Numerical simulations reveal the formation of singular structures in the polymer stress field of a viscoelastic fluid modeled by the Oldroyd-B equations driven by a simple body force. These singularities emerge exponentially in time at hyperbolic stagnation points in the flow and their algebraic structure depends critically on the Weissenberg number. Beyond a first critical Weissenberg number t...

We present a second-order finite-difference scheme for viscoelastic flows based on a recent reformulation of the constitutive laws as equations for the matrix logarithm of the conformation tensor. We present a simple analysis that clarifies how the passage to logarithmic variables remedies the high-Weissenberg numerical instability. As a stringent test, we simulate an Oldroyd-B fluid in a lid-d...

We study the deformation of flexible polymers whose contour length lies in the inertial range of a homogeneous and isotropic turbulent flow. By using the elastic dumbbell model and a stochastic velocity field with nonsmooth spatial correlations, we obtain the probability density function of the extension as a function of the Weissenberg number and of the scaling exponent of the velocity structu...

Stability of a second-order finite element/finite volume hybrid scheme is investigated on the basis of flows with increasing Weissenberg number. Finite elements are used to discretise the balances of mass and momentum. For the stress equation a finite volume method is used, based on the recent development with fluctuation distribution schemes for pure convection problems. Examples considered in...

The log conformation representation proposed in [1] has been implemented in a fem context using the DEVSS/DG formulation for viscoelastic fluid flow. We present a stability analysis in 1D and attribute the high Weissenberg problem to the failure of the numerical scheme to balance exponential growth. A slightly different derivation of the log based evolution equation than in [1] is also presente...

We have argued that magnetohydrodynamic (MHD) turbulence in an accretion disk naturally produces hoop-stresses, and that in a geometrically-thick flow these stresses could both drive and collimate an outflow. We based this argument on an analogy of turbulent MHD fluids to viscoelastic fluids, in which azimuthal shear flow creates hoop-stresses that cause a variety of flow phenomena, including t...

Peristaltic motion of viscoelastic incompressible fluid in an axisymmetric tube with a sinusoidal wave is studied theoretically in the case that the radius of the tube is small relative to the wavelength. Oldroyd flow has been considered in this study and the problem is formulated and analyzed using a perturbation expansion in terms of the variation of the wave number. This analysis can model t...

We study the dynamics of the Taylor-Couette flow of shear banding wormlike micelles. We focus on the high shear rate branch of the flow curve and show that for sufficiently high Weissenberg numbers, this branch becomes unstable. This instability is strongly subcritical and is associated with a shear stress jump. We find that this increase of the flow resistance is related to the nucleation of t...

We have argued that MHD turbulence in an accretion disk naturally produces hoop-stresses, and that in a geometrically-thick flow these stresses could both drive and collimate an outflow. We based this argument on an analogy of turbulent MHD fluids to viscoelastic fluids, in which azimuthal shear flow creates hoop-stresses that cause a variety of flow phenomena, including the Weissenberg effect ...

The objective of this work is to study the Williamson fluid flow with a chemically reactive species.The governing equations of Williamson model in two dimensional flows are constructed by using scaling transformation under a Reynolds and Weissenberg numbers approximation. The analytic solution of the system of nonlinear ordinary differential equations (ODEs) is constructed in the series form by...