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The numerical prediction of planar viscoelastic contraction flows using the pom-pom model and higher-order finite volume schemes

Aguayo, J. P., Phillips, P. M., Phillips, Timothy Nigel, Tamaddon-Jahromi, H. R., Snigerev, B. A. and Webster, M. F. 2007. The numerical prediction of planar viscoelastic contraction flows using the pom-pom model and higher-order finite volume schemes. Journal of Computational Physics 220 (2) , pp. 586-611. 10.1016/j.jcp.2006.05.039

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Abstract

This study investigates the numerical solution of viscoelastic flows using two contrasting high-order finite volume schemes. We extend our earlier work for Poiseuille flow in a planar channel and the single equation form of the extended pom–pom (SXPP) model [M. Aboubacar, J.P. Aguayo, P.M. Phillips, T.N. Phillips, H.R. Tamaddon-Jahromi, B.A. Snigerev, M.F. Webster, Modelling pom–pom type models with high-order finite volume schemes, J. Non-Newtonian Fluid Mech. 126 (2005) 207–220], to determine steady-state solutions for planar 4:1 sharp contraction flows. The numerical techniques employed are time-stepping algorithms: one of hybrid finite element/volume type, the other of pure finite volume form. The pure finite volume scheme is a staggered-grid cell-centred scheme based on area-weighting and a semi-Lagrangian formulation. This may be implemented on structured or unstructured rectangular grids, utilising backtracking along the solution characteristics in time. For the hybrid scheme, we solve the momentum-continuity equations by a fractional-staged Taylor–Galerkin pressure-correction procedure and invoke a cell-vertex finite volume scheme for the constitutive law. A comparison of the two finite volume approaches is presented, concentrating upon the new features posed by the pom–pom class of models in this context of non-smooth flows. Here, the dominant feature of larger shear and extension in the entry zone influences both stress and stretch, so that larger stretch develops around the re-entrant corner zone as Weissenberg number increases, whilst correspondingly stress levels decline.

Item Type: Article
Date Type: Publication
Status: Published
Schools: Mathematics
Subjects: Q Science > QC Physics
Uncontrolled Keywords: Pom–pom model ; pure finite volume ; hybrid finite element/volume ; abrupt contraction ; viscoelasticity
Publisher: Elsevier
ISSN: 0021-9991
Last Modified: 04 Jun 2017 02:48
URI: http://orca.cf.ac.uk/id/eprint/12347

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