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Constrained energy minimization based upscaling for coupled flow and mechanics

Maria Vasilyeva Tsz Shun Eric CHUNG Yalchin Efendiev Jihoon Kim

Fluid Dynamics and Shock Waves mathscidoc:1910.43502

Journal of Computational Physics, 376, 660-674, 2019.1
In this paper, our aim is to present (1) an embedded fracture model (EFM) for coupled flow and mechanics problem based on the dual continuum approach on the fine grid and (2) an upscaled model for the resulting fine grid equations. The mathematical model is described by the coupled system of equation for displacement, fracture and matrix pressures. For a fine grid approximation, we use the finite volume method for flow problem and finite element method for mechanics. Due to the complexity of fractures, solutions have a variety of scales, and fine grid approximation results in a large discrete system. Our second focus in the construction of the upscaled coarse grid poroelasticity model for fractured media. Our upscaled approach is based on the nonlocal multicontinuum (NLMC) upscaling for coupled flow and mechanics problem, which involves computations of local basis functions via an energy minimization
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@inproceedings{maria2019constrained,
  title={Constrained energy minimization based upscaling for coupled flow and mechanics},
  author={Maria Vasilyeva, Tsz Shun Eric CHUNG, Yalchin Efendiev, and Jihoon Kim},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020181157466986031},
  booktitle={Journal of Computational Physics},
  volume={376},
  pages={660-674},
  year={2019},
}
Maria Vasilyeva, Tsz Shun Eric CHUNG, Yalchin Efendiev, and Jihoon Kim. Constrained energy minimization based upscaling for coupled flow and mechanics. 2019. Vol. 376. In Journal of Computational Physics. pp.660-674. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020181157466986031.
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