Robust stabilised finite element solvers for generalised Newtonian fluid flows

Richard Schussnig*, Douglas R.Q. Pacheco, Thomas Peter Fries

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


Various materials and solid-fluid mixtures of engineering and biomedical interest can be modelled as generalised Newtonian fluids, as their apparent viscosity depends locally on the flow field. Despite the particular features of such models, it is common practice to combine them with numerical techniques originally conceived for Newtonian fluids, which can bring several issues such as spurious pressure boundary layers, unsuitable natural boundary conditions and coupling terms spoiling the efficiency of nonlinear solvers and preconditioners. In this work, we present a finite element framework dealing with such issues while maintaining low computational cost and simple implementation. The building blocks of our algorithm are (i) an equal-order stabilisation method preserving consistency even for lowest-order discretisations, (ii) robust extrapolation of velocities in the time-dependent case to decouple the rheological law from the overall system, (iii) adaptive time step selection and (iv) a fast physics-based preconditioned Krylov subspace solver, to tackle the relevant range of discretisation parameters including highly varying viscosity. Selected numerical experiments are provided demonstrating the potential of our approach in terms of robustness, accuracy and efficiency for problems of practical interest.

Original languageEnglish
Article number110436
JournalJournal of Computational Physics
Publication statusPublished - 1 Oct 2021


  • Adaptive time-stepping
  • Generalised Newtonian fluid
  • Incompressible flow
  • Navier–Stokes equations
  • Schur complement preconditioner
  • Stabilised finite elements

ASJC Scopus subject areas

  • Numerical Analysis
  • Modelling and Simulation
  • Physics and Astronomy (miscellaneous)
  • Physics and Astronomy(all)
  • Computer Science Applications
  • Computational Mathematics
  • Applied Mathematics

Fields of Expertise

  • Information, Communication & Computing


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