Implementation of mixed-dimensional models for flow in fractured porous media

TL;DR

This paper develops a simulation framework for flow in fractured porous media using mixed-dimensional models, representing complex fracture networks as graphs and coupling different dimensions non-intrusively.

Contribution

It introduces a flexible, reusable simulation approach that leverages existing discretization tools for mono-dimensional problems in mixed-dimensional geometries.

Findings

Successful simulation of flow in 3D fracture networks

Application of finite volume and virtual finite element methods

Framework applicable to various mixed-dimensional problems

Abstract

Models that involve coupled dynamics in a mixed-dimensional geometry are of increasing interest in several applications. Here, we describe the development of a simulation model for flow in fractured porous media, where the fractures and their intersections form a hierarchy of interacting subdomains. We discuss the implementation of a simulation framework, with an emphasis on reuse of existing discretization tools for mono-dimensional problems. The key ingredients are the representation of the mixed-dimensional geometry as a graph, which allows for convenient discretization and data storage, and a non-intrusive coupling of dimensions via boundary conditions and source terms. This approach is applicable for a wide class of mixed-dimensional problems. We show simulation results for a flow problem in a three-dimensional fracture geometry, applying both finite volume and virtual finite element discretizations.