Comparison of the response to geometrical complexity of methods for unstationary simulations in discrete fracture networ
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ORIGINAL PAPER
Comparison of the response to geometrical complexity of methods for unstationary simulations in discrete fracture networks with conforming, polygonal, and non-matching grids Andrea Borio1 · Alessio Fumagalli1,2
· Stefano Scialo` 1
Received: 11 August 2019 / Accepted: 6 August 2020 © The Author(s) 2020
Abstract The aim of this study is to compare numerical methods for the simulation of single-phase flow and transport in fractured media, described here by means of the discrete fracture network (DFN) model. A Darcy problem is solved to compute the advective field, then used in a subsequent time-dependent transport-diffusion-reaction problem. The numerical schemes are benchmarked in terms of flexibility in handling geometrical complexity, mass conservation, and stability issues for advection-dominated flow regimes. To this end, two benchmark cases, along with an additional one from a previous work, have been specifically designed and are here proposed and investigated, representing some of the most critical issues encountered in DFN simulations. Keywords Discrete fracture network · Benchmark · Discretization methods · Domain decomposition · Non-matching grids · Polygonal grids Mathematics Subject Classification (2010) 02.60.Cb · 02.60.Lj · 02.70.Dh
1 Introduction The movement of liquids in the underground is heavily influenced by the presence of fractures and their relative intersections [25, 27, 28, 30, 41]. Fractures are discontinuities (here assumed planar) along which a rock has been broken, mainly due to geological movements or to artificial stimulation [48]. In this work, we are considering only open structures, characterized by a geometrical aperture, Members of the INdAM research group GNCS. Andrea Borio
[email protected] Alessio Fumagalli [email protected]; [email protected] Stefano Scial`o [email protected] 1
Dipartimento di Scienze Matematiche, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy
2
Present address: MOX - Dipartimento di Matematica “F. Brioschi”, Politecnico di Milano, via Bonardi 9, 20133 Milan, Italy
that allow a liquid to flow through [28]. Possibilities are actual fractures, faults, and joints. We are thus excluding low permeable (closed/impervious) objects such as veins or dykes. For particular underground compositions (e.g., granite, shale, or sandstone), the rock permeability is several orders of magnitude smaller than the fracture permeability. It is a common choice and a reasonable approximation to ignore the rock matrix effect in the simulations and rely only on the fractures. The framework is the discrete fracture network model (DFN), where the aperture is not a geometrical constraint but a parameter in the bidimensional representation of the fractures by reduced models; see [47] and the forthcoming references. The geometrical complexity of natural fracture networks may impose difficulties in the numerical simulations, due to the presence of small intersections between fractures, different intersection con
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