Previous |  Up |  Next


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:
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:
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


Files Size Format View
Kybernetika_43-2007-4_17.pdf 773.7Kb application/pdf View/Open
Back to standard record
Partner of
EuDML logo