A maximum entropy principle based closure method for macro-micro models of polymeric materials

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June 2008, 1(2): 171-184. doi: 10.3934/krm.2008.1.171

A maximum entropy principle based closure method for macro-micro models of polymeric materials

Yunkyong Hyon ^1, , José A. Carrillo ^2, , Qiang Du ^1, and Chun Liu ^3,

1.	Department of Mathematics, Pennsylvania State University, University Park, PA 16802, United States
2.	ICREA-Departament de Matemàtiques, Universitat Autònoma de Barcelona, E-08193 Bellaterra, Spain
3.	Department of Mathematics, The Pennsylvania State University, University Park, PA 16802

Received January 2008 Revised January 2008 Published May 2008

Abstract
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We consider the finite extensible nonlinear elasticity (FENE) dumbbell model in viscoelastic polymeric fluids. We employ the maximum entropy principle for FENE model to obtain the solution which maximizes the entropy of FENE model in stationary situations. Then we approximate the maximum entropy solution using the second order terms in microscopic configuration field to get an probability density function (PDF). The approximated PDF gives a solution to avoid the difficulties caused by the nonlinearity of FENE model. We perform the moment-closure approximation procedure with the PDF approximated from the maximum entropy solution, and compute the induced macroscopic stresses. We also show that the moment-closure system satisfies the energy dissipation law. Finally, we show some numerical simulations to verify the PDF and moment-closure system.

Keywords: numerical simulations., non-newtonian fluid, multiscale modeling, FENE model, maximum entropy principle, polymeric fluid, Fokker-Planck equation, macro-micro dynamics, moment closure.

Mathematics Subject Classification: Primary: 76A05, 76M99 ; Secondary: 65C3.

Citation: Yunkyong Hyon, José A. Carrillo, Qiang Du, Chun Liu. A maximum entropy principle based closure method for macro-micro models of polymeric materials. Kinetic & Related Models, 2008, 1 (2) : 171-184. doi: 10.3934/krm.2008.1.171

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