dc.contributor.author Alotaibi, M. dc.contributor.author Calo, Victor dc.contributor.author Efendiev, Y. dc.contributor.author Galvis, J. dc.contributor.author Ghommem, M. dc.date.accessioned 2017-03-24T11:53:50Z dc.date.available 2017-03-24T11:53:50Z dc.date.created 2017-03-23T06:59:55Z dc.date.issued 2015 dc.identifier.citation Alotaibi, M. and Calo, V. and Efendiev, Y. and Galvis, J. and Ghommem, M. 2015. Global-local nonlinear model reduction for flows in heterogeneous porous media. Computer Methods in Applied Mechanics and Engineering. 292: pp. 122-137. dc.identifier.uri http://hdl.handle.net/20.500.11937/51533 dc.identifier.doi 10.1016/j.cma.2014.10.034 dc.description.abstract In this paper, 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 a 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 significantly reduces 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. dc.title Global-local nonlinear model reduction for flows in heterogeneous porous media dc.type Journal Article dcterms.source.volume 292 dcterms.source.startPage 122 dcterms.source.endPage 137 dcterms.source.issn 0045-7825 dcterms.source.title Computer Methods in Applied Mechanics and Engineering curtin.department Department of Applied Geology curtin.accessStatus Open access
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