A globally conforming method for solving flow in discrete fracture networks using the Virtual Element Method

Benedetto, Matías Fernando; Berrone, Stefano; Scialò, Stefano

doi:10.1016/j.finel.2015.10.003

Cited by 92 publications

(92 citation statements)

References 33 publications

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“…A second approach, based on a globally conforming discretization of the DFN is proposed in in [10], where the matching conditions at the traces are strongly enforced by means of Lagrange multipliers. We set, on each fracture F i , i ∈ I, and on each trace Γ m , m ∈ M i , the discretization induced by T gc δi , excluding the two extreme points (tips) of the trace, and we build, on this mesh the finite dimensional space…”

Section: A Globally Conforming Approachmentioning

confidence: 99%

“…[28]). Further, within this framework it is possible to use preconditioning techniques borrowed from domain decomposition method, as for example the one-level FETI preconditioner [25], as shown in [10]. …”

Section: A Globally Conforming Approachmentioning

confidence: 99%

“…In this work we recall some results concerning the application of the Virtual Element Method [4,3,2] to the steady state simulation of the flow in DFNs [1,22,27,30,24,32,23,15,16,17,18,19,9,10,8,13]. In this approach we can exploit the flexibility of VEM in order to tackle the geometrical complexity.…”

Section: Introductionmentioning

confidence: 99%

“…Here, the VEM will be used within several possible approaches to the problem: in conjunction with a totally conforming polygonal mesh [10] and with a Mortar approach [8]. Indeed, taking advantage from the great flexibility of VEM in allowing the use of rather general polygonal mesh elements, a suitable mesh for representing the solution and imposing matching conditions between the solutions on different fractures can be easily obtained, starting from an arbitrary triangular mesh independently built on each fracture, and independent of the trace disposition.…”

Section: Introductionmentioning

confidence: 99%

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The Virtual Element Method for Discrete Fracture Network Flow and Transport Simulations

Benedetto¹,

Berrone²,

Borio³

et al. 2016

Proceedings of the VII European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS Congress 2016)

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Abstract. We discuss several issues concerning the application of the Virtual Element Method (VEM) to the flow in fractured media modeled by the Discrete Fracture Network (DFN) model. Due to the stochastic nature of the computational domains, several geometrical complexities make the computations very challenging. The geometrical flexibility provided by the Virtual Element Method can be exploited to mutually couple local problems, either by resorting to a Mortar approach, or by allowing for the global conformity of the local meshes, while keeping the computational cost under control. We describe these two approaches in detail and we test them on a realistic test case, showing the viability of the two approaches.

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Section: A Globally Conforming Approachmentioning

confidence: 99%

Section: A Globally Conforming Approachmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

The Virtual Element Method for Discrete Fracture Network Flow and Transport Simulations

Benedetto¹,

Berrone²,

Borio³

et al. 2016

Proceedings of the VII European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS Congress 2016)

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“…In addition, thanks to this added flexibility, it was discovered [12,6] that virtual elements can also be used to build global discrete spaces of arbitrary regularity (C 1 and more) that are quite simple in terms of degrees of freedom and coding. So far, VEM has been applied to a variety of different problems [11,1,5,9,10,16,18,20,21,2]. However, apart from [17] a systematic study of the impact of VEM on topology optimization problems is still in its infancy.…”

Section: Introductionmentioning

confidence: 99%

Vem and Topology Optimization on Polygonal Meshes

Antonietti¹,

Bruggi²,

Scacchi³

et al. 2016

Proceedings of the VII European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS Congress 2016)

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Abstract. Topology optimization is a fertile area of research that is mainly concerned with the automatic generation of optimal layouts to solve design problems in Engineering. The classical formulation addresses the problem of finding the best distribution of an isotropic material that minimizes the work of the external loads at equilibrium, while respecting a constraint on the assigned amount of volume. This is the so-called minimum compliance formulation that can be conveniently employed to achieve stiff truss-like layout within a two-dimensional domain. A classical implementation resorts to the adoption of four node displacement-based finite elements that are coupled with an elementwise discretization of the (unknown) density field. When regular meshes made of square elements are used, well-known numerical instabilities arise, see in particular the so-called checkerboard patterns. On the other hand, when unstructured meshes are needed to cope with geometry of any shape, additional instabilities can steer the optimizer towards local minima instead of the expected global one. Unstructured meshes approximate the strain energy of truss-like members with an accuracy that is strictly related to the geometrical features of the discretization, thus remarkably affecting the achieved layouts. In this paper we will consider several benchmarks of truss design and explore the performance of the recently proposed technique known as the Virtual Element Method (VEM) in driving the topology optimization procedure. In particular, we will show how the capability of VEM of efficiently approximating elasticity equations on very general polygonal meshes can contribute to overcome the aforementioned mesh-dependent instabilities exhibited by classical finite element based discretization techniques.

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Uncertainty Quantification in Discrete Fracture Network Models: Stochastic Geometry

Berrone

Canuto

Pieraccini

et al. 2018

Water Resources Research

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We consider the problem of uncertainty quantification analysis of the output of underground flow simulations. We consider in particular fractured media described via the discrete fracture network model; within this framework, we address the relevant case of networks in which the geometry of the fractures is described by stochastic parameters. In this context, due to a possible lack of smoothness in the quantity of interest with respect to the stochastic parameters, well assessed techniques such as stochastic collocation may fail in providing reliable estimates of first‐order moments of the quantity of interest. In this paper, we overcome this issue by applying the Multilevel Monte Carlo method, using as underlying solver an extremely robust method.

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A globally conforming method for solving flow in discrete fracture networks using the Virtual Element Method

Cited by 92 publications

References 33 publications

The Virtual Element Method for Discrete Fracture Network Flow and Transport Simulations

The Virtual Element Method for Discrete Fracture Network Flow and Transport Simulations

Vem and Topology Optimization on Polygonal Meshes

Uncertainty Quantification in Discrete Fracture Network Models: Stochastic Geometry

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