On the numerical simulation of Bingham viscoplastic flow: old and new results. (English) Zbl 1107.76061

Dean, Edward J.; Glowinski, Roland; Guidoboni, Giovanna

J. Non-Newton. Fluid Mech. 142, No. 1-3, 36-62 (2007).

Summary: The main goal is to review various results and methods concerning the numerical simulation of Bingham viscoplastic 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 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 time discretization of unsteady flow models. The results of numerical experiments are presented, including the simulation of wall-driven flow in square cavities.

MSC:

76M99	Basic methods in fluid mechanics
76A05	Non-Newtonian fluids
76-02	Research exposition (monographs, survey articles) pertaining to fluid mechanics

Keywords:

duality-penalty method; Newton-conjugate gradient-Uzawa algorithm; square cavities