TY - JOUR
T1 - Robust stabilised finite element solvers for generalised Newtonian fluid flows
AU - Schussnig, Richard
AU - Pacheco, Douglas R.Q.
AU - Fries, Thomas Peter
N1 - Funding Information:
The authors gratefully acknowledge Graz University of Technology for the financial support of the Lead-project: Mechanics, Modeling and Simulation of Aortic Dissection.
Publisher Copyright:
© 2021 The Author(s)
PY - 2021/10/1
Y1 - 2021/10/1
N2 - 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.
AB - 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.
KW - Adaptive time-stepping
KW - Generalised Newtonian fluid
KW - Incompressible flow
KW - Navier–Stokes equations
KW - Schur complement preconditioner
KW - Stabilised finite elements
UR - http://www.scopus.com/inward/record.url?scp=85105260385&partnerID=8YFLogxK
U2 - 10.1016/j.jcp.2021.110436
DO - 10.1016/j.jcp.2021.110436
M3 - Article
AN - SCOPUS:85105260385
SN - 0021-9991
VL - 442
JO - Journal of Computational Physics
JF - Journal of Computational Physics
M1 - 110436
ER -