On the numerical simulation of Bingham visco-plastic flow: Old and new results

The main goal of this article is to review various results and methods concerning the numerical simulation of Bingham visco-plastic flow; these results have been obtained from the early 1970s to now. We consider first the case of flow in cylindrical pipes and then flow in multi-dimensional cavities. The methods to be discussed include classical ones relying on regularization, (kind of) Lagrange multipliers and augmented Lagrangian techniques; they include also a duality-penalty method whose implementation relies on a Newton-Conjugate Gradient-Uzawa algorithm which seems to be new (in this context at least). Other issues are addressed; they concern particularly the accelerated calculation of steady state solutions and the time discretization of the unsteady flow models. The results of numerical experiments are presented, including the simulation of the wall driven flow in square cavities.