Unified approach to discretization of flow in fractured porous media

Abstract

In this paper, we introduce a mortar-based approach to discretizing flow in fractured porous media, which we term the mixed-dimensional flux coupling scheme. Our formulation is agnostic to the discretizations used to discretize the fluid flow equations in the porous medium and in the fractures, and as such it represents a unified approach to integrated fractured geometries into any existing discretization framework. In particular, several existing discretization approaches for fractured porous media can be seen as special instances of the approach proposed herein. We provide an abstract stability theory for our approach, which provides explicit guidance into the grids used to discretize the fractures and the porous medium, as dependent on discretization methods chosen for the respective domains. The theoretical results are sustained by numerical examples, wherein we utilize our framework to simulate flow in 2D and 3D fractured media using control volume methods (both two-point and multi-point flux), Lagrangian finite element methods, mixed finite element methods, and virtual element methods. As expected, regardless of the ambient methods chosen, our approach leads to stable and convergent discretizations for the fractured problems considered, within the limits of the discretization schemes.

References in corpus (3)

• Benchmarks for single-phase flow in fractured porous media
• PorePy: An Open-Source Simulation Tool for Flow and Transport in Deformable Fractured Rocks
• Modeling, Structure and Discretization of Mixed-dimensional Partial Differential Equations

Cited by in corpus (22)

• Verification benchmarks for single-phase flow in three-dimensional fractured porous media
• A fully coupled numerical model of thermo-hydro-mechanical processes and fracture contact mechanics in porous media
• Flow and Transport in Three-Dimensional Discrete Fracture Matrix Models using Mimetic Finite Difference on a Conforming Multi-Dimensional Mesh
• Multifidelity Computing for Coupling Full and Reduced Order Models
• A mathematical model for thermal single-phase flow and reactive transport in fractured porous media
• A hybrid-mixed finite element method for single-phase Darcy flow in fractured porous media
• Energy-stable discretization of two-phase flows in deformable porous media with frictional contact at matrix-fracture interfaces
• Gradient discretization of two-phase poro-mechanical models with discontinuous pressures at matrix fracture interfaces
• Interface learning of multiphysics and multiscale systems
• A Parameter-Robust Iterative Method for Stokes-Darcy Problems Retaining Local Mass Conservation
• Effective Preconditioners for Mixed-Dimensional Scalar Elliptic Problems
• Multiscale simulation of injection-induced fracture slip and wing-crack propagation in poroelastic media
• A double-layer reduced model for fault flow on slipping domains with hybrid finite volume scheme
• Gradient discretization of two-phase flows coupled with mechanical deformation in fractured porous media
• Block Preconditioners for Mixed-dimensional Discretization of Flow in Fractured Porous Media
• Numerical analysis of a mixed-dimensional poromechanical model with frictionless contact at matrix-fracture interfaces
• Modelling and discretization of flow in porous media with thin, full-tensor permeability inclusions
• Analysis of conforming, non-matching, and polygonal methods for Darcy and advection-diffusion-reaction simulations in discrete fracture networks
• A block preconditioner for thermo-poromechanics with frictional deformation of fractures
• Monolithic mixed-dimensional multigrid methods for single-phase flow in fractured porous media
• Linearisation of the Travel Time Functional in Porous Media Flows
• Model adaptation in a discrete fracture network: existence of solutions and numerical strategies