Parametric Nonlinear Model Reduction Using K-Means Clustering for Miscible Flow Simulation
Joint Authors
Sukuntee, Norapon
Chaturantabut, Saifon
Source
Journal of Applied Mathematics
Issue
Vol. 2020, Issue 2020 (31 Dec. 2020), pp.1-12, 12 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2020-09-04
Country of Publication
Egypt
No. of Pages
12
Main Subjects
Abstract EN
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.
American Psychological Association (APA)
Sukuntee, Norapon& Chaturantabut, Saifon. 2020. Parametric Nonlinear Model Reduction Using K-Means Clustering for Miscible Flow Simulation. Journal of Applied Mathematics،Vol. 2020, no. 2020, pp.1-12.
https://search.emarefa.net/detail/BIM-1174515
Modern Language Association (MLA)
Sukuntee, Norapon& Chaturantabut, Saifon. Parametric Nonlinear Model Reduction Using K-Means Clustering for Miscible Flow Simulation. Journal of Applied Mathematics No. 2020 (2020), pp.1-12.
https://search.emarefa.net/detail/BIM-1174515
American Medical Association (AMA)
Sukuntee, Norapon& Chaturantabut, Saifon. Parametric Nonlinear Model Reduction Using K-Means Clustering for Miscible Flow Simulation. Journal of Applied Mathematics. 2020. Vol. 2020, no. 2020, pp.1-12.
https://search.emarefa.net/detail/BIM-1174515
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1174515