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H 1 Multiscale model reduction for flows in heterogeneous porous media

Auteurs : Calo, Victor (Auteur de la Conférence)
CIRM (Editeur )

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    Résumé : 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 the 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 enables a significant reduction in 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.

    Keywords: generalized multiscale finite element method - nonlinear PDEs - heterogeneous porous media - discrete empirical interpolation - proper orthogonal decomposition

    Codes MSC :
    35-XX - Partial differential equations
    65-XX - Numerical analysis
    86-XX - Geophysics [See also 76U05, 76V05]

      Informations sur la Vidéo

      Langue : Anglais
      Date de publication : 27/11/14
      Date de captation : 19/11/14
      Collection : Research talks ; Analysis and its Applications ; Computer Science ; Control Theory and Optimization ; Partial Differential Equations ; Mathematical Physics ; Mathematics in Science and Technology ; Numerical Analysis and Scientific Computing
      Format : quicktime ; audio/x-aac
      Durée : 00:55:02
      Domaine : Analysis and its Applications ; Numerical Analysis & Scientific Computing ; Computer Science ; Control Theory & Optimization ; PDE ; Mathematical Physics ; Mathematics in Science & Technology
      Audience : Chercheurs ; Doctorants , Post - Doctorants
      Download : https://videos.cirm-math.fr/2014-11-19_Calo_1.mp4

    Informations sur la rencontre

    Nom de la rencontre : MoMaS Conference / Colloque MoMaS
    Organisateurs de la rencontre : Allaire, Grégoire ; Cances, Clément ; Ern, Alexandre ; Herbin, Raphaèle ; Lelièvre, Tony
    Dates : 17/11/14 - 20/11/14
    Année de la rencontre : 2014
    URL Congrès : https://www.cirm-math.fr/Archives/?EX=in...

    Citation Data

    DOI : 10.24350/CIRM.V.18630803
    Cite this video as: Calo, Victor (2014). Multiscale model reduction for flows in heterogeneous porous media. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.18630803
    URI : http://dx.doi.org/10.24350/CIRM.V.18630803


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