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Kinetic structure simulations of nematic polymers in plane Couette cells. I: The algorithm and benchmarks. (English) Zbl 1108.76010
This paper displays simulation results for a class of nematic polymers in a one-dimensional plane Couette flow described by the Smoluchowski equation. The key is that the three independent variables so involved by the model require each its own numerical strategy. The probability distributed function is expanded by using spherical harmonic functions and by this way the Smoluchowski equation is converted into a set of PDEs which then are converted into ODEs by means of fourth-order finite difference methods. And finally the integration with respect to time is performed with Euler method.

MSC:
76A15 Liquid crystals
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
65M20 Method of lines for initial value and initial-boundary value problems involving PDEs
76M20 Finite difference methods applied to problems in fluid mechanics
82D30 Statistical mechanical studies of random media, disordered materials (including liquid crystals and spin glasses)
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