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# Article

 Title: A novel approach to modelling of flow in fractured porous medium (English) Author: Šembera, Jan Author: Maryška, Jiří Author: Královcová, Jiřina Author: Severýn, Otto Language: English Journal: Kybernetika ISSN: 0023-5954 Volume: 43 Issue: 4 Year: 2007 Pages: 577-588 Summary lang: English . Category: math . Summary: There are many problems of groundwater flow in a disrupted rock massifs that should be modelled using numerical models. It can be done via “standard approaches” such as increase of the permeability of the porous medium to account the fracture system (or double-porosity models), or discrete stochastic fracture network models. Both of these approaches appear to have their constraints and limitations, which make them unsuitable for the large- scale long-time hydrogeological calculations. In the article, a new approach to the modelling of groudwater flow in fractured porous medium, which combines the above-mentioned models, is described. This article presents the mathematical formulation and demonstration of numerical results obtained by this new approach. The approach considers three substantial types of objects within a structure of modelled massif important for the groudwater flow – small stochastic fractures, large deterministic fractures, and lines of intersection of the large fractures. The systems of stochastic fractures are represented by blocks of porous medium with suitably set hydraulic conductivity. The large fractures are represented as polygons placed in 3D space and their intersections are represented by lines. Thus flow in 3D porous medium, flow in 2D and 1D fracture systems, and communication among these three systems are modelled together. (English) Keyword: finite element method Keyword: Darcy’s flow Keyword: fractured porous medium MSC: 65N30 MSC: 76M10 MSC: 76S05 MSC: 86A05 idZBL: Zbl 1220.76042 idMR: MR2377934 . Date available: 2009-09-24T20:27:16Z Last updated: 2013-09-21 Stable URL: http://hdl.handle.net/10338.dmlcz/135798 . Reference: [1] Bogdanov I. I., Mourzenko V. V., Thovert J. F., Adler P. M.: Effective permeability of fractured porous media in steady state flow.Water Res. Research 39 (2003), 1023–1038 Reference: [2] Diodato D. M.: Compendium of Fracture Flow Models.Center for Environmental Restoration Systems, Energy Systems Division, Argonne National Laboratory, USA 1994. Available on: http://www.thehydrogeologist.com/docs/cffm/cffmtoc.htm Reference: [3] Kaasschieter E. F., Huijben A. J. M.: Mixed-hybrid finite elements and streamline computation for the potential flow problem.Numer. Methods Partial Differential Equations 8 (1992), 221–266 Zbl 0767.76029, MR 1158244, 10.1002/num.1690080302 Reference: [4] Maryška J.: Approximation of the Mixed-hybrid Formulation of the Porous Media Flow Problem (in Czech).Technical Report No. 609, Institute of Computer Science of the Academy of Sciences of the Czech Republic, Prague 1995 Reference: [5] Maryška J., Rozložník, M., Tůma M.: Mixed-hybrid finite-element approximation of the potential fluid-flow problem.J. Comput. Appl. Math. 63 (1995), 383–392 Zbl 0852.76045, MR 1365577, 10.1016/0377-0427(95)00066-6 Reference: [6] Maryška J., Rozložník, M., Tůma M.: Schur complement systems in the mixed-hybrid finite element approximation of the potential fluid flow problem.SIAM J. Sci. Comput. 22 (2000), 704–723 Zbl 0978.76052, MR 1780621, 10.1137/S1064827598339608 Reference: [7] Maryška J., Severýn, O., Vohralík M.: Mixed-hybrid finite elements and streamline computation for the potential flow problem.Computational Geosciences 18 (2005), 8/3, 217–234 Reference: [8] Vohralík M., Maryška, J., Severýn O.: Mixed and nonconforming finite element methods on a system of polygons.To appear in Appl. Numer. Math Zbl 1112.65123, MR 2294120 .

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