On the use of enriched finite element method to model subsurface features in porous media flow problems

Huang, Hao; Long, Ted; Wan, Jing; Brown, William P.

doi:10.1007/s10596-011-9239-1

Cited by 38 publications

(19 citation statements)

References 26 publications

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“…to allow fractures to cross the elements of a coarse and regular background grid. In this case, the presence of the interfaces can be accounted for by suitable enrichments of the finite element spaces, exploiting the eXtended Finite Element Method, see [21,31]. We point out that some methods allow for partial nonconformity of the grids, i.e.…”

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confidence: 99%

Analysis of a mimetic finite difference approximation of flows in fractured porous media

2018

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confidence: 99%

Analysis of a mimetic finite difference approximation of flows in fractured porous media

2018

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“…Since then, the combined X-FEM/levelset approach has been extended to model interfacial failure in composites (see Hettich and Ramm, 2006;Hettich et al, 2008), for obtaining homogenized properties for heterogeneous structures (see Legrain et al, 2011), and for obtaining effective elastic modulii in nanocomposites (Yvonnet et al, 2008). For geo-mechanical problems, X-FEM has been employed to model faulting (see the work of Borja, 2009, 2010a), earthquake ruptures (Coon et al, 2011) and subsurface flow (Huang et al, 2011). …”

Section: Introductionmentioning

confidence: 99%

An efficient finite element method for embedded interface problems

Dolbow

Harari

2008

Numerical Meth Engineering

217

223

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We focus on developing a computationally efficient finite element method for interface problems. Finite element methods are severely constrained in their ability to resolve interfaces. Many of these limitations stem from their inability in independently representing interface geometry from the underlying discretization. We propose an approach that facilitates such an independent representation by embedding interfaces in the underlying finite element mesh. This embedding, however, raises stability concerns for existing algorithms used to enforce interfacial kinematic constraints. To address these stability concerns, we develop robust methods to enforce interfacial kinematics over embedded interafces.We begin by examining embedded Dirichlet problems -a simpler class of embedded constraints. We develop both stable methods, based on Lagrange multipliers, and stabilized methods, based on Nitsche's approach, for enforcing Dirichlet constraints over three-dimensional embedded surfaces and compare and contrast their performance. We then extend these methods to enforce perfectly-tied kinematics for elastodynamics with explicit time integration. In particular, we examine the coupled aspects of spatial and temporal stability for Nitsche's approach. We address the incompatibility of Nitsche's method for explicit time integration by (a) proposing a modified weighted stress variational form, and (b) proposing a novel mass-lumping procedure.We revisit Nitsche's method and inspect the effect of this modified variational iv form on the interfacial quantities of interest. We establish that the performance of this method, with respect to recovery of interfacial quantities, is governed significantly by the choice for the various method parameters viz. stabilization and weighting. We establish a relationship between these parameters and propose an optimal choice for the weighting. We further extend this approach to handle non-linear, frictional sliding constraints at the interface. The naturally non-symmetric nature of these problems motivates us to omit the symmetry term arising in Nitsche's method.We contrast the performance of the proposed approach with the more commonly used penalty method. Through several numerical examples, we show that with the proposed choice of weighting and stabilization parameters, Nitsche's method achieves the right balance between accurate constraint enforcement and flux recovery -a balance hard to achieve with existing methods. Finally, we extend the proposed approach to intersecting interfaces and conduct numerical studies on problems with junctions and complex topologies.v To Amma (mom) and Nannagaru (dad), vi

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“…To be able to represent the discontinuities in the solution, i.e., the jump and the average term, we use the extended finite element method as it is described for example by Dolbow et al [13], Hansbo and Hansbo [17], and Mohammadi [22]. XFEM is used in the context of fractured porous media for example in D'Angelo and Scotti [9], Fumagalli and Scotti [16] for lower dimensional fractures introducing a discontinuous solution in the matrix, for lower dimensional fracture networks having different permeabilities in the network and therefore also discontinuities [8], as well as for thin heterogeneities (equi-dimensional) which are not resolved directly with the grid but rather with the XFEM, [19]. The system is completely assembled and solved with a direct solver.…”

Section: Reduced Modelmentioning

confidence: 99%

Dimensionally reduced flow models in fractured porous media: crossings and boundaries

et al. 2015

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For the simulation of fractured porous media, a common approach is the use of co-dimension one models for the fracture description. In order to simulate correctly the behavior at fracture crossings, standard models are not sufficient because they either cannot capture all important flow processes or are computationally inefficient. We propose a new concept to simulate co-dimension one fracture crossings and show its necessity and accuracy by means of an example and a comparison to a literature benchmark. From the application point of view, often the pressure is known only at a limited number of discrete points and an interpolation is used to define the boundary condition at the remaining parts of the boundary. The quality of the interpolation, especially in fracture models, influences the global solution significantly. We propose a new method to interpolate boundary conditions on boundaries that are intersected by fractures and show the advantages over standard interpolation methods.

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On the use of enriched finite element method to model subsurface features in porous media flow problems

Cited by 38 publications

References 26 publications

Analysis of a mimetic finite difference approximation of flows in fractured porous media

Analysis of a mimetic finite difference approximation of flows in fractured porous media

An efficient finite element method for embedded interface problems

Dimensionally reduced flow models in fractured porous media: crossings and boundaries

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