In this paper we present a reduced basis method for the parametrized Fokker–Planck equation associated with evolution of Finitely Extensible Nonlinear Elastic (FENE) dumbbells in a Newtonian solvent for a (prescribed) extensional macroscale flow. There are two new important ingredients: a projection–based POD–Greedy sampling procedure for the stable identification of optimal reduced basis space...

We present a new finite-difference formulation to update the conformation tensor in dumbbell models (e.g., Oldroyd-B, FENE-P, Giesekus) that guarantees positive eigenvalues of the tensor (i.e., the tensor remains positive definite) and prevents over-extension for finite-extensible models. The formulation is a generalization of the second-order, central difference scheme developed by Kurganov an...

The effects of stiffness on the diffusion-limited dynamics of dumbbells in solution is studied numerically. The Langevin equation is used with two different models, the so-called Fraenkel and FENE dumbbells. It is found that the dynamics of rotation and stretching are dictated by the two following trends: (i) the density-density correlation function for these modes decays more slowly for larger...

We examine, with asymptotic analysis and numerical simulation, the iterated stretching dynamics of FENE and Oldroyd-B jets of initial radius r0 , shear viscosity n, Weissenberg number We, retardation number S, and capillary number Ca. The usual Rayleigh instability stretches the local uniaxial extensional flow region near a minimum in jet radius into a primary filament of radius @Ca(12S)/We#r0 ...

We study the existence of global-in-time weak solutions to a coupled microscopic-macroscopic bead-spring model which arises from the kinetic theory of dilute solutions of polymeric liquids with noninteracting polymer chains. The model consists of the unsteady incompressible Navier–Stokes equations in a bounded domain Ω ⊂ R, d = 2 or 3, for the velocity and the pressure of the fluid, with an ela...