Journal
SIAM JOURNAL ON SCIENTIFIC COMPUTING
Volume 32, Issue 2, Pages 793-817Publisher
SIAM PUBLICATIONS
DOI: 10.1137/090759239
Keywords
reduced basis methods; POD; greedy algorithm; a posteriori error estimation; Fokker-Planck equation; FENE dumbbells; polymeric fluids; micro-macro model
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Funding
- AFOSR [FA 9550-07-1-0425]
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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.
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