Reliable a posteriori mesh adaptivity in Discrete Fracture Network flow simulations

Berrone, Stefano; Borio, Andrea; Vicini, Fabio

doi:10.1016/j.cma.2019.06.007

Cited by 17 publications

(11 citation statements)

References 40 publications

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“…In Table 3, we report the value of δ C obtained by varying the air-gap with both VEM formulations. Such values are close to zero so we have a good agreement with (7). Moreover, we observe that the potential VEM formulation gains one order with respect to the Kukuchi one.…”

Section: Permanent Magnet Circuitsupporting

confidence: 78%

“…• the possibility of using hanging nodes in the decomposition without special treatments [7]; • the compatibility with finite element method (FEM), meaning that VEM and FEM can both be used at the same time; • excellent robustness with respect to degeneracies of the mesh (polygons/polyhedra with small edges/faces) [8,9]; • sound mathematical analysis [10].…”

Section: Introductionmentioning

confidence: 99%

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Virtual element method and permanent magnet simulations: potential and mixed formulations

Dassi

Barba²,

Russo

2020

IET Science, Measurement &Amp; Technology

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The methodological background of the virtual element method is presented and applied to model permanent magnets via the Kikuchi formulation, considering both linear and non-linear magnetic permeability of the ferromagnetic regions. The authors examine several study cases: a permanent magnet in free space, a permanent magnet energising a ferromagnetic core, a four-pole permanent-magnet motor. In order to validate the proposed approach, comparisons with both virtual and finite element potential formulations are presented and discussed.

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Section: Permanent Magnet Circuitsupporting

confidence: 78%

Section: Introductionmentioning

confidence: 99%

Virtual element method and permanent magnet simulations: potential and mixed formulations

Dassi

Barba²,

Russo

2020

IET Science, Measurement &Amp; Technology

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“…In [11,12,[14][15][16][17], a PDE-constrained optimization approach is proposed, based on non-conforming meshes, that can be applied both to Problems 3 and 5. In this framework, the problem is rewritten as a minimization problem for a functional measuring the error in fulfilling matching conditions, constrained by local PDEs on each fracture.…”

Section: Non-matching Mesh Discretization At Tracesmentioning

confidence: 99%

“…Two aspects are to be remarked: first, the non-conforming approaches are capable of producing reasonable approximations of the solution also on the coarse mesh, which can be greatly improved refining the mesh and still using a fraction of the degrees of freedom required by the conforming approaches, see, e.g., the last two plots in the third column of Fig. 7; second, nonconforming-mesh approaches allow to freely choose the refinement level of the mesh, thus allowing to efficiently use mesh adaptation strategies, only refining the mesh where required, independently of the geometrical constraints [12]. As the non-conforming mesh approaches XFEMSUPG and FEMSUPG are non locally conservative, Fig.…”

Section: Vanishing Trace Between Intersecting Fracturesmentioning

confidence: 99%

Comparison of the response to geometrical complexity of methods for unstationary simulations in discrete fracture networks with conforming, polygonal, and non-matching grids

2020

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The aim of this study is to compare numerical methods for the simulation of single-phase flow and transport in fractured media, described here by means of the discrete fracture network (DFN) model. A Darcy problem is solved to compute the advective field, then used in a subsequent time-dependent transport-diffusion-reaction problem. The numerical schemes are benchmarked in terms of flexibility in handling geometrical complexity, mass conservation, and stability issues for advection-dominated flow regimes. To this end, two benchmark cases, along with an additional one from a previous work, have been specifically designed and are here proposed and investigated, representing some of the most critical issues encountered in DFN simulations.

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“…In this respect, several advanced techniques have been recently developed and documented in literature. In [12,8,7], non-conforming meshes independently built on each fracture are used, and the minimization of a cost functional is applied to enforce a coupling of domain decomposition method and error estimators to control the accuracy of the solution. Techniques based on conforming polygonal meshes of complex DFNs have also been proposed, e.g.…”

mentioning

confidence: 99%

Discontinuous Boundary Elements for Fluid Flow Problems in Discrete Fracture Networks

Wang¹,

Feng²,

Zhou³

et al. 2019

Preprint

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Modeling fluid flow in three-dimensional (3D) Discrete Fracture Networks (DFNs) is of relevance in many engineering applications, such as hydraulic fracturing, oil/gas production, geothermal energy extraction, nuclear waste disposal and CO2 sequestration. A new Boundary Element Method (BEM) technique with discontinuous quadratic elements and a parallel Domain Decomposition Method (DDM) is presented herein for the simulation of the steady-state fluid flow in 3D DFN systems with wellbores, consisting of planar fractures having arbitrary properties and wellbore trajectories. Numerical examples characterized by DFNs of increasing complexity are investigated to evaluate the accuracy and efficiency of the presented technique. The results show that accurate solutions can be obtained with less nodes than with mesh-based methods (e.g. Finite Element Method). In addition, the DDM algorithm used provides a quite fast convergence. The simulation results of the fluid flow around intersections among traces (linear intersections between fractures), intersections between traces and a fracture boundaries, and wellbore intersections is accurate. Source code is available at : https://github.com/BinWang0213/PyDFN3D.

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Reliable a posteriori mesh adaptivity in Discrete Fracture Network flow simulations

Cited by 17 publications

References 40 publications

Virtual element method and permanent magnet simulations: potential and mixed formulations

Virtual element method and permanent magnet simulations: potential and mixed formulations

Comparison of the response to geometrical complexity of methods for unstationary simulations in discrete fracture networks with conforming, polygonal, and non-matching grids

Discontinuous Boundary Elements for Fluid Flow Problems in Discrete Fracture Networks

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