Mode decomposition methods for flows in high-contrast porous media. Global-local approach
KAUST DepartmentNumerical Porous Media SRI Center (NumPor)
Applied Mathematics and Computational Science Program
Earth Science and Engineering Program
Physical Sciences and Engineering (PSE) Division
Environmental Science and Engineering Program
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
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AbstractIn 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)  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.
SponsorsYE's work is partially supported by the US DoD, DOE and NSF (DMS 0934837, DMS 0724704, and DMS 0811180).
JournalJournal of Computational Physics