Application of the natural stress formulation for solving unsteady viscoelastic contraction flows

Jonathan D. Evans, Hugo L. França, Cassio M. Oishi

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We present a numerical scheme for a previously unexploited formulation of the equations for unsteady viscoelastic flow. The formulation aligns the polymer stress along particle paths/streamlines, utilising the characteristic curves associated with the hyperbolic part of the constitutive equations. We illustrate the approach for the Oldroyd-B model in the benchmark 4:1 contraction for moderate elasticity numbers. We show that the scheme is able to accurately capture the re-entrant corner singularity for the polymer stresses and the pressure, the latter variable being inaccurately determined by schemes using the traditional formulation in terms of Cartesian polymer stresses. A space-step restriction for stability is derived, which can be numerically limiting in certain recirculation regions. This contrasts with the equivalent space-step restriction for the formulation in Cartesian stresses, which is limiting in flow regions of high velocity gradients, for example, at sharp corners in contraction flows.

Original languageEnglish
Pages (from-to)462-489
Number of pages28
JournalJournal of Computational Physics
Early online date23 Mar 2019
Publication statusPublished - 1 Jul 2019


  • Natural Stress Formulation
  • Numerical simulation
  • Sharp corner flows
  • Unsteady viscoelastic flows

ASJC Scopus subject areas

  • Physics and Astronomy (miscellaneous)
  • Computer Science Applications


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