OpenFOAM® pp 269-280 | Cite as

Improving the Numerical Stability of Steady-State Differential Viscoelastic Flow Solvers in OpenFOAM\(^{\textregistered }\)

  • Célio Fernandes
  • Manoel S. B. Araujo
  • Luís L. Ferrás
  • J. Miguel NóbregaEmail author


This work reports the developments made in improving the numerical stability of the viscoelastic solvers available in the open-source finite volume computational library \(OpenFOAM^{\textregistered }\). For this purpose, we modify the usual both-side diffusion (BSD) technique, using a new approach to discretize the explicit diffusion operator. Calculations performed with the new solver, for two benchmark 2D case studies of an upper-convected Maxwell (UCM) fluid, are presented and compared with literature results, namely the 4:1 planar contraction flow and the flow around a confined cylinder. In the 4:1 planar contraction flow, the corner vortex size predictions agree well with the literature, and a relative error below \(5.3 \%\) is obtained for \(De \le 5\). In the flow around a confined cylinder, the predictions of the drag coefficient on the cylinder are similar to reference data, with a relative error below \(0.16 \%\) for \(De \le 0.9\).



This work is funded by FEDER funds through the COMPETE 2020 Programme and National Funds through FCT—Portuguese Foundation for Science and Technology under the project UID/CTM/50025/2013 and under the scholarship SFRH/BPD/100353/2014. The author M.S.B. Araujo acknowledges funding from CAPES (Coordenação de Aperfeiçoamento de Pessoal de Nível Superior) proc. BEX 1902-14-8. The authors would like to acknowledge the Minho University cluster under the project Search-ON2: Revitalization of HPC infrastructure of UMinho, (NORTE-07-0162-FEDER-000086), co-funded by the North Portugal Regional Operational Programme (ON.2-0 Novo Norte), under the National Strategic Reference Framework (NSRF), through the European Regional Development Fund (ERDF).


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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Célio Fernandes
    • 1
  • Manoel S. B. Araujo
    • 2
  • Luís L. Ferrás
    • 1
  • J. Miguel Nóbrega
    • 1
    Email author
  1. 1.Institute for Polymers and Composites/i3NUniversity of MinhoGuimarãesPortugal
  2. 2.Instituto de Ciências Exatas e Naturais, Faculdade de MatemáticaUniversidade Federal do ParáBelemBrazil

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