A Certified Reduced Basis Method for the Fokker-Planck Equation of Dilute Polymeric Fluids: FENE Dumbbells in Extensional Flow
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Patera_A certified.pdf
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Author(s)
Knezevic, David
Patera, Anthony T.
Date Issued
March 2010
Journal
SIAM Journal of Scientific Computing
Publisher
Society for Industrial and Applied Mathematics (SIAM)
Citation
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
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Author's final manuscript
Abstract
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.
MIT Department
Massachusetts Institute of Technology. Department of Mechanical Engineering
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DOI of Published Version
https://doi.org/10.1137/090759239
