A toolbox for the development and reduction of the dynamical models of nonequilibrium systems is presented. The main components of this toolbox are: Legendre integrators, dynamical postprocessing, and thermodynamic projector. Thermodynamic projector is the tool to transform almost arbitrary anzatz to a thermodynamically consistent model, the postprocessing is the cheapest way to improve the sol...

We consider stagnation point flow away from a wall for creeping flow of dilute polymer solutions. For a simplified flow geometry, we explicitly show that a narrow region of strong polymer extension (a birefringent strand) forms downstream of the stagnation point in the UCM model and extensions, like the FENE-P model. These strands are associated with the existence of an essential singularity in...

A toolbox for the development and reduction of the dynamical models of nonequilibrium systems is presented. The main components of this toolbox are: Legendre integrators, dynamical post-processing, and the thermodynamic projector. The thermodynamic projector is the tool to transform almost any anzatz to a thermodynamically consistent model. The post-processing is the cheapest way to improve the...

In this paper, the two-dimensional Kelvin–Helmholtz (KH) instability occurring in shear flow of polymer fluids is modeled by dissipative particle dynamics (DPD) method at coarse-grained molecular level. A revised FENE model proposed to properly describe chains. model, elastic repulsion and tension are both considered between adjacent beads, bond length which set as one segment’s equilibrium len...

The finitely extensible nonlinear elastic (FENE) dumbbell model consists of the incompressible Navier–Stokes equation for the solvent and the Fokker–Planck equation for the polymer distribution. In such a model, the polymer elongation cannot exceed a limit m0 which yields all interesting features of solutions near this limit. This work is concerned with the sharpness of boundary conditions in t...

– We study the dynamics of a single polymer subject to thermal fluctuations in a linear shear flow. The polymer is modeled as a finitely extendable nonlinear elastic (FENE) dumbbell. Both orientation and elongation dynamics are investigated numerically as a function of the shear strength, by means of a new efficient integration algorithm. The results are in agreement with recent experiments. In...

Abstract A Taylor–Galerkin finite element time marching scheme is derived to numerically simulate the flow of a compressible and nonisothermal viscoelastic liquid between eccentrically rotating cylinders. Numerical approximations governing constitutive equations are computed over custom refined unstructured grid piecewise linear Galerkin elements. An original extension DEVSS formulation for flu...