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...

The mirror fluid method is proposed for simulating viscous tubular flow of a Newtonian or non-Newtonian fluid past an irregular solid obstacle using a simple finite difference method for discretization. Suitable flow parameters in the solid domain are assigned by a mirror relation to ensure the surface segment is subjected to zero net shear and normal forces and the boundary conditions are enfo...

We examine Oldroyd’s 1950 paper On the Formulation of Rheological Equations State (Oldroyd, 1950) in which he introduced upper and lower convected time-derivatives, along with Oldroyd-A Oldroyd-B model fluids. Those developments are placed context prior ideas his own subsequent papers on constitutive equations. The choice between A B models is addressed by looking at micro-structural studies, f...

In this paper we discuss simulation techniques for a rising bubble in viscoelastic fluids via numerical methods based on high order FEM. A level set approach based on the work in [9] is used for interface tracking between the bubble and the surrounding fluid. The two matters obey the Newtonian and the Oldroyd-B constitutive law in the case of a viscoelastic fluid while the flow model is given b...

We investigate the dynamics of the two-dimensional periodic Kolmogorov flow of a viscoelastic fluid, described by the Oldroyd-B model, by means of direct numerical simulations. Above a critical Weissenberg number the flow displays a transition from stationary to randomly fluctuating states, via periodic ones. The increasing complexity of the flow in both time and space at progressively higher v...

This paper studies the unsteady magnetohydrodynamics (MHD) thin film flow of an incompressible Oldroyd-B fluid over an oscillating inclined belt making a certain angle with the horizontal. The problem is modeled in terms of non-linear partial differential equations with some physical initial and boundary conditions. This problem is solved for the exact analytic solutions using two efficient tec...

This paper looks at the series solutions of three dimensional boundary layer flow. An Oldroyd-B fluid with variable thermal conductivity is considered. The flow is induced due to stretching of a surface. Analysis has been carried out in the presence of heat generation/absorption. Homotopy analysis is implemented in developing the series solutions to the governing flow and energy equations. Grap...