Stabilized mixed approximations for inertial viscoplastic fluid flows

In this article, mixed approximations for inertial viscoplastic fluid flows are considered. The governing equations for incompressible flows, coupled with the Bingham model modified by the Papanastasiou (1987) regularization, are approximated by a Galerkin-least-squares-type formulation. Numerical simulations of flows inside a lid-driven cavity and trough a sudden expansion are carried out to investigate the influence of inertia and yield limit on yield surfaces shapes, with Reynolds and Bingham numbers taken up to 1000. In all computations, a combination of equal-order bi-linear interpolations for the pair velocity–pressure is used – a choice a priori interdicted by the Babuška–Brezzi condition.