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

Mehdi Ghommem, Michael Presho, Victor M. Calo, Yalchin R. Efendiev

Research output: Contribution to journalArticlepeer-review

50 Scopus citations

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.
Original languageEnglish (US)
Pages (from-to)226-238
Number of pages13
JournalJournal of Computational Physics
Volume253
DOIs
StatePublished - Nov 2013

ASJC Scopus subject areas

  • Physics and Astronomy (miscellaneous)
  • Computer Science Applications

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