Uncertainty quantification of groundwater contamination

Abstract

In many countries, groundwater is the strategic reserve, which is used as drinking water and as an irrigation resource. Therefore, accurate modeling of the pollution of the soil and groundwater aquifer is highly important. As a model, we consider a density-driven groundwater flow problem with uncertain porosity and permeability. This problem may arise in geothermal reservoir simulation, natural saline-disposal basins, modeling of contaminant plumes and subsurface flow. This strongly non-linear problem describes how salt or polluted water streams down building ''fingers". The solving process requires a very fine unstructured mesh and, therefore, high computational resources. Consequently, we run the parallel multigrid solver UG4 (https://github.com/UG4/ughub.wiki.git) on Shaheen II supercomputer. The parallelization is done in both - the physical space and the stochastic space. The novelty of this work is the estimation of risks that the pollution will achieve a specific critical concentration. Additionally, we demonstrate how the multigrid UG4 solver can be run in a black-box fashion for testing different scenarios in the density-driven flow. We solve Elder's problem in 2D and 3D domains, where unknown porosity and permeability are modeled by random fields. For approximations in the stochastic space, we use the generalized polynomial chaos expansion. We compute different quantities of interest such as the mean, variance and exceedance probabilities of the concentration. As a reference solution, we use the solution, obtained from the quasi-Monte Carlo method.