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Center for Nonlinear Studies |
Porous media are ubiquitous in various engineering applications. I shall mention some of the applications, and what makes modelling of flow through porous media challenging, first from a theoretical standpoint. After a brief overview of the most important modelling approaches, I shall introduce the most commonly used continuum models for flow through porous media and the problem of computation in highly heterogeneous porous media. Following this, my talk will focus on a particular class of such media, comprised of fractured rock where the fractures form the dominant pathways of flow. The paradigm of Discrete Fracture Networks, which is one way to model these media, will be introduced, along with the concept of topological uncertainty that engenders a daunting computational challenge. However, it is known from experiments that not all fractures in the network participate equally in flow and transport, and there exists a "backbone", which is a subset of the full network that dominates overall behavior. One way to circumvent the computational overhead is then to identify the backbone of the flow. The last part of my talk will be devoted to a discussion of system- reduction techniques based on graph-theory and machine learning that can help identify such "backbones" in these fracture networks.