Analysis of conforming, non-matching, and polygonal methods for Darcy and advection-diffusion-reaction simulations in discrete fracture networks

TL;DR

This paper compares various numerical methods for simulating flow and transport in fractured media using the Discrete Fracture Network model, focusing on their ability to handle complex geometries, conservation, and stability in advection-dominated regimes.

Contribution

It introduces a benchmark framework with three critical cases to evaluate the performance of conforming, non-matching, and polygonal numerical methods for DFN simulations.

Findings

Different methods show varying levels of flexibility in complex geometries.

Mass conservation and stability are key factors influencing method performance.

The benchmark cases reveal strengths and weaknesses of each numerical approach.

Abstract

The aim of this study is to compare numerical methods for the simulation of single-phase flow and transport in fractured media, described here by means of the Discrete Fracture Network (DFN) model. A Darcy problem is solved to compute the advective field, then used in a subsequent time dependent transport-diffusion-reaction problem. The numerical schemes are benchmarked in terms of flexibility in handling geometrical complexity, mass conservation and stability issues for advection dominated flow regimes. To this end, three benchmark cases have been specifically designed and are here proposed, representing some of the most critical issues encountered in DFN simulations.