieve an accurate numerical solution, fine spatial resolution with an unstructured mesh and, therefore, high computational resources are required. Here we run a parallelized simulation toolbox ug4 with a geometric multigrid solver on a parallel cluster, and the parallelization is carried out in physical and stochastic spaces. Additionally, we demonstrate how the ug4 toolbox can be run in a black-box fashion for testing different scenarios in the density-driven flow. As a benchmark, we solve the Elder-like problem in a 3D domain. For approximations in the stochastic space, we use the generalized polynomial chaos expansion. We compute the mean, variance, and exceedance probabilities for the mass fraction. We use the solution obtained from the quasi-Monte Carlo method as a reference solution.
    Citation
    Litvinenko, A., Logashenko, D., Tempone, R., Wittum, G., & Keyes, D. (2020). Solution of the 3D density-driven groundwater flow problem with uncertain porosity and permeability. GEM - International Journal on Geomathematics, 11(1). doi:10.1007/s13137-020-0147-1
    Sponsors
    Open Access funding provided by Projekt DEAL. This work was supported by funding from the Alexander von Humboldt foundation (chair of Mathematics for Uncertainty Quantification at RWTH Aachen), KAUST core lab, Extreme Computing Research Center, SRI-UQ Strategic Initiative and Computational Bayesian group at King Abdullah University of Science and Technology. We also thank two anonymous reviewers and the associate editor for providing a number of helpful comments on an earlier draft of the paper.
    Publisher
    Springer Nature
    Journal
    GEM - International Journal on Geomathematics
    DOI
    10.1007/s13137-020-0147-1
    arXiv
    1906.01632
    Additional Links
    http://link.springer.com/10.1007/s13137-020-0147-1
    ae974a485f413a2113503eed53cd6c53
    10.1007/s13137-020-0147-1
    Scopus Count
    Collections
    Articles; Applied Mathematics and Computational Science Program; Extreme Computing Research Center; Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division

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