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International Journal for Multiscale Computational Engineering
IF: 1.016 5-Year IF: 1.194 SJR: 0.554 SNIP: 0.68 CiteScore™: 1.18

ISSN Print: 1543-1649
ISSN Online: 1940-4352

International Journal for Multiscale Computational Engineering

DOI: 10.1615/IntJMultCompEng.v9.i1.60
pages 73-88

THE PREDICTION OF PLANE COUETTE FLOW FOR A FENEFLUID USING A REDUCED BASIS APPROXIMATION OF THE FOKKER-PLANCK EQUATION

G. M. Leonenko
School of Mathematics, Cardiff University, Cardiff, CF24 4AG, United Kingdom
T. N. Phillips
School of Mathematics, Cardiff University, Cardiff, CF24 4AG, United Kingdom

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.

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