Nitsche’s extended finite element method for a fracture model in porous media

Capatina, Daniela; Luce, Robert; El-Otmany, Hammou; Barrau, Nelly

doi:10.1080/00036811.2015.1075007

Cited by 16 publications

(26 citation statements)

References 13 publications

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“…The fractures are modeled as embedded surfaces with high permeability. Our model is essentially the same as the one presented in [1,13]. It was further studied in [11], where it was extended to bifurcating cracks.…”

Section: Pressure Problemmentioning

confidence: 99%

“…The embedded model is derived as the asymptotic limit in the weak formulation as the fracture aperture goes to zero and the fracture permeability goes to infinity. We refer to [1,13] for further details.…”

Section: Pressure Problemmentioning

confidence: 99%

“…The last equation (2.5c) is another coupling term, and represents a reasonable assumption for high conductive fractures. The model can also be extended to a non-zero pressure jump [13]. We equip the governing equations with Dirichlet and Neumann boundary conditions, i.e.,…”

Section: C)mentioning

confidence: 99%

“…To account for more general fracture shapes, the model in [2,1] was extended to curved fractures in [33,13]. These models are derived by considering the asymptotic limit in the weak formulation as the fracture width tends to zero and the fracture permeability tends to infinity.…”

Section: Introductionmentioning

confidence: 99%

“…In this limit, the condition of a continuous pressure follows. We mention that this model was extended to allow for pressure jumps across the interface in [13].…”

Section: Introductionmentioning

confidence: 99%

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A simple embedded discrete fracture–matrix model for a coupled flow and transport problem in porous media

Odsæter

Kvamsdal

Larson

2019

Computer Methods in Applied Mechanics and Engineering

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Accurate simulation of fluid flow and transport in fractured porous media is a key challenge in subsurface reservoir engineering. Due to the high ratio between its length and width, fractures can be modeled as lower dimensional interfaces embedded in the porous rock. We apply a recently developed embedded finite element method (EFEM) for the Darcy problem. This method allows for general fracture geometry, and the fractures may cut the finite element mesh arbitrarily. We present here a velocity model for EFEM and couple the Darcy problem to a transport problem for a passive solute. The main novelties of this work is a locally conservative velocity approximation derived from the EFEM solution, and the development of a lowest order upwind finite volume method for the transport problem. This numerical model is compatible with EFEM in the sense that the same computational mesh may be applied, so that we retain the same flexibility with respect to fracture geometry and meshing. Hence, our coupled solution strategy represents a simple approach in terms of formulation, implementation and meshing. We demonstrate our model by some numerical examples on both synthetic and realistic problems, including a benchmark study for single-phase flow. Despite the simplicity of the method, the results are promising.

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Section: Pressure Problemmentioning

confidence: 99%

Section: Pressure Problemmentioning

confidence: 99%

Section: C)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…In this limit, the condition of a continuous pressure follows. We mention that this model was extended to allow for pressure jumps across the interface in [13].…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

A simple embedded discrete fracture–matrix model for a coupled flow and transport problem in porous media

Odsæter

Kvamsdal

Larson

2019

Computer Methods in Applied Mechanics and Engineering

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A cut finite element method for a model of pressure in fractured media

2020

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We develop a robust cut finite element method for a model of diffusion in fractured media consisting of a bulk domain with embedded cracks. The crack has its own pressure field and can cut through the bulk mesh in a very general fashion. Starting from a common background bulk mesh, that covers the domain, finite element spaces are constructed for the interface and bulk subdomains leading to efficient computations of the coupling terms. The crack pressure field also uses the bulk mesh for its representation. The interface conditions are a generalized form of conditions of Robin type previously considered in the literature which allows the modeling of a range of flow regimes across the fracture. The method is robust in the following way: (1) Stability of the formulation in the full range of parameter choices; and (2) Not sensitive to the location of the interface in the background mesh. We derive an optimal order a priori error estimate and present illustrating numerical examples.

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Mixed-dimensional multi-scale poroelastic modeling of adipose tissue for subcutaneous injection

Leng

Wang

Lucio

et al. 2022

Biomech Model Mechanobiol

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Subcutaneous injection of therapeutic monoclonal antibodies (mAbs) has gained increasing interest in the pharmaceutical industry. The transport, distribution and absorption of mAbs in the skin after injection are not yet well-understood. Experiments have shown that fibrous septa form preferential channels for fluid flow in the tissue. The majority of mAbs can only be absorbed through lymphatics which follow closely the septa network. Therefore, studying drug transport in the septa network is vital to the understanding of drug absorption. In this work, we present a mixed-dimensional multi-scale (MDMS) poroelastic model of adipose tissue for subcutaneous injection. More specifically, we model the fibrous septa as reduced-dimensional microscale interfaces embedded in the macroscale tissue matrix. The model is first verified by comparing numerical results against the full-dimensional model where fibrous septa are resolved using fine meshes. Then, we apply the MDMS model to study subcutaneous injection. It is found that the permeability ratio between the septa and matrix, volume capacity of the septa network, and concentration-dependent drug viscosity are important factors affecting the amount of drug entering the septa network which are paths to lymphatics. Our results show that septa play a critical role in the transport of mAbs in the subcutaneous tissue, and this role was previously overlooked.

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Nitsche’s extended finite element method for a fracture model in porous media

Cited by 16 publications

References 13 publications

A simple embedded discrete fracture–matrix model for a coupled flow and transport problem in porous media

A simple embedded discrete fracture–matrix model for a coupled flow and transport problem in porous media

A cut finite element method for a model of pressure in fractured media

Mixed-dimensional multi-scale poroelastic modeling of adipose tissue for subcutaneous injection

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