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A THEORETICAL AND NUMERICAL STUDY FOR THE ROD-LIKE MODEL OF A POLYMERIC FLUID

Hui Zhang and Ping-wen Zhang
Journal of Computational Mathematics
Vol. 22, No. 2, SPECIAL ISSUE DEDICATED TO THE 70TH BIRTHDAY OF PROFESSOR ZHONG-CI SHI (MARCH 2004), pp. 319-330
Stable URL: http://www.jstor.org/stable/43693157
Page Count: 12
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
A THEORETICAL AND NUMERICAL STUDY FOR THE ROD-LIKE MODEL OF A POLYMERIC FLUID
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Abstract

The first part of this paper is concerned with the well-posedness for the rigid rod-like model in shear flow of a polymeric fluid. The constitutive relations considered in this work are motivated by the kinetic theory. The stress tensor is given by an integral which involves the solution of the Fokker-Planck equation. A novel numerical scheme for the Fokker-Planck equation is proposed, which preserves the positivity of the distribution function. Another part of this work establishes the convergence theory of the fully discretized schemes for a simple micro-macro simulation of a polymeric flow.

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