An equal-order finite element framework for incompressible non-newtonian flow problems

Douglas R.Q. Pacheco*, Olaf Steinbach

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference paperpeer-review


Various materials of engineering and biomedical interest can be modelled as generalised Newtonian fluids, i.e., via an apparent viscosity depending locally on the flow field. In spite of the particular features of those models, they are often handled in practice by classical numerical techniques originally conceived for Newtonian fluids. Methods designed specifically for the generalised case are rather scarce in the literature, as well as their use in practical applications. As it turns out, tackling nonNewtonian problems with standard finite element formulations can have undesired consequences such as the induction of spurious pressure boundary layers and the emergence of natural boundary conditions not suitable for realistic flow scenarios. In this context, we introduce a novel framework that deals with those issues while maintaining simplicity and low computational cost. The new stabilised formulation is based on a modified system combining the continuity equation with a Poisson equation for the pressure and consistent pressure boundary conditions. A weak enforcement of the rheological law is employed to enable full consistency even for first-order finite element pairs. Simple numerical examples are provided to demonstrate the potential of our method in yielding accurate solutions for relevant problems.

Original languageEnglish
Title of host publicationWCCM-ECCOMAS 2020
PublisherScipedia S.L.
Number of pages12
Publication statusPublished - 2021
Event14th World Congress of Computational Mechanics and ECCOMAS Congress: WCCM-ECCOMAS 2020 - Virtuell, Austria
Duration: 11 Jan 202115 Jan 2021


Conference14th World Congress of Computational Mechanics and ECCOMAS Congress
Abbreviated titleWCCM-ECCOMAS 2020


  • Hemodynamics
  • Incompressible flows
  • Non-Newtonian fluids
  • Pressure boundary conditions
  • Residualbased stabilisation
  • Stabilised finite element methods

ASJC Scopus subject areas

  • Mechanical Engineering

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