Coupling of multiscale and multi-continuum approaches

Tsz Shun Eric CHUNG Yalchin Efendiev Tat Leung Maria Vasilyeva

Numerical Analysis and Scientific Computing mathscidoc:1910.43485

GEM-International Journal on Geomathematics, 8, (1), 9-41, 2017.4
Simulating complex processes in fractured media requires some type of model reduction. Well-known approaches include multi-continuum techniques, which have been commonly used in approximating subgrid effects for flow and transport in fractured media. Our goal in this paper is to (1) show a relation between multi-continuum approaches and Generalized Multiscale Finite Element Method (GMsFEM) and (2) to discuss coupling these approaches for solving problems in complex multiscale fractured media. The GMsFEM, a systematic approach, constructs multiscale basis functions via local spectral decomposition in pre-computed snapshot spaces. We show that GMsFEM can automatically identify separate fracture networks via local spectral problems. We discuss the relation between these basis functions and continuums in multi-continuum methods. The GMsFEM can automatically detect each
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  title={Coupling of multiscale and multi-continuum approaches},
  author={Tsz Shun Eric CHUNG, Yalchin Efendiev, Tat Leung, and Maria Vasilyeva},
  booktitle={GEM-International Journal on Geomathematics},
Tsz Shun Eric CHUNG, Yalchin Efendiev, Tat Leung, and Maria Vasilyeva. Coupling of multiscale and multi-continuum approaches. 2017. Vol. 8. In GEM-International Journal on Geomathematics. pp.9-41.
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