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...

The aim of this paper is to study a finite element numerical approximation of steady flows of an incompressible viscoelastic Oldroyd-B fluid in curved pipes of arbitrary cross-section and curvature ratio. Using rectangular toroidal coordinates, existence and uniqueness of approximated solutions are proved as well as a priori error estimates, under a natural restriction on the pipe curvature ratio.

The free surface flow of an Oldroyd-B viscoelastic fluid is considered, following [1]. When removing a term in the extra-stress constitutive relation, the description of an elastic incompressible solid is obtained, in Eulerian coordinates, with the velocity field as unknown, rather than the usual deformation field. Two simulations are proposed, a bouncing ball and an oscillating beam.

We implement a volume-of-fluid algorithm with a parabolic re-construction of the interface for the calculation of the surface tension force VOF-PROST). This achieves higher accuracy for drop deformation simulations in comparison with existing VOF methods based on a piecewise inear interface re-construction. The algorithm is formulated for the Giesekus constitutive law. The evolution of a drop s...

We prove global existence and uniqueness of solutions of Oldroyd-B systems with relatively small data in Rd, in a large functional setting (Cα ∩ L1). This is a stability result, solutions select an equilibrium and converge exponentially to it. Large spatial derivatives of the initial density and stress are allowed, provided the L∞ norm of the density and stress are small enough. We prove global...

A hybrid combined finite element–finite volume method has been developed for the numerical simulation of shear-dependent viscoelastic flow problems governed by a generalized Oldroyd-B model with a non-constant viscosity function. The method is applied to the 4:1 planar contraction benchmark problem, to investigate the influence of the viscosity effects on the flow and results are compared with ...