The virtual element method for discrete fracture network simulations

By Matías Fernando Benedetto, Stefano Berrone, Sandra Pieraccini, Stefano Scialò. 2014

221 citations recorded by the source corpus.

Subfields: Computational Mechanics, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/4a38c0a1739e617524ca4db7450842130d7b8b4f

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In Computational Mechanics

In Mechanics of Materials

Citations in the corpus

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].”
Extended virtual element method for the Laplace problem with singularities and discontinuities (2019, methodology): “Notable among these are the use of VEM to simulate flow in discrete fracture networks [14, 15], modeling of zero-thickness interface elements for fracture in heterogeneous materials [16], and the application of the VEM to 2D elastic fracture simulations [17].”
Virtual Element Methods for general second order elliptic problems on polygonal meshes (2014, unknown): “See in particular, for Mimetic Finite Diﬀerences, [3], [13], [14], [17], [24], [26], [27], [25], and mostly [16], [49] (and the references therein), and [1], [2], [19], [10], [11], [18], [28], [29], [45], [46], [50], [53], [64] for Virtual Elements.”
A globally conforming method for solving flow in discrete fracture networks using the Virtual Element Method (2016, background): “Some of the ideas presented here where present in a previous work by the authors [8], that introduced Virtual Elements (VEM) to DFNs.”
A residual a posteriori error estimate for the Virtual Element Method (2017, unknown): “This very simple model is, anyway, interesting in several applications like, for example, geological ﬂow simulations 28 , 17 , 18 , 15 where the geometrical complexities can be extremely challenging.”
A multigrid algorithm for the $p$-version of the Virtual Element Method (2017, background): “For discrete topology optimization and fracture networks problems we refer to [11] and [29], respectively.”
Conforming and nonconforming virtual element methods for elliptic problems (2015, unknown): “…has been extended to the solution of plate-bending problems [14], linear elasticity problems in two and three spatial dimensions [6, 21], the Steklov eigenvalue problem [27], the simulation of discrete fracture networks [11], and the two-dimensional streamline formulation of the Stokes problem [2].”
The nonconforming virtual element method (2014, methodology): “Despite of its infancy, the conforming VEM laid in [7] has been already extended to a variety of two dimensional problems: plate problems are studied in [13], linear elasticity in [8], mixed methods for H(div;Ω)approximations are introduced in [16], and very recently the VEM has been extended to sim”
Divergence free Virtual Elements for the Stokes problem on polygonal meshes (2015, methodology): “The Virtual Element Method has been applied successfully for a large range of problems, for instance a non exhaustive list being [4, 20, 5, 1, 11, 18, 2, 27, 12, 29, 10, 38, 3].”
Virtual Element Methods for general second order elliptic problems on polygonal meshes (2016, unknown): “See in particular, for Mimetic Finite Diﬀerences 15 , and mostly 10 , 27 (and the references therein), and 1 , 2 , 11 , 6 , 7 , 16 , 17 , 26 , 28 , 30 for Virtual Elements.”
A Plane Wave Virtual Element Method for the Helmholtz Problem (2015, background): “The basic VEM introduced on the Poisson problem has then been extended to highly regular [11], non conforming [2] and discontinuous approximating spaces [16], to general elliptic [8] and mixed problems [6,7,14], as well as to Stokes [1], plate problems [15], linear and non linear elasticity [5, 10, ”