•We propose an axisymmetric solver for two-phase viscoelastic fluid flows. •The method can be used for solving viscoelastic problems at a wide range of Weissenberg numbers. •The numerical algorithm is assessed for several benchmark tests from the Computational Rheology literature. •A detailed numerical study of the Weissenberg or Rod-Climbing effect is presented. •Transient peculiar behaviors observed in the Weissenberg effect problem are numerically captured, as for example, the “breathing instability”.
International Journal of Multiphase Flow – Elsevier
Published: Sep 1, 2016
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