Equidimensional modelling of flow and transport processes in fractured porous systems I

Gebauer, Susanna; Neunhäuserer, Lina; Kornhuber, Ralf; Ochs, Steffen; Hinkelmann, Reinhard; Helmig, Rainer

doi:10.1016/s0167-5648(02)80080-6

Cited by 12 publications

(7 citation statements)

References 5 publications

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“…A single fracture can be expanded in variety of ways, see e.g. [35,53,52,54,59]. This topic will not be investigated further in this work, here we use a single triangle as shown in Figure 2 (Left).…”

Section: Expansion Of Fracturesmentioning

confidence: 99%

Comparison of cell- and vertex-centered discretization methods for flow in a two-dimensional discrete-fracture–matrix system

Haegland¹,

Assteerawatt

Dahle

et al. 2009

Advances in Water Resources

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Abstract. Simulations of flow for a discrete fracture model in fractured porous rocks have gradually become more practical, as a consequence of increased computer power and improved simulation and characterization techniques. Discrete fracture models can be formulated in a lower-dimensional framework, where the fractures are modeled in a lower dimension than the matrix, or in an equi-dimensional form, where the fractures and the matrix have the same dimension.When the velocity of the flow field is needed explicitly, as in streamline simulation of advective transport, only the equi-dimensional approach can be used directly. The velocity field for the lower-dimensional model can then be recovered by post-processing which involves expansion of the lower-dimensional fractures to equi-dimensional ones.In this paper, we propose a technique for expanding lower-dimensional fractures and we compare two different discretization methods for the pressure equation; one vertex-centered approach which can be implemented as either a lower-or an equi-dimensional method, and a cellcentered method using the equi-dimensional formulation. The methods are compared with respect to accuracy, convergence, condition number, and computer efficiency.

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Section: Expansion Of Fracturesmentioning

confidence: 99%

Comparison of cell- and vertex-centered discretization methods for flow in a two-dimensional discrete-fracture–matrix system

Haegland¹,

Assteerawatt

Dahle

et al. 2009

Advances in Water Resources

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“…For similar results we refer to Bramble and Zhang [2] and the references cited therein. Finally note that the "robust" smoothers proposed by Gebauer et al [10] for the multigrid solution of problems on S …”

Section: An Inexact Versionmentioning

confidence: 99%

“…For example, outward normal flow and mass conservation across the interface are not incorporated. This motivated recent work on equidimensional discretizations [9,10,14,15].…”

Section: Introductionmentioning

confidence: 99%

Hierarchical decomposition of domains with fractures

2005

Self Cite

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Abstract. We consider the efficient and robust numerical solution of elliptic problems with jumping coefficients occurring on a network of thin fractures. We present an iterative solution concept based on a hierarchical separation of the fractures and the surrounding rock matrix. Upper estimates for the convergence rates are independent of the width of the fractures and of the jumps of the coefficients. Inexact solution of the local subproblems is also considered. The theoretical results are illustrated by numerical experiments.

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“…In particular, for models based on an equi-dimensional representation of the fractures, i.e., models in which the fractures have the same dimension of the embedding background, the generation of meshes is one of the major challenges. This finds its expression in the fact that the use of equi-dimensional models have so far been limited to small numbers of the fractures [6,14,5]. Among the methods based on an equi-dimensional representation, the mimetic finite difference (MFD) is the most successful one, as it is robust even on anisotropic and distorted meshes [1].…”

Section: Introductionmentioning

confidence: 99%

An Equi-Dimensional Finite Element Approach for Flow Problems in Fractured Porous Media

Favino¹,

Nestola²

2021

14th WCCM-ECCOMAS Congress

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We propose a novel approach for flow simulations in fractured porous media based on an equi-dimensional representation of the fractures and a standard continuous finite element (FE) method. We employ an adaptive mesh refinement strategy to automatically adjust an initial regular mesh to any fracture distribution with a desired accuracy. The proposed approach is easily implementable in any FE software, does not involve the coupling of different discretizations, and provides symmetric and positive definite stiffness matrices. We provide a systematic validation of our method and we show that it can be used to simulate fluid flow for fracture networks of realistic complexity.

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Equidimensional modelling of flow and transport processes in fractured porous systems I

Cited by 12 publications

References 5 publications

Comparison of cell- and vertex-centered discretization methods for flow in a two-dimensional discrete-fracture–matrix system

Comparison of cell- and vertex-centered discretization methods for flow in a two-dimensional discrete-fracture–matrix system

Hierarchical decomposition of domains with fractures

An Equi-Dimensional Finite Element Approach for Flow Problems in Fractured Porous Media

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