Unified approach to discretization of flow in fractured porous media

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...

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Vydáno v:Computational geosciences Ročník 23; číslo 2; s. 225 - 237
Hlavní autoři: Nordbotten, J. M., Boon, W. M., Fumagalli, A., Keilegavlen, E.
Médium: Journal Article
Jazyk:angličtina
Vydáno: Cham Springer International Publishing 01.04.2019
Springer Nature B.V
Témata:
Computational fluid dynamics
Computer simulation
Control methods
Discretization
Domains
Earth and Environmental Science
Earth Sciences
Finite element method
Flow equations
Fluid flow
Fractures
Frameworks
Geotechnical Engineering & Applied Earth Sciences
Hydrogeology
Mathematical analysis
Mathematical Modeling and Industrial Mathematics
Mortars (material)
Original Paper
Porous media
Porous media flow
Soil Science & Conservation
Stability
Three dimensional flow
Two dimensional flow
Flux mortars
Discretization methods
Mixed-dimensional
ISSN:1420-0597, 1573-1499
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Popis
Shrnutí: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- 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.
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ISSN:1420-0597
1573-1499
DOI:10.1007/s10596-018-9778-9