An adaptive finite element method for viscoplastic fluid flows in pipes Original Research Article

The numerical modelling of the fully developed Poiseuille flow of a yield stress fluid in a square section is presented. The dead regions in outer corners and the plug region in the center are exhibited. Numerical computations cover the complete range of the dimensionless number describing the yield stress effect, from a Newtonian flow to a fully stopped flow. The resolution of variational inequalities describing the flow is based on the augmented Lagrangian method and a specific mixed finite element method. The localization of yield surfaces is approximated by an anisotropic auto-adaptive mesh procedure. The limit load analysis and the associated limit yield surface are obtained by an extrapolation procedure.