The prediction of plane Couette flow for a FENE fluid using a reduced basis approximation of the Fokker-Planck equation

Leonenko, Ganna M. ORCID: https://orcid.org/0000-0001-8025-661X and Phillips, Timothy Nigel ORCID: https://orcid.org/0000-0001-6455-1205 2011. The prediction of plane Couette flow for a FENE fluid using a reduced basis approximation of the Fokker-Planck equation. International Journal for Multiscale Computational Engineering 9 (1) , pp. 73-88. 10.1615/IntJMultCompEng.v9.i1.60

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Abstract

The start-up of plane Couette flow of a finitely extensible nonlinear elastic (FENE) fluid is considered. A numerical method for solving this problem based on a decoupled micro{macro approach is described. The polymeric stress is determined in the microscopic part of the calculation by computing the solution of a Fokker-Planck equation for the configuration probability density function. The solution of this equation often suffers from the so-called problem of "curse of dimensionality." An efficient solution procedure is described based on the use of an adaptive reduced basis function technique in conjunction with high-order spectral approximations. A substantial reduction in the number of degrees of freedom to achieve a required level of accuracy is obtained compared with standard tensor product representation of the basis. Some sample numerical results are presented to highlight properties of the model and the numerical scheme.

Item Type:	Article
Status:	Published
Schools:	Advanced Research Computing @ Cardiff (ARCCA) Mathematics Medicine MRC Centre for Neuropsychiatric Genetics and Genomics (CNGG)
Subjects:	Q Science > QA Mathematics
Uncontrolled Keywords:	Fokker-Planck equation ; FENE dumbbell mode ; Reduced basis functions ; Couette flow ; Spectral expansion
ISSN:	1543-1649
Last Modified:	18 Oct 2022 13:02
URI:	https://orca.cardiff.ac.uk/id/eprint/12139

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