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International Journal for Multiscale Computational Engineering

Erscheint 6 Ausgaben pro Jahr

ISSN Druckformat: 1543-1649

ISSN Online: 1940-4352

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

Volumen 9, Ausgabe 1, 2011, pp. 73-88
DOI: 10.1615/IntJMultCompEng.v9.i1.60
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ABSTRAKT

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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