From discrete to continuum concepts of flow in fractured porous media

Tatomir, A.B.

doi:10.18419/opus-476

Cited by 5 publications

(2 citation statements)

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“…Hackbusch (1989); Helmig (1997)), the box-dfm scheme was introduced in Reichenberger et al (2006) for two-phase flow in fractured porous media. The reduction to single-phase flow is straightforward, and we refer to Reichenberger et al (2006); Tatomir (2012) for further details. It should be mentioned that this scheme does not exactly solve (8)-( 11).…”

Section: Discretization Schemesmentioning

confidence: 99%

Comparison of cell- and vertex-centered finite-volume schemes for flow in fractured porous media

Gläser¹,

Schneider²,

Flemisch³

et al. 2020

Preprint

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Flow in fractured porous media is of high relevance in a variety of geotechnical applications, given the fact that they ubiquitously occur in nature and that they can have a substantial impact on the hydraulic properties of rock. As a response to this, an active field of research has developed over the past decades, focussing on the development of mathematical models and numerical methods to describe and simulate the flow processes in fractured rock. In this work, we present a comparison of different finite volume-based numerical schemes for the simulation of flow in fractured porous media by means of numerical experiments. Two novel vertex-centered approaches are presented and compared to well-established numerical schemes in terms of convergence behaviour and their performance on benchmark studies taken from the literature. The new schemes show to produce results that are in good agreement with those of established methods while being computationally less expensive on unstructured simplex grids.

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Section: Discretization Schemesmentioning

confidence: 99%

Comparison of cell- and vertex-centered finite-volume schemes for flow in fractured porous media

Gläser¹,

Schneider²,

Flemisch³

et al. 2020

Preprint

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“…1) Partial differential equations solvers (referred to here as direct simulations, DS) using the finite element method (FEM), the finite volume method (FVM), or other methods on discrete meshes [e.g. Pruess et al, 1999, Diersch, 2013, Tatomir, 2013, Lang et al, 2014, Hyman et al, 2015, Settgast et al, 2017. 2) Analytical approximations of the equivalent permeability of the fractured rock, based on fracture and fracture-network properties [e.g.…”

Section: Introductionmentioning

confidence: 99%

Estimating fluid flow rates through fracture networks using combinatorial optimization

Hobé

Vogler

Seybold

et al. 2018

Advances in Water Resources

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To enable fast uncertainty quantification of fluid flow in a discrete fracture network (DFN), we present two approaches to quickly compute fluid flow in DFNs using combinatorial optimization algorithms. Specifically, the presented Hanan Shortest Path Maxflow (HSPM) and Intersection Shortest Path Maxflow (ISPM) methods translate DFN geometries and properties to a graph on which a max flow algorithm computes a combinatorial flow, from which an overall fluid flow rate is estimated using a shortest path decomposition of this flow. The two approaches are assessed by comparing their predictions with results from explicit numerical simulations of simple test cases as well as stochastic DFN realizations covering a range of fracture densities. Both methods have a high accuracy and very low computational cost, which can facilitate much-needed in-depth analyses of the propagation of uncertainty in fracture and fracture-network properties to fluid flow rates.

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A hybrid-dimensional discrete fracture model for non-isothermal two-phase flow in fractured porous media

et al. 2019

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From discrete to continuum concepts of flow in fractured porous media

Cited by 5 publications

References 0 publications

Comparison of cell- and vertex-centered finite-volume schemes for flow in fractured porous media

Comparison of cell- and vertex-centered finite-volume schemes for flow in fractured porous media

Estimating fluid flow rates through fracture networks using combinatorial optimization

A hybrid-dimensional discrete fracture model for non-isothermal two-phase flow in fractured porous media

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