Parametric Nonlinear Model Reduction Using K-Means Clustering for Miscible Flow Simulation
This work considers the model order reduction approach for parametrized viscous fingering in a horizontal flow through a 2D porous media domain. A technique for constructing an optimal low-dimensional basis for a multidimensional parameter domain is introduced by combining K-means clustering with pr...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2020-01-01
|
| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2020/3904606 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832554347694653440 |
|---|---|
| author | Norapon Sukuntee Saifon Chaturantabut |
| author_facet | Norapon Sukuntee Saifon Chaturantabut |
| author_sort | Norapon Sukuntee |
| collection | DOAJ |
| description | This work considers the model order reduction approach for parametrized viscous fingering in a horizontal flow through a 2D porous media domain. A technique for constructing an optimal low-dimensional basis for a multidimensional parameter domain is introduced by combining K-means clustering with proper orthogonal decomposition (POD). In particular, we first randomly generate parameter vectors in multidimensional parameter domain of interest. Next, we perform the K-means clustering algorithm on these parameter vectors to find the centroids. POD basis is then generated from the solutions of the parametrized systems corresponding to these parameter centroids. The resulting POD basis is then used with Galerkin projection to construct reduced-order systems for various parameter vectors in the given domain together with applying the discrete empirical interpolation method (DEIM) to further reduce the computational complexity in nonlinear terms of the miscible flow model. The numerical results with varying different parameters are demonstrated to be efficient in decreasing simulation time while maintaining accuracy compared to the full-order model for various parameter values. |
| format | Article |
| id | doaj-art-302a11f45c4644f9a1b30551b8087f0e |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-302a11f45c4644f9a1b30551b8087f0e2025-02-03T05:51:47ZengWileyJournal of Applied Mathematics1110-757X1687-00422020-01-01202010.1155/2020/39046063904606Parametric Nonlinear Model Reduction Using K-Means Clustering for Miscible Flow SimulationNorapon Sukuntee0Saifon Chaturantabut1Department of Mathematics and Statistics, Faculty of Science and Technology, Thammasat University, Pathum Thani 12120, ThailandDepartment of Mathematics and Statistics, Faculty of Science and Technology, Thammasat University, Pathum Thani 12120, ThailandThis work considers the model order reduction approach for parametrized viscous fingering in a horizontal flow through a 2D porous media domain. A technique for constructing an optimal low-dimensional basis for a multidimensional parameter domain is introduced by combining K-means clustering with proper orthogonal decomposition (POD). In particular, we first randomly generate parameter vectors in multidimensional parameter domain of interest. Next, we perform the K-means clustering algorithm on these parameter vectors to find the centroids. POD basis is then generated from the solutions of the parametrized systems corresponding to these parameter centroids. The resulting POD basis is then used with Galerkin projection to construct reduced-order systems for various parameter vectors in the given domain together with applying the discrete empirical interpolation method (DEIM) to further reduce the computational complexity in nonlinear terms of the miscible flow model. The numerical results with varying different parameters are demonstrated to be efficient in decreasing simulation time while maintaining accuracy compared to the full-order model for various parameter values.http://dx.doi.org/10.1155/2020/3904606 |
| spellingShingle | Norapon Sukuntee Saifon Chaturantabut Parametric Nonlinear Model Reduction Using K-Means Clustering for Miscible Flow Simulation Journal of Applied Mathematics |
| title | Parametric Nonlinear Model Reduction Using K-Means Clustering for Miscible Flow Simulation |
| title_full | Parametric Nonlinear Model Reduction Using K-Means Clustering for Miscible Flow Simulation |
| title_fullStr | Parametric Nonlinear Model Reduction Using K-Means Clustering for Miscible Flow Simulation |
| title_full_unstemmed | Parametric Nonlinear Model Reduction Using K-Means Clustering for Miscible Flow Simulation |
| title_short | Parametric Nonlinear Model Reduction Using K-Means Clustering for Miscible Flow Simulation |
| title_sort | parametric nonlinear model reduction using k means clustering for miscible flow simulation |
| url | http://dx.doi.org/10.1155/2020/3904606 |
| work_keys_str_mv | AT noraponsukuntee parametricnonlinearmodelreductionusingkmeansclusteringformiscibleflowsimulation AT saifonchaturantabut parametricnonlinearmodelreductionusingkmeansclusteringformiscibleflowsimulation |