# Flow and Transport in Three-Dimensional Discrete Fracture Matrix Models using Mimetic Finite Difference on a Conforming Multi-Dimensional Mesh

**Authors:** Jeffrey D. Hyman, Matthew R. Sweeney, Carl W. Gable, Daniil Svyatsky, Konstantin Lipnikov, J. David Moulton  
**arXiv:** [2112.12592](https://arxiv.org/abs/2112.12592)  
**Date:** 2021-12-20  
**Summary page:** https://www.summarizepaper.com/en/paper/2112.12592v1/

## Key points

- Authors present a comprehensive workflow for simulating single-phase flow and transport in fractured porous media utilizing the discrete fracture matrix approach
- Method for generating conforming meshes around a complex three-dimensional fracture network
- Discretization of governing equations through a second-order mimetic finite difference method
- Implementation of numerical methods tailored for high-performance computing environments
- Technique introduced to create a conforming Delaunay tetrahedralization surrounding the fracture network, addressing common mesh quality issues
- Open-source subsurface simulator employs a hierarchy of process kernels allowing for strong and weak coupling of fracture and matrix domains
- Verification tests based on analytic solutions provided alongside demonstrations of numerical convergence
- Authors showcase method's robustness by exploring scenarios where fracture network acts as flow barrier, primary pathway, or offers resistance similar to surrounding matrix
- Multiple applications demonstrated in complex fracture networks, including scenarios involving different behaviors of the fracture network in relation to flow dynamics

## Summary

In their paper titled "Flow and Transport in Three-Dimensional Discrete Fracture Matrix Models using Mimetic Finite Difference on a Conforming Multi-Dimensional Mesh," authors Jeffrey D. Hyman, Matthew R. Sweeney, Carl W. Gable, Daniil Svyatsky, Konstantin Lipnikov, and J. David Moulton present a comprehensive workflow for simulating single-phase flow and transport in fractured porous media utilizing the discrete fracture matrix approach. The <kw1>workflow</kw1> consists of three primary components: (1) a method for generating conforming meshes around a complex three-dimensional fracture network, (2) the discretization of governing equations through a second-order mimetic finite difference method, and (3) the implementation of numerical methods tailored for high-performance computing environments. The authors introduce a technique to create a conforming Delaunay tetrahedralization surrounding the fracture network, where triangular cells within the fracture mesh serve as faces in the volume mesh. This addresses common issues that arise and compromise mesh quality. Their open-source subsurface simulator employs a hierarchy of process kernels—one per physical process—allowing for both strong and weak coupling of the fracture and matrix domains. Verification tests based on analytic solutions for flow and transport are provided alongside demonstrations of numerical convergence. The authors showcase the method's robustness by exploring scenarios where the fracture network acts as a flow barrier, primary pathway, or offers resistance similar to the surrounding matrix. Furthermore, they present multiple applications of their method in complex fracture networks. In one example, they demonstrate robustness through two scenarios involving different behaviors of the fracture network in relation to flow dynamics. In another test case, they illustrate flow and transport through a stochastically generated three-dimensional network containing 257 fractures. Overall, this work contributes significantly to advancing our understanding of flow and transport phenomena in fractured porous media by providing an innovative workflow that combines advanced mesh generation techniques with efficient numerical methods tailored for high-performance computing environments.