# Propagation of Uncertainties in Density-Driven Flow

## TL;DR

This paper presents a parallelized method using generalized polynomial chaos to efficiently quantify how uncertainties in permeability and porosity affect density-driven flow and pollution dispersal in subsurface environments.

## Contribution

It introduces a low-cost gPC surrogate model combined with parallelized solvers to accurately propagate uncertainties in density-driven flow simulations.

## Key findings

- Effective uncertainty quantification in subsurface flow models.
- Parallelized gPC method reduces computational cost.
- Validated approach on Elder-like benchmark problem.

## Abstract

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