Augmented Lagrangian simulations study of yield-stress fluid flows in expansion-contraction and comparisons with physical experiments

Arthur Marly (1, 2) , Paul Vigneaux (1, 2)

1 NUMED - Numerical Medicine
2 UMPA-ENSL - Unité de Mathématiques Pures et Appliquées

We present numerical simulations of viscoplastic flows in expansion-contraction geometry and compare them with physical experiments of [Chevalier et al. Europhys. Lett. 102, 48002 (2013)] and [Luu et al. Phys. Rev. E 91, 013013 (2015)]. Numerical resolution is done with Augmented Lagrangian (following the Glowinski and coworkers' approach) and Finite-Differences (for the space discretization) methods. We show that good agreement is obtained between the numerical results and the physical experiments. In particular, we retrieve the slip line effect of Luu et al. and give numerical evidence of non-monotone shear effect in the boundary layer between the two unyielded regions in the cavity region. We also give some more detailed measures of the size of the plug and dead zones.

Keywords: Parallel multifrontal solver; Finite-Differences; Viscoplastic flows; yielded boundary layer; Augmented Lagrangian methods; expansion-contraction geometry; Bingham fluid

Domains: Numerical Analysis [math.NA]; Fluid mechanics [physics.class-ph]

Arthur Marly, Paul Vigneaux. Augmented Lagrangian simulations study of yield-stress fluid flows in expansion-contraction and comparisons with physical experiments. Journal of Non-Newtonian Fluid Mechanics, 2017, 239, pp.35 - 52. ⟨10.1016/j.jnnfm.2016.12.004⟩. ⟨hal-01432028⟩