An adaptive finite element method for viscoplastic flows in a square pipe with stick–slip at the wall

This paper presents the numerical solution of non-linear yield stress phenomena by using a new mixed anisotropic auto-adaptive finite element method. The Poiseuille flow of a Bingham fluid with slip yield boundary condition at the wall is considered. Despite its practical interest, for instance for pipeline flows of yield-stress fluids such as concrete and cements, this problem has not been addressed yet to our knowledge. The case of a pipe with a square section has been investigated in detail. The computations cover the full range of the two main dimensionless numbers and exhibit complex flow patterns: all the different flow regimes are completely identified.