  Accurate modeling of contamination in subsurface flow and water aquifers is
crucial for agriculture and environmental protection. Here, we demonstrate a
parallel method to quantify the propagation of the uncertainty in the dispersal
of pollution in subsurface flow. Specifically, we consider the density-driven
flow and estimate how uncertainty from permeability and porosity propagates to
the solution. We take an Elder-like problem as a numerical benchmark and we use
random fields to model the limited knowledge on the porosity and permeability.
We construct a low-cost generalized polynomial chaos expansion (gPC) surrogate
model, where the gPC coefficients are computed by projection on sparse and full
tensor grids. We parallelize both the numerical solver for the deterministic
problem based on the multigrid method, and the quadrature over the parametric
space
