We study a defect correction method for the approximation of viscoelastic fluid flow. In the defect step, the constitutive equation is computed with an artificially reduced Weissenberg parameter for stability, and the resulting residual is corrected in the correction step. We prove the convergence of the defect correction method and derive an error estimate for the Oseen-viscoelastic model prob...

The flow field around a sphere falling at its terminal velocity in a column of viscoelastic non-shear-thinning fluid is experimentally measured with digital particle image velocimetry. The working fluid is an extensively characterized, monodisperse, polystyrene based Boger fluid. The sphere radius relative to the radius of the column of fluid is small (a/rc50.083). The Weissenberg number (lUt /...

Elasto-inertial turbulence (EIT) is a new state of turbulence found in inertial flows with polymer additives. The dynamics of turbulence generated and controlled by such additives is investigated from the perspective of the coupling between polymer dynamics and flow structures. Direct numerical simulations of channel flow with Reynolds numbers ranging from 1000 to 6000 (based on the bulk and th...

Polymers exposed to shear flow exhibit a remarkably rich tumbling dynamics. While rigid rods rotate on Jeffery orbits, a flexible polymer stretches and coils up during tumbling. Theoretical results show that in both of these asymptotic regimes the corresponding tumbling frequency f(c) in a linear shear flow of strength γ scales as a power law Wi(2/3) in the Weissenberg number Wi = γτ, where τ i...

A multi-scale phase-field approach, which couples the mesoscopic crystallization with the microscopic orientation of chain segments and macroscopic viscoelastic melt flow, is proposed to study how the crystal growth of semi-crystalline polymers is affected by flows. To make the simulation feasible, we divide the problem into three parts. In the first part, a finitely extensible nonlinear elasti...

We study the dynamics of a layer of viscoelastic fluid, in the Stokesian regime, that is driven from below by a 4 4 checkerboard pattern of rotating and counter-rotating disks. At low disk rotation rate (low Weissenberg number) the fluid flow response is slaved to the geometry of this forcing and divides into many steadily rotating cells, each contained within invariant manifolds issuing from h...

Direct numerical simulations are carried out to study the effect of finite Weissenberg number up $Wi=16$ on laminar and turbulent channel flows an elastoviscoplastic (EVP) fluid, at a fixed bulk Reynolds $2800$ . The incompressible flow equations coupled with evolution equation for EVP stress tensor by modified Saramito model that extends both Bingham viscoplastic extensible nonlinear elastic-P...

This paper presents a numerical evaluation of two different artificial stress diffusion techniques for the stabilization viscoelastic Oldroyd-B fluid flows at high Weissenberg numbers. The standard in form Laplacian extra tensor is compared with newly proposed approach using discrete time derivative tensor. Both methods are implemented finite element code and demonstrated solution flow two-dime...

The effect of temperature in viscoelastic fluid flows is studied applying a stabilized finite element formulation based on both standard and log-conformation reformulation (LCR), the Variational Multiscale (VMS) method as stabilization technique. turns out to be crucial solve cases with high Weissenberg number. Regarding coupling, two-way coupling strategy employed: one hand, dependence paramet...

In this work, we optimise microfluidic converging/diverging geometries in order to produce constant strain-rates along the centreline of the flow, for performing studies under homogeneous extension. The design is examined for both two-dimensional and three-dimensional flows where the effects of aspect ratio and dimensionless contraction length are investigated. Initially, pressure driven flows ...