Global-local nonlinear model reduction for flows in heterogeneous porous media
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 po...
| Main Authors: | , , , , |
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| Format: | Journal Article |
| Published: |
2015
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| Online Access: | http://hdl.handle.net/20.500.11937/51533 |
| _version_ | 1848758722113830912 |
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| author | Alotaibi, M. Calo, Victor Efendiev, Y. Galvis, J. Ghommem, M. |
| author_facet | Alotaibi, M. Calo, Victor Efendiev, Y. Galvis, J. Ghommem, M. |
| author_sort | Alotaibi, M. |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | 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. |
| first_indexed | 2025-11-14T09:48:30Z |
| format | Journal Article |
| id | curtin-20.500.11937-51533 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T09:48:30Z |
| publishDate | 2015 |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-515332017-09-13T15:47:18Z Global-local nonlinear model reduction for flows in heterogeneous porous media Alotaibi, M. Calo, Victor Efendiev, Y. Galvis, J. Ghommem, M. 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. 2015 Journal Article http://hdl.handle.net/20.500.11937/51533 10.1016/j.cma.2014.10.034 fulltext |
| spellingShingle | Alotaibi, M. Calo, Victor Efendiev, Y. Galvis, J. Ghommem, M. Global-local nonlinear model reduction for flows in heterogeneous porous media |
| title | Global-local nonlinear model reduction for flows in heterogeneous porous media |
| title_full | Global-local nonlinear model reduction for flows in heterogeneous porous media |
| title_fullStr | Global-local nonlinear model reduction for flows in heterogeneous porous media |
| title_full_unstemmed | Global-local nonlinear model reduction for flows in heterogeneous porous media |
| title_short | Global-local nonlinear model reduction for flows in heterogeneous porous media |
| title_sort | global-local nonlinear model reduction for flows in heterogeneous porous media |
| url | http://hdl.handle.net/20.500.11937/51533 |