Mode decomposition methods for flows in high-contrast porous media. Global-local approach Academic Article uri icon

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.

published proceedings

  • JOURNAL OF COMPUTATIONAL PHYSICS

author list (cited authors)

  • Ghommem, M., Presho, M., Calo, V. M., & Efendiev, Y.

citation count

  • 51

complete list of authors

  • Ghommem, Mehdi||Presho, Michael||Calo, Victor M||Efendiev, Yalchin

publication date

  • November 2013