A globally conforming method for solving flow in discrete fracture networks using the Virtual Element Method
By Matías Fernando Benedetto, Stefano Berrone, Stefano Scialò. 2016
102 citations recorded by the source corpus.
A new approach for numerically solving flow in Discrete Fracture Networks (DFN) is developed in this work by means of the Virtual Element Method (VEM). Taking advantage of the features of the VEM, we obtain global conformity of all fracture meshes while preserving a fracture-independent meshing process. This new approach is based on a generalization of globally conforming Finite Elements for polygonal meshes that avoids complications arising from the meshing process. The approach is robust enough to treat many DFNs with a large number of fractures with arbitrary positions and orientations, as shown by the simulations. Higher order Virtual Element spaces are also included in the implementation with the corresponding convergence results and accuracy aspects. HighlightsThe Virtual Element method allows for meshes made up by arbitrary polygonal elements.Guaranteed local and global conformity with no alteration of the geometry of the DFN.Unconstrained fracture-independent meshing.Application of domain decomposition preconditioners.
Subfields: Civil and Structural Engineering, Computational Mechanics, Mechanics of Materials
View Paper: https://www.semanticscholar.org/paper/6a769549b1d6b28c247dec537538affd29c431eb
How researchers see this paper
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In Civil and Structural Engineering
- Gianmarco Manzini
- Andrea Borio
- Andrea Chiozzi
- Natarajan Sukumar
- Stefano Berrone
- Elena Benvenuti
- E. Ooi
- Chongmin Song
In Computational Mechanics
- Gianmarco Manzini
- Paola Francesca Antonietti
- Stefano Berrone
- Marco Verani
- Andrea Borio
- Elena Benvenuti
- Natarajan Sukumar
- Luca Formaggia
In Mechanics of Materials
- Gianmarco Manzini
- Paola Francesca Antonietti
- Marco Verani
- Elena Benvenuti
- Andrea Chiozzi
- Andrea Borio
- Luca Formaggia
- Natarajan Sukumar
Citations in the corpus
- Orthogonal polynomials in badly shaped polygonal elements for the Virtual Element Method (2017, unknown): “The VEM applied to this problem has proved a good reliability in dealing with these complexities, but, sometimes, some fracture configurations have lead to unfeasible numerical solutions [2].”
- A residual a posteriori error estimate for the Virtual Element Method (2017, methodology): “In particular, we show that the estimates can be effectively applied to a model representing the pressure distribution of a Darcy flow within a fractured medium, modeled by a Discrete Fracture Network approach.(28,30,29,25,18,15) Finally, in Appendix 7 we discuss a stability issue concerning a funda”
- Extended virtual element method for the Laplace problem with singularities and discontinuities (2019, methodology): “Two such elements have so-called hanging nodes on the common edge that lie on the material interface (weak discontinuity), but the VEM approximation is, however, C0-conforming along the edge [15], whereas the nodes that lie on a traction-free crack in elastic media are duplicated (similar to the FEM”
- MIMETIC FINITE DIFFERENCE APPROXIMATION OF FLOWS IN FRACTURED POROUS MEDIA (2016, methodology): “Moreover, very recently VEM and MFD have been employed to model flows in networks of fractures [16, 17] and flows in fractured porous media [2].”