Robust stabilised finite element solvers for generalised Newtonian fluid flows

JOURNAL OF COMPUTATIONAL PHYSICS

卷:442

Article

Schussnig, Richard^1,2  Pacheco, Douglas R. Q.^2,3  Fries, Thomas-Peter^1,2 

[1] Graz Univ Technol, Inst Struct Anal, Lessingstr 25-2, A-8010 Graz, Austria

[2] Graz Ctr Computat Engn, Krenngasse 37-1, A-8010 Graz, Austria

[3] Graz Univ Technol, Inst Appl Math, Steyrergasse 30-3, A-8010 Graz, Austria

关键词: Stabilised finite elements;    Generalised Newtonian fluid;    Incompressible flow;    Adaptive time-stepping;    Schur complement preconditioner;    Navier-Stokes equations;   

DOI  :  10.1016/j.jcp.2021.110436

来源: Elsevier

【 摘 要 】

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. (C) 2021 The Author(s). Published by Elsevier Inc.

【 授权许可】

Free