The breakdown of finite element (FEM) computations for the flow of an Oldroyd-B fluid around a cylinder confined between parallel plates, at Weissenberg numbers Wi = O(1), is shown to arise due to a coil-stretch transition experienced by polymer molecules traveling along the centerline in the wake of the cylinder. With increasing Wi, the coil-stretch transition leads to an unbounded growth in t...

We present a new closure for the mean rate of stretching of a dissolved polymer by homogeneous isotropic turbulence. The polymer is modeled by a bead-spring-type model (e.g., Oldroyd B, FENE-P, Giesekus) and the analytical closure is obtained assuming the Lagrangian velocity gradient can be modeled as a Gaussian, white-noise stochastic process. The resulting closure for the mean stretching depe...

In this paper, we propose a new entropy satisfying finite volume method to solve the FokkerPlanck equation of FENE dumbbell model for polymers, subject to homogeneous fluids. Both semi-discrete and fully discrete schemes satisfy all three desired properties: i) mass conservation, ii) positivity preserving, and iii) entropy satisfying. These ensure that the computed solution is a probability den...

We review recent analytical and computational results for macroscopic-microscopic beadspring models that arise from the kinetic theory of dilute solutions of incompressible polymeric fluids with noninteracting polymer chains, involving the coupling of the unsteady Navier– Stokes system in a bounded domain Ω ⊂ Rd, d = 2 or 3, with an elastic extra-stress tensor as right-hand side in the momentum...

We investigate finite amplitude stability of spatially inhomogeneous steady state an incompressible viscoelastic fluid which occupies a mechanically isolated vessel with walls kept at non-uniform temperature. For wide class models including the Oldroyd-B model, Giesekus FENE-P Johnson–Segalman and Phan–Thien–Tanner model we prove that is stable subject to any perturbation.

A new method for stabilizing viscoelastic flows is proposed suitable for high-order discretizations. It employs a mode-dependent diffusion operator that guarantees monotonicity while maintaining the formal accuracy of the discretization. Other features of the method are: a high-order time-splitting scheme, modal spectral element expansions on a single grid, and the use of a finitely extensible ...

Viscoelastic flow in a square cavity is studied in detail for the FENE-CR model with a given value of extensibility. A finite volume method was employed to predict both the steady flows resulting from movement of the top cavity wall and also the recoil flows that follow the cessation of that lid-wall motion, when the fluid possesses viscoelastic properties. It is shown that this recoil flow can...