  As groundwater is an essential nutrition and irrigation resource, its
pollution may lead to catastrophic consequences. 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 nonlinear time-dependent problem describes the
convection of the two-phase flow. This liquid streams under the gravity force,
building so-called "fingers". The accurate numerical solution requires fine
spatial resolution with an unstructured mesh and, therefore, high computational
resources. Consequently, we run the parallelized simulation toolbox \myug with
the geometric multigrid solver on Shaheen II supercomputer. The parallelization
is done in physical and stochastic spaces. Additionally, we demonstrate how the
\myug 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 of the mass fraction. As a reference solution, we use the
solution, obtained from the quasi-Monte Carlo method.
