Self-organized percolation in multi-layered structures

Parteli, Eric J. R.; Silva, Luciano R. da; Andrade, José S.

doi:10.1088/1742-5468/2010/03/p03026

Cited by 15 publications

(9 citation statements)

References 42 publications

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“…Another system where a comparison should be possible is slow drainage in layered porous media which produces multiple sheetlike structures. A model exists [12], but to our knowledge no experimental results have been produced so far. In this case, data of sufficient quality should be obtainable.…”

Section: Introductionmentioning

confidence: 99%

Topological impact of constrained fracture growth

et al. 2015

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The topology of two discrete fracture network models is compared to investigate the impact of constrained fracture growth. In the Poissonian discrete fracture network model the fractures are assigned length, position and orientation independent of all other fractures, while in the mechanical discrete fracture network model the fractures grow and the growth can be limited by the presence of other fractures. The topology is found to be impacted by both the choice of model, as well as the choice of rules for the mechanical model. A significant difference is the degree mixing. In two dimensions the Poissonian model results in assortative networks, while the mechanical model results in disassortative networks. In three dimensions both models produce disassortative networks, but the disassortative mixing is strongest for the mechanical model.

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Section: Introductionmentioning

confidence: 99%

Topological impact of constrained fracture growth

et al. 2015

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“…the connected phase (L y = 0). This behavior is similar, for instance, to the transition of percolation from the connected to the disconnected phase as the probability p that a site in the graph is open decreases below a critical value p c (Herrmann and Roux, 1990;Stauffer and Aharony, 1994;Bunde and Havlin, 1996;Araújo et al, 2002;Parteli et al, 2010). In other words, in the system of Fig.…”

Section: Two-fences Experiments Elucidate the Critical Dependence Of mentioning

confidence: 59%

CFD simulation of the wind field over a terrain with sand fences: Critical spacing for the wind shear velocity

et al. 2020

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“…The pore network model and the self-organized percolation (SOP) model may perform well compared with computational fluid dynamics modeling and the lattice Boltzmann method [32,33]. In contrast with other numerical methods, we developed a meshless method using the Trefftz space-time basis function.…”

Section: Introductionmentioning

confidence: 99%

Modeling Transient Flows in Heterogeneous Layered Porous Media Using the Space–Time Trefftz Method

Hong

Liu

et al. 2021

Applied Sciences

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In this study, we developed a novel boundary-type meshless approach for dealing with two-dimensional transient flows in heterogeneous layered porous media. The novelty of the proposed method is that we derived the Trefftz space–time basis function for the two-dimensional diffusion equation in layered porous media in the space–time domain. The continuity conditions at the interface of the subdomains were satisfied in terms of the domain decomposition method. Numerical solutions were approximated based on the superposition principle utilizing the space–time basis functions of the governing equation. Using the space–time collocation scheme, the numerical solutions of the problem were solved with boundary and initial data assigned on the space–time boundaries, which combined spatial and temporal discretizations in the space–time manifold. Accordingly, the transient flows through the heterogeneous layered porous media in the space–time domain could be solved without using a time-marching scheme. Numerical examples and a convergence analysis were carried out to validate the accuracy and the stability of the method. The results illustrate that an excellent agreement with the analytical solution was obtained. Additionally, the proposed method was relatively simple because we only needed to deal with the boundary data, even for the problems in the heterogeneous layered porous media. Finally, when compared with the conventional time-marching scheme, highly accurate solutions were obtained and the error accumulation from the time-marching scheme was avoided.

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Self-organized percolation in multi-layered structures

Cited by 15 publications

References 42 publications

Topological impact of constrained fracture growth

Topological impact of constrained fracture growth

CFD simulation of the wind field over a terrain with sand fences: Critical spacing for the wind shear velocity

Modeling Transient Flows in Heterogeneous Layered Porous Media Using the Space–Time Trefftz Method

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