Mode decomposition methods for flows in high-contrast porous media. Global-local approach
Type
ArticleKAUST Department
Applied Mathematics and Computational Science ProgramComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Earth Science and Engineering Program
Environmental Science and Engineering Program
Numerical Porous Media SRI Center (NumPor)
Physical Science and Engineering (PSE) Division
Date
2013-11Preprint Posting Date
2013-01-24Permanent link to this record
http://hdl.handle.net/10754/563058
Metadata
Show full item recordAbstract
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.Citation
Ghommem, M., Presho, M., Calo, V. M., & Efendiev, Y. (2013). Mode decomposition methods for flows in high-contrast porous media. Global–local approach. Journal of Computational Physics, 253, 226–238. doi:10.1016/j.jcp.2013.06.033Sponsors
YE's work is partially supported by the US DoD, DOE and NSF (DMS 0934837, DMS 0724704, and DMS 0811180).Publisher
Elsevier BVJournal
Journal of Computational PhysicsarXiv
1301.5742Additional Links
http://arxiv.org/abs/arXiv:1301.5742v1ae974a485f413a2113503eed53cd6c53
10.1016/j.jcp.2013.06.033