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    Global-local nonlinear model reduction for flows in heterogeneous porous media

    250790.pdf (469.5Kb)
    Access Status
    Open access
    Authors
    Alotaibi, M.
    Calo, Victor
    Efendiev, Y.
    Galvis, J.
    Ghommem, M.
    Date
    2015
    Type
    Journal Article
    
    Metadata
    Show full item record
    Citation
    Alotaibi, M. and Calo, V. and Efendiev, Y. and Galvis, J. and Ghommem, M. 2015. Global-local nonlinear model reduction for flows in heterogeneous porous media. Computer Methods in Applied Mechanics and Engineering. 292: pp. 122-137.
    Source Title
    Computer Methods in Applied Mechanics and Engineering
    DOI
    10.1016/j.cma.2014.10.034
    ISSN
    0045-7825
    School
    Department of Applied Geology
    URI
    http://hdl.handle.net/20.500.11937/51533
    Collection
    • Curtin Research Publications
    Abstract

    In this paper, we combine discrete empirical interpolation techniques, global mode decomposition methods, and local multiscale methods, such as the Generalized Multiscale Finite Element Method (GMsFEM), to reduce the computational complexity associated with nonlinear flows in highly-heterogeneous porous media. To solve the nonlinear governing equations, we employ the GMsFEM to represent the solution on a coarse grid with multiscale basis functions and apply proper orthogonal decomposition on a coarse grid. Computing the GMsFEM solution involves calculating the residual and the Jacobian on a fine grid. As such, we use local and global empirical interpolation concepts to circumvent performing these computations on the fine grid. The resulting reduced-order approach significantly reduces the flow problem size while accurately capturing the behavior of fully-resolved solutions. We consider several numerical examples of nonlinear multiscale partial differential equations that are numerically integrated using fully-implicit time marching schemes to demonstrate the capability of the proposed model reduction approach to speed up simulations of nonlinear flows in high-contrast porous media.

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