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    Mode decomposition methods for flows in high-contrast porous media. Global-local approach

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    Type
    Article
    Authors
    Ghommem, Mehdi
    Presho, Michael
    Calo, Victor M. cc
    Efendiev, Yalchin R. cc
    KAUST Department
    Applied Mathematics and Computational Science Program
    Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
    Earth Science and Engineering Program
    Environmental Science and Engineering Program
    Numerical Porous Media SRI Center (NumPor)
    Physical Science and Engineering (PSE) Division
    Date
    2013-11
    Preprint Posting Date
    2013-01-24
    Permanent link to this record
    http://hdl.handle.net/10754/563058
    
    Metadata
    Show full item record
    Abstract
    In this paper, we combine concepts of the generalized multiscale finite element method (GMsFEM) and mode decomposition methods to construct a robust global-local approach for model reduction of flows in high-contrast porous media. This is achieved by implementing Proper Orthogonal Decomposition (POD) and Dynamic Mode Decomposition (DMD) techniques on a coarse grid computed using GMsFEM. The resulting reduced-order approach enables a significant reduction in the flow problem size while accurately capturing the behavior of fully-resolved solutions. We consider a variety of high-contrast coefficients and present the corresponding numerical results to illustrate the effectiveness of the proposed technique. This paper is a continuation of our work presented in Ghommem et al. (2013) [1] where we examine the applicability of POD and DMD to derive simplified and reliable representations of flows in high-contrast porous media on fully resolved models. In the current paper, we discuss how these global model reduction approaches can be combined with local techniques to speed-up the simulations. The speed-up is due to inexpensive, while sufficiently accurate, computations of global snapshots. © 2013 Elsevier Inc.
    Citation
    Ghommem, M., Presho, M., Calo, V. M., & Efendiev, Y. (2013). Mode decomposition methods for flows in high-contrast porous media. Global–local approach. Journal of Computational Physics, 253, 226–238. doi:10.1016/j.jcp.2013.06.033
    Sponsors
    YE's work is partially supported by the US DoD, DOE and NSF (DMS 0934837, DMS 0724704, and DMS 0811180).
    Publisher
    Elsevier BV
    Journal
    Journal of Computational Physics
    DOI
    10.1016/j.jcp.2013.06.033
    arXiv
    1301.5742
    Additional Links
    http://arxiv.org/abs/arXiv:1301.5742v1
    ae974a485f413a2113503eed53cd6c53
    10.1016/j.jcp.2013.06.033
    Scopus Count
    Collections
    Articles; Environmental Science and Engineering Program; Applied Mathematics and Computational Science Program; Physical Science and Engineering (PSE) Division; Earth Science and Engineering Program; Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division

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