Robust stabilised finite element solvers for generalised Newtonian fluid flows

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