We have implemented the log-conformation method for two-dimensional viscoelastic flow in COMSOL, a commercial high-level finite element package. The code is verified for an Oldroyd-B fluid flowing past a confined cylinder. We are also able to describe the well-known bistability of the viscoelastic flow in a crossslot geometry for a FENE-CR fluid, and we describe the changes required for perform...

We study the impact of the Peterlin approximation on the statistics of the end-to-end separation of polymers in a turbulent flow. The finitely extensible nonlinear elastic (FENE) model and the FENE model with the Peterlin approximation (FENE-P) are numerically integrated along a large number of Lagrangian trajectories resulting from a direct numerical simulation of three-dimensional homogeneous...

bstract We investigate four crucial properties for testing and evaluating a moment closure approximation of the FENE dumbbell model for dilute olymer solutions: non-negative configuration distribution function, energy dissipation, accuracy of approximation and computational expense. hrough mathematical analysis, numerical experiments and comparisons with closure model FENE-P and FENE-YDL, we pr...

One of the most classical closures approximation of the FENE model of polymeric flows is the one proposed by Peterlin, namely the FENE-P model. We prove global existence of weak solutions to the FENE-P model. The proof is based on the propagation of some defect measures that control the lack of strong convergence in an approximating sequence. Using a similar argument, we also prove global exist...

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...

Rheological models for polymer solutions and melts based on the finitely extensible non-linear elastic (FENE) dumbbell theory are reviewed in this study. The FENE-P model that is a well-known Peterlin approximation of the FENE model, indicates noticeable deviation from original FENE predictions and also experimental results, especially in the transient flow. In addition, both FENE and FENE-P mo...

We consider a polymeric fluid model, consisting of the incompressible Navier-Stokes equations coupled to a non-symmetric Fokker-Planck equation. First, steady states and exponential convergence to them in relative entropy are proved for the linear Fokker-Planck equation in the Hookean case. The FENE model is also addressed proving the existence of stationary states and the convergence towards t...

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.