Advertisement

A Reduced Model for Flow and Transport in Fractured Porous Media with Non-matching Grids

  • A. FumagalliEmail author
  • A. ScottiEmail author
Conference paper

Abstract

In this work we focus on a model reduction approach for the treatment of fractures in a porous medium, represented as interfaces embedded in a n-dimensional domain, in the form of a (n − 1)-dimensional manifold, to describe fluid flow and transport in both domains. We employ a method that allows for non-matching grids, thus very advantageous if the position of the fractures is uncertain and multiple simulations are required. To this purpose we adopt an extended finite element approach, XFEM, to represent discontinuities of the variables at the interfaces, which can arbitrarily cut the elements of the grid. The method is applied to the solution of the Darcy and advection-diffusion problems in porous media.

Keywords

Porous Medium Transport Problem Passive Scalar Mixed Finite Element Mixed Finite Element Method 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    Clarisse Alboin, Jérôme Jaffré, Jean E. Roberts, Xuewen Wang, and Christophe Serres. Domain decomposition for some transmission problems in flow in porous media, volume 552 of Lecture Notes in Phys., pages 22–34. Springer, Berlin, 2000.Google Scholar
  2. 2.
    Philippe Angot, Franck Boyer, and Florence Hubert. Asymptotic and numerical modelling of flows in fractured porous media. M2AN Math. Model. Numer. Anal., 43(2):239–275, 2009.Google Scholar
  3. 3.
    Fabian Brunner, Florin Adrian Radu, Markus Bause, and Peter Knabner. Optimal order convergence of a modified BDM 1 mixed finite element scheme for reactive transport in porous media. Advances in Water Resources, 35:163–171, 2012.Google Scholar
  4. 4.
    Carlo D’Angelo and Anna Scotti. A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis, 46(02):465–489, 2012.CrossRefGoogle Scholar
  5. 5.
    Alessio Fumagalli. Numerical Modelling of Flows in Fractured Porous Media by the XFEM Method. PhD thesis, Politecnico di Milano, 2012.Google Scholar
  6. 6.
    Alessio Fumagalli and Anna Scotti. Numerical modelling of multiphase subsurface flow in the presence of fractures. Communications in Applied and Industrial Mathematics, December 2011. In press.Google Scholar
  7. 7.
    Anita Hansbo and Peter Hansbo. An unfitted finite element method, based on Nitsche’s method, for elliptic interface problems. Comput. Methods Appl. Mech. Engrg., 191(47–48):5537–5552, 2002.Google Scholar
  8. 8.
    Vincent Martin, Jérôme Jaffré, and Jean E. Roberts. Modeling fractures and barriers as interfaces for flow in porous media. SIAM J. Sci. Comput., 26(5):1667–1691, 2005.Google Scholar
  9. 9.
    Nicolas Moës, John Dolbow, and Ted Belytschko. A finite element method for crack growth without remeshing. Int. J. for Numerical Methods in Eng., 46(1):131–150, 1999.Google Scholar
  10. 10.
    Florin Adrian Radu, Iuliu Sorin Pop, and Sabine Attinger. Analysis of an Euler implicit - mixed finite element scheme for reactive solute transport in porous media. Numer. Methods Part. Differ. Equat., 26:320–344, 2010.Google Scholar
  11. 11.
    Riccardo Sacco and Fausto Saleri. Stabilized mixed finite volume methods for convection-diffusion problems. East-West J. Numer. Math., 5(4):291–311, 1997.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.MOX Laboratory, Department of MathematicsPolitecnico di MilanoMilanItaly

Personalised recommendations