Solution of the 3D density-driven groundwater flow problem with uncertain porosity and permeability
KAUST DepartmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Applied Mathematics and Computational Science Program
Extreme Computing Research Center
Office of the President
Preprint Posting Date2019-05-31
Online Publication Date2020-03-02
Print Publication Date2020-12
Embargo End Date2021-03-02
Permanent link to this recordhttp://hdl.handle.net/10754/655509
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AbstractThe 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.
CitationLitvinenko, 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
SponsorsOpen 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.