# Solution of the 3D density-driven groundwater flow problem with uncertain porosity and permeability

## TL;DR

This paper models 3D density-driven groundwater flow with uncertain properties, using advanced parallelized simulations and stochastic methods to analyze contaminant transport and build a benchmark for future studies.

## Contribution

It introduces a parallelized simulation toolbox for 3D density-driven flow with uncertainty, employing stochastic expansions and benchmark solutions.

## Key findings

- Successful simulation of 3D flow with uncertainty using exttt{myug} toolbox.
- Quantitative analysis of mean, variance, and exceedance probabilities.
- Benchmark solution for Elder-like problem in 3D domain.

## Abstract

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.