article

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

Authors:

P. M. Phillips,

T. N. Phillips,

H. R. Tamaddon-Jahromi,

B. A. Snigerev,

M. F. WebsterAuthors Info & Claims

Journal of Computational Physics, Volume 220, Issue 2

Pages 586 - 611

https://doi.org/10.1016/j.jcp.2006.05.039

Published: 01 January 2007 Publication History

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.

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Cited By

Al-Muslimawi A(2016)Numerical study for differential constitutive equations with polymer melts by using a hybrid finite-element/volume methodJournal of Computational and Applied Mathematics10.1016/j.cam.2016.06.007308:C(488-498)Online publication date: 15-Dec-2016
https://dl.acm.org/doi/10.1016/j.cam.2016.06.007

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

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Published In

cover image Journal of Computational Physics

Journal of Computational Physics Volume 220, Issue 2

January, 2007

429 pages

ISSN:0021-9991

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Copyright © Elsevier Inc. © 2006.

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Academic Press Professional, Inc.

United States

Publication History

Published: 01 January 2007

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Cited By

Al-Muslimawi A(2016)Numerical study for differential constitutive equations with polymer melts by using a hybrid finite-element/volume methodJournal of Computational and Applied Mathematics10.1016/j.cam.2016.06.007308:C(488-498)Online publication date: 15-Dec-2016
https://dl.acm.org/doi/10.1016/j.cam.2016.06.007

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