Non-local multi-continua upscaling for flows in heterogeneous fractured media

Tsz Shun Eric CHUNG Yalchin Efendiev Wing Tat Leung Maria Vasilyeva Yating Wang

Fluid Dynamics and Shock Waves mathscidoc:1910.43491

Journal of Computational Physics, 372, 22-34, 2018.11
In this paper, we propose a rigorous and accurate non-local (in the oversampled region) upscaling framework based on some recently developed multiscale methods [10]. Our proposed method consists of identifying multi-continua parameters via local basis functions and constructing non-local (in the oversampled region) transfer and effective properties. To achieve this, we significantly modify our recent work proposed within Generalized Multiscale Finite Element Method (GMsFEM) in [10] and derive appropriate local problems in oversampled regions once we identify important modes representing each continuum. We use piecewise constant functions in each fracture network and in the matrix to write an upscaled equation. Thus, the resulting upscaled equation is of minimal size and the unknowns are average pressures in the fractures and the matrix. Note that the use of non-local upscaled model for porous
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@inproceedings{tsz2018non-local,
  title={Non-local multi-continua upscaling for flows in heterogeneous fractured media},
  author={Tsz Shun Eric CHUNG, Yalchin Efendiev, Wing Tat Leung, Maria Vasilyeva, and Yating Wang},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020180814702563020},
  booktitle={Journal of Computational Physics},
  volume={372},
  pages={22-34},
  year={2018},
}
Tsz Shun Eric CHUNG, Yalchin Efendiev, Wing Tat Leung, Maria Vasilyeva, and Yating Wang. Non-local multi-continua upscaling for flows in heterogeneous fractured media. 2018. Vol. 372. In Journal of Computational Physics. pp.22-34. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020180814702563020.
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