A Certified Reduced Basis Method for the Fokker-Planck Equation of Dilute Polymeric Fluids: FENE Dumbbells in Extensional Flow
In this paper we present a reduced basis method for the parametrized Fokker–Planck equation associated with evolution of finitely extensible nonlinear elastic (FENE) dumbbells in a Newtonian solvent for a (prescribed) extensional macroscale flow. We apply a proper orthogonal decomposition (POD)–gree...
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| Format: | Article |
| Language: | en_US |
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Society for Industrial and Applied Mathematics (SIAM)
2011
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| Online Access: | http://hdl.handle.net/1721.1/61956 https://orcid.org/0000-0002-2631-6463 |
| _version_ | 1826194309538381824 |
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| author | Knezevic, David Patera, Anthony T. |
| author2 | Massachusetts Institute of Technology. Department of Mechanical Engineering |
| author_facet | Massachusetts Institute of Technology. Department of Mechanical Engineering Knezevic, David Patera, Anthony T. |
| author_sort | Knezevic, David |
| collection | MIT |
| description | In this paper we present a reduced basis method for the parametrized Fokker–Planck equation associated with evolution of finitely extensible nonlinear elastic (FENE) dumbbells in a Newtonian solvent for a (prescribed) extensional macroscale flow. We apply a proper orthogonal decomposition (POD)–greedy sampling procedure for the stable identification of optimal reduced basis spaces, and we develop a rigorous finite-time a posteriori bound for the error in the reduced basis prediction of the two outputs of interest—the optical anisotropy and the first normal stress difference. We present numerical results for stress-conformation hysteresis as a function of Weissenberg number and final time that demonstrate the rapid convergence of the reduced basis approximation and the effectiveness of the a posteriori error bounds. |
| first_indexed | 2024-09-23T09:54:04Z |
| format | Article |
| id | mit-1721.1/61956 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T09:54:04Z |
| publishDate | 2011 |
| publisher | Society for Industrial and Applied Mathematics (SIAM) |
| record_format | dspace |
| spelling | mit-1721.1/619562022-09-26T14:24:31Z A Certified Reduced Basis Method for the Fokker-Planck Equation of Dilute Polymeric Fluids: FENE Dumbbells in Extensional Flow Knezevic, David Patera, Anthony T. Massachusetts Institute of Technology. Department of Mechanical Engineering Patera, Anthony T. Knezevic, David Patera, Anthony T. In this paper we present a reduced basis method for the parametrized Fokker–Planck equation associated with evolution of finitely extensible nonlinear elastic (FENE) dumbbells in a Newtonian solvent for a (prescribed) extensional macroscale flow. We apply a proper orthogonal decomposition (POD)–greedy sampling procedure for the stable identification of optimal reduced basis spaces, and we develop a rigorous finite-time a posteriori bound for the error in the reduced basis prediction of the two outputs of interest—the optical anisotropy and the first normal stress difference. We present numerical results for stress-conformation hysteresis as a function of Weissenberg number and final time that demonstrate the rapid convergence of the reduced basis approximation and the effectiveness of the a posteriori error bounds. United States. Air Force Office of Scientific Research (AFOSR Grant FA 9550-07-1-0425) 2011-03-24T22:31:36Z 2011-03-24T22:31:36Z 2010-03 2009-05 Article http://purl.org/eprint/type/JournalArticle 1064-8275 1095-7197 http://hdl.handle.net/1721.1/61956 Knezevic, David J., and Anthony T. Patera. “A Certified Reduced Basis Method for the Fokker–Planck Equation of Dilute Polymeric Fluids: FENE Dumbbells in Extensional Flow.” SIAM Journal on Scientific Computing 32.2 (2010): 793. © 2010 Society for Industrial and Applied Mathematics https://orcid.org/0000-0002-2631-6463 en_US http://dx.doi.org/10.1137/090759239 SIAM Journal of Scientific Computing Creative Commons Attribution-Noncommercial-Share Alike 3.0 http://creativecommons.org/licenses/by-nc-sa/3.0/ application/pdf Society for Industrial and Applied Mathematics (SIAM) MIT web domain |
| spellingShingle | Knezevic, David Patera, Anthony T. A Certified Reduced Basis Method for the Fokker-Planck Equation of Dilute Polymeric Fluids: FENE Dumbbells in Extensional Flow |
| title | A Certified Reduced Basis Method for the Fokker-Planck Equation of Dilute Polymeric Fluids: FENE Dumbbells in Extensional Flow |
| title_full | A Certified Reduced Basis Method for the Fokker-Planck Equation of Dilute Polymeric Fluids: FENE Dumbbells in Extensional Flow |
| title_fullStr | A Certified Reduced Basis Method for the Fokker-Planck Equation of Dilute Polymeric Fluids: FENE Dumbbells in Extensional Flow |
| title_full_unstemmed | A Certified Reduced Basis Method for the Fokker-Planck Equation of Dilute Polymeric Fluids: FENE Dumbbells in Extensional Flow |
| title_short | A Certified Reduced Basis Method for the Fokker-Planck Equation of Dilute Polymeric Fluids: FENE Dumbbells in Extensional Flow |
| title_sort | certified reduced basis method for the fokker planck equation of dilute polymeric fluids fene dumbbells in extensional flow |
| url | http://hdl.handle.net/1721.1/61956 https://orcid.org/0000-0002-2631-6463 |
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