Gradient discretization of hybrid-dimensional Darcy flow in fractured porous media with discontinuous pressures at matrix–fracture interfaces

Brenner, Konstantin; Hennicker, Julian; Masson, Roland; Samier, Pierre

doi:10.1093/imanum/drw044

Cited by 52 publications

(99 citation statements)

References 25 publications

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“…The Neumann boundary condition (3c) has been used for immersed fracture tips. The case where the fracture is fully immersed in the domain Ω can be also considered, and it leads to a homogeneous Neumann boundary condition (3c) on the whole fracture boundary; for further details, we refer to [2, Section 2.2.3], [17] or more recently [31]. (1) and (3) are coupled by the following interface conditions:…”

Section: 22mentioning

confidence: 99%

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A Hybrid High-Order Method for Darcy Flows in Fractured Porous Media

Chave¹,

Pietro²,

Formaggia³

2018

SIAM J. Sci. Comput.

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We develop a novel Hybrid High-Order method for the simulation of Darcy flows in fractured porous media. The discretization hinges on a mixed formulation in the bulk region and a primal formulation inside the fracture. Salient features of the method include a seamless treatment of nonconforming discretizations of the fracture, as well as the support of arbitrary approximation orders on fairly general meshes. For the version of the method corresponding to a polynomial degree k ě 0, we prove convergence in h k`1 of the discretization error measured in an energy-like norm. In the error estimate, we explicitly track the dependence of the constants on the problem data, showing that the method is fully robust with respect to the heterogeneity of the permeability coefficients, and it exhibits only a mild dependence on the square root of the local anisotropy of the bulk permeability. The numerical validation on a comprehensive set of test cases confirms the theoretical results.

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Section: 22mentioning

confidence: 99%

“…The model could be extended to fracture networks. In this case, additional coupling conditions enforcing the mass conservation and pressure continuity at fracture intersections should be included; see e.g., [17,16].…”

Section: Coupling Conditions the Subproblemsmentioning

confidence: 99%

A Hybrid High-Order Method for Darcy Flows in Fractured Porous Media

Chave¹,

Pietro²,

Formaggia³

2018

SIAM J. Sci. Comput.

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“…This approach has been successfully applied to different kind of physics, ranging from advection of a passive scalar, heat transport, multi-phase flow. An incomplete list of references is the following [31,35,23,3,32,26,12,19,18,33,22,37,30,38,13,1,10,27,8,4,39,17,7,9,34].…”

Section: Introductionmentioning

confidence: 99%

A multi-layer reduced model for flow in porous media with a fault and surrounding damage zones

Fumagalli

Scotti

2020

Comput Geosci

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In this work we present a new conceptual model to describe fluid flow in a porous media system in presence of a large fault. Geological faults are often modeled simply as interfaces in the rock matrix, but they are complex structure where the high strain core is surrounded by the so called damage zones, characterized by the presence of smaller fractures which enhance the permeability of the medium. To obtain reliable simulation outcomes these damage zone, as well as the fault, have to be accurately described. The new model proposed in this work considers both these two regions as lower dimensional and embedded in the rock matrix. The model is presented, analyzed, and tested in several configurations to prove its robustness and ability to capture many important features, such as hight contrast and heterogeneity of permeability.

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“…Suitable interface conditions are derived and applied in order to close the problem. This approach is usually denoted by reduced Darcy model and is followed for example in [5,2,6,7,8,9,10,11]. Another possible approach is based, e.g., on hybridgrid models, where fractures are n−1-dimensional only in the geometric grid, whereas an n-dimensional grid taking into account fracture aperture is then used for computations, as done, among others, in [12,13].…”

Section: Introductionmentioning

confidence: 99%

“…It is also available a vast literature on finite volumes, two point flux approximation (TPFA) or multi-point flux approximation (MPFA) [31], (see e.g. [32,6,33,13,8,34,35,36]), also recently studied in the general framework of gradient schemes [11].…”

Section: Introductionmentioning

confidence: 99%

Flow simulations in porous media with immersed intersecting fractures

Berrone

Pieraccini

Scialò

2017

Journal of Computational Physics

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A novel approach for fully 3D flow simulations in porous media with immersed networks of fractures is presented. The method is based on the discrete fracture model, in which fractures are represented as n − 1-dimensional objects in an n-dimensional porous matrix. The problem, written in primal formulation on both the fractures and the porous matrix, is solved resorting to the constrained minimization of a properly designed cost functional that expresses the matching conditions at fracture-fracture and fracture-matrix interfaces. The method, originally conceived for intricate fracture networks in impervious rock matrices, is here extended to fractures in a porous permeable rock matrix. The purpose of the optimization approach is to allow for an easy meshing process, independent of the geometrical complexity of the domain, and for a robust and efficient resolution tool, relying on a strong parallelism. The present work is devoted to the presentation of the new method and of its applicability to flow simulations in poro-fractured domains.

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Gradient discretization of hybrid-dimensional Darcy flow in fractured porous media with discontinuous pressures at matrix–fracture interfaces

Cited by 52 publications

References 25 publications

A Hybrid High-Order Method for Darcy Flows in Fractured Porous Media

A Hybrid High-Order Method for Darcy Flows in Fractured Porous Media

A multi-layer reduced model for flow in porous media with a fault and surrounding damage zones

Flow simulations in porous media with immersed intersecting fractures

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