Steady bubble rise in Herschel-Bulkley fluids and comparison of predictions via the Augmented Lagrangian Method with those via the Papanastasiou model

► Comparison of Augmented Lagrangian Method and Papanastasiou approximation for freesurface viscoplastic flows. ► Acceleration of the Augmented Lagrangian Method. ► Accurate predictions for the flow of a rising bubble in a Herschel-Bulkley fluid. ► Comparison with experimental data.