Barrett, John W. and Suli, Endre (2007) Numerical approximation of corotational dumbbell models for dilute polymers. Technical Report. Unspecified. (Submitted)

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Abstract
We construct a general family of Galerkin methods for the numerical approximation of weak solutions to a coupled microscopicmacroscopic beadspring model that arises from the kinetic theory of dilute solutions of polymeric liquids with noninteracting polymer chains. The model consists of the unsteady incompressible NavierStokes equations in a bounded domain Ω in R d, d=2 or 3, for the velocity and the pressure of the fluid, with an elastic extrastress tensor as righthand side in the momentum equation. The extrastress tensor stems from the random movement of the polymer chains and is defined through the associated probability density function which satisfies a FokkerPlanck type parabolic equation, a crucial feature of which is the presence of a centreofmass diffusion term. We focus on finitelyextensible nonlinear elastic, FENEtype, dumbbell models. In the case of a corotational drag term we perform a rigorous passage to the limit as the spatial and temporal discretization parameters tend to zero, and show that a (sub)sequence of numerical solutions converges to a weak solution of this coupled NavierStokesFokkerPlanck system.
Item Type:  Technical Report (Technical Report) 

Subjects:  H  N > Numerical analysis 
Research Groups:  Numerical Analysis Group 
ID Code:  1083 
Deposited By:  Lotti Ekert 
Deposited On:  07 May 2011 08:04 
Last Modified:  29 May 2015 18:46 
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