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

•Fast parallelized 2D Finite-Differences Augmented Lagrangian Bingham code.•Simulations on very fine structured meshes with very demanding convergence criteria compared to previous literature.•Providing all internal computational costs for benchmarking.•Successful comparison of the code with 2 kinds of physical experiments in cavities.•Detailed pseudo-plug zones and dead zones' horizontal lengths.

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.

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