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

In: Numerical Mathematics and Advanced Applications 2011

Author

Listed:
  • A. Fumagalli

    (Politecnico di Milano, MOX Laboratory, Department of Mathematics)

  • A. Scotti

    (Politecnico di Milano, MOX Laboratory, Department of Mathematics)

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.

Suggested Citation

  • A. Fumagalli & A. Scotti, 2013. "A Reduced Model for Flow and Transport in Fractured Porous Media with Non-matching Grids," Springer Books, in: Andrea Cangiani & Ruslan L. Davidchack & Emmanuil Georgoulis & Alexander N. Gorban & Jeremy Levesley (ed.), Numerical Mathematics and Advanced Applications 2011, edition 127, pages 499-507, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-33134-3_53
    DOI: 10.1007/978-3-642-33134-3_53
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