Benchmarks for single-phase flow in fractured porous media

TL;DR

This paper introduces benchmark test cases for numerical schemes solving single-phase flow in fractured porous media, comparing various methods across complex geometries and physical parameters to facilitate future research and validation.

Contribution

It provides a comprehensive set of benchmark problems and compares multiple numerical schemes, including finite volume, finite element, and discrete fracture models, with publicly available data.

Findings

Different schemes show varying accuracy and computational efficiency.

The benchmarks reveal challenges in handling complex fracture networks.

Data and meshes are publicly available for further research.

Abstract

This paper presents several test cases intended to be benchmarks for numerical schemes for single-phase fluid flow in fractured porous media. A number of solution strategies are compared, including a vertex and a cell-centered finite volume method, a non-conforming embedded discrete fracture model, a primal and a dual extended finite element formulation, and a mortar discrete fracture model. The proposed benchmarks test the schemes by increasing the difficulties in terms of network geometry, e.g. intersecting fractures, and physical parameters, e.g. low and high fracture-matrix permeability ratio as well as heterogeneous fracture permeabilities. For each problem, the results presented by the participants are the number of unknowns, the approximation errors in the porous matrix and in the fractures with respect to a reference solution, and the sparsity and condition number of the discretized linear system. All data and meshes used in this study are publicly available for further comparisons.