Upscaled Model for Mixed Dimensional Coupled Flow Problem in Fractured Porous Media Using Non-local Multicontinuum (NLMC) Method

  • Maria VasilyevaEmail author
  • Eric T. Chung
  • Yalchin Efendiev
  • Wing Tat Leung
  • Yating Wang
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11386)


In this paper, we consider a mixed dimensional discrete fracture model with highly conductive fractures. Mathematically the problem is described by a coupled system of equations consisting a d - dimensional equation for flow in porous matrix and a \((d-1)\) - dimensional equation for fracture networks with a specific exchange term for coupling them. For the numerical solution on the fine grid, we construct unstructured mesh that is conforming with fracture surface and use the finite element approximation. Fine grid approximation typically leads to very large systems of equations since it resolves the fracture networks, and therefore some multiscale methods or upscaling methods should be applied. The main contribution of this paper is that we propose a new upscaled model using Non-local multi-continuum (NLMC) method and construct an effective coarse grid approximation. The upscaled model has only one additional coarse degree of freedom (DOF) for each fracture network. We will present results of the numerical simulations using our proposed upscaling method to illustrate its performance.


Fractured porous media Fluid flow Coupled system Upscaling Multiscale method Non-local multi-continuum method 



MV’s work is supported by the grant of the Russian Scientific Found N17-71-20055. YE’s is supported by the mega-grant of the Russian Federation Government (N 14.Y26.31.0013). EC’s work is partially supported by Hong Kong RGC General Research Fund (Project 14317516) and CUHK Direct Grant for Research 2016-17


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Maria Vasilyeva
    • 1
    • 2
    Email author
  • Eric T. Chung
    • 3
  • Yalchin Efendiev
    • 1
    • 4
  • Wing Tat Leung
    • 5
  • Yating Wang
    • 4
  1. 1.Institute for Scientific ComputationTexas A&M UniversityCollege StationUSA
  2. 2.North-Eastern Federal UniversityYakutskRussia
  3. 3.Department of MathematicsThe Chinese University of Hong Kong (CUHK)ShatinHong Kong
  4. 4.Department of MathematicsTexas A&M UniversityCollege StationUSA
  5. 5.Institute of Computational Engineering and SciencesUniversity of Texas at AustinAustinUSA

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