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 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...

Abstract Systems coupling fluids and polymers are of great interest in many branches of sciences. One of the most classical models to describe them is the FENE (Finite Extensible Nonlinear Elastic) dumbbell model. We prove global existence of weak solutions to the FENE dumbbell model of polymeric flows. The main difficulty is the passage to the limit in a nonlinear term that has no obvious comp...

System parameters and steady-state convergence criteria For purposes of this work, a mesh size of was used. Steady state equilibrium was determined using the less stringent of the two error criteria as defined below: \* MERGEFORMAT (1) \* MERGEFORMAT (2) The time step used was determined using the maximum value of the FENE force relative to the spatial discretization and rounded for convenience...

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 ...

We prove global existence of weak solutions for the co-rotational FENE dumbbell model and the Doi model also called the Rod model. The proof is based on propagation of compactness, namely if we take a sequence of weak solutions which converges weakly and such that the initial data converges strongly then the weak limit is also a solution. To cite this article: A. Name1, A. Name2, C. R. Acad. Sc...

This paper is concerned with the analysis and implementation of spectral Galerkin methods for a class of Fokker–Planck equations that arises from the kinetic theory of dilute polymers. A relevant feature of the class of equations under consideration from the viewpoint of mathematical analysis and numerical approximation is the presence of an unbounded drift coefficient, involving a smooth conve...