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

Borio, Andrea; Fumagalli, Alessio; Scialò, Stefano

doi:10.1007/s10596-020-09996-9

Cited by 10 publications

(6 citation statements)

References 62 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…A variable mesh resolution in non-conforming schemes could drastically reduce the number of nodes in the mesh while retaining the the ability to retain higher orders of accuracy. However it is rarely implemented due to the associated meshing complications [10].…”

Section: Discrete Fracture Network: Mesh Generation Backgroundmentioning

confidence: 99%

Maximal Poisson-disk Sampling for Variable Resolution Conforming Delaunay Mesh Generation: Applications for Three-Dimensional Discrete Fracture Networks and the Surrounding Volume

Krotz¹,

Sweeney²,

Gable³

et al. 2021

Preprint

View full text Add to dashboard Cite

We propose a two-stage algorithm for generating Delaunay triangulations in 2D and Delaunay tetrahedra in 3D that employs near maximal Poisson-disk sampling. The method generates a variable resolution mesh in 2-and 3-dimensions in linear run time. The effectiveness of the algorithm is demonstrated by generating an unstructured 3D mesh on a discrete fracture network (DFN). Even though Poisson-disk sampling methods do not provide triangulation quality bounds in more than two-dimensions, we found that low quality tetrahedra are infrequent enough and could be successfully removed to obtain high quality balanced three-dimensional meshes with topologically acceptable tetrahedra.

show abstract

Section: Discrete Fracture Network: Mesh Generation Backgroundmentioning

confidence: 99%

Maximal Poisson-disk Sampling for Variable Resolution Conforming Delaunay Mesh Generation: Applications for Three-Dimensional Discrete Fracture Networks and the Surrounding Volume

Krotz¹,

Sweeney²,

Gable³

et al. 2021

Preprint

View full text Add to dashboard Cite

show abstract

“…where we recall that Ψ is given in (17) and û := û is as in Lemma 4.2. We can use the direct method of the calculus of variations on E in the Euclidean topology in R. Let (α n ) n∈N ⊂ R be a minimizing sequence for E. Using a similar calculation as in the proof of Theorem 4.7, thanks to (10) we can show that (α n ) n∈N is bounded in R. Therefore, there exists a subsequence of (α n ) n∈N , still denoted by (α n ) n∈N , converging to some α ∈ R. By continuity of Ψ and Fatou's lemma we get that E is lower semi-continuous on R, so that…”

Section: Case λ 1 > λmentioning

confidence: 99%

“…For some specific problems the contribution of the rock matrix is negligible and can be omitted, obtaining the so-called discrete fracture network (DFN) models. On this topic, the reader may refer to [7,10,12,13,17,21,22,28,30] and the references therein. Especially in the presence of complex constitutive equations in the fractures, the authors in [1,2] showed that it is possible to separate the contribution of the porous medium from the fracture network via a Robin-to-Neumann operator.…”

Section: Introductionmentioning

confidence: 99%

Model adaptation in a discrete fracture network: existence of solutions and numerical strategies

Fumagalli,

Patacchini

2021

Preprint

Self Cite

View full text Add to dashboard Cite

Fractures are normally present in the underground and are, for some physical processes, of paramount importance. Their accurate description is fundamental to obtain reliable numerical outcomes useful, e.g., for energy management. Depending on the physical and geometrical properties of the fractures, fluid flow can behave differently, going from a slow Darcian regime to more complicated Brinkman or even Forchheimer regimes for high velocity. The main problem is to determine where in the fractures one regime is more adequate than others. In order to determine these low-speed and high-speed regions, this work proposes an adaptive strategy which is based on selecting the appropriate constitutive law linking velocity and pressure according to a threshold criterion on the magnitude of the fluid velocity itself. Both theoretical and numerical aspects are considered and investigated, showing the potentiality of the proposed approach. From the analytical viewpoint, we show existence of weak solutions to such model under reasonable hypotheses on the constitutive laws. To this end, we use a variational approach identifying solutions with minimizers of an underlying energy functional. From the numerical viewpoint, we propose a one-dimensional algorithm which tracks the interface between the low-and high-speed regions. By running numerical experiments using this algorithm, we illustrate some interesting behaviors of our adaptive model on a single fracture and small networks of intersecting fractures.

show abstract

“…Using a variable mesh resolution in non-conforming schemes could drastically reduce the number of nodes in the mesh while retaining the the ability to retain a high order of accuracy. However, it is rarely implemented due to the associated meshing complications [8].…”

Section: Discrete Fracture Network and Mesh Generationmentioning

confidence: 99%

Variable resolution Poisson-disk sampling for meshing discrete fracture networks

Krotz¹,

Sweeney²,

Hyman³

et al. 2021

Preprint

View full text Add to dashboard Cite

We present the near-Maximal Algorithm for Poisson-disk Sampling (nMAPS) to generate point distributions for variable resolution Delaunay triangular and tetrahedral meshes in two and three-dimensions, respectively. nMAPS consists of two principal stages. In the first stage, an initial point distribution is produced using a cell-based rejection algorithm. In the second stage, holes in the sample are detected using an efficient background grid and filled in to obtain a nearmaximal covering. Extensive testing shows that nMAPS generates a variable resolution mesh in linear run time with the number of accepted points. We demonstrate nMAPS capabilities by meshing three-dimensional discrete fracture networks (DFN) and the surrounding volume. The discretized boundaries of the fractures, which are represented as planar polygons, are used as the seed of 2D-nMAPS to produce a conforming Delaunay triangulation. The combined mesh of the DFN is used as the seed for 3D-nMAPS, which produces conforming Delaunay tetrahedra surrounding the network. Under a set of conditions that naturally arise in maximal Poisson-disk samples and are satisfied by nMAPS, the two-dimensional Delaunay triangulations are guaranteed to only have wellbehaved triangular faces. While nMAPS does not provide triangulation quality bounds in more than two dimensions, we found that low-quality tetrahedra in 3D are infrequent, can be readily detected and removed, and a high quality balanced mesh is produced.

show abstract

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

Cited by 10 publications

References 62 publications

Maximal Poisson-disk Sampling for Variable Resolution Conforming Delaunay Mesh Generation: Applications for Three-Dimensional Discrete Fracture Networks and the Surrounding Volume

Maximal Poisson-disk Sampling for Variable Resolution Conforming Delaunay Mesh Generation: Applications for Three-Dimensional Discrete Fracture Networks and the Surrounding Volume

Model adaptation in a discrete fracture network: existence of solutions and numerical strategies

Variable resolution Poisson-disk sampling for meshing discrete fracture networks

Contact Info

Product

Resources

About