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arXiv · 1712.07392

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

Eirik Keilegavlen·Alessio Fumagalli·Runar Berge·Ivar Stefansson
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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.

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Eirik Keilegavlen, Alessio Fumagalli, Runar Berge, Ivar Stefansson. 2017-12-20. Implementation of mixed-dimensional models for flow in fractured porous media. https://arxiv.org/abs/1712.07392

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