A numerical investigation of inertia flows of Bingham-Papanastasiou fluids by an extra stress-pressure-velocity galerkin least-squares method

This article is concerned with finite element approximations for yield stress fluid flows through a sudden planar expansion. The mechanical model is composed by mass and momentum balance equations, coupled with the Bingham viscoplastic model regularized by Papanastasiou (1987) equation. A multi-field Galerkin least-squares method in terms of stress, velocity and pressure is employed to approximate the flows. This method is built to circumvent compatibility conditions involving pressure-velocity and stress-velocity finite element subspaces. In addition, thanks to an appropriate design of its st...