Journal
JOURNAL OF NON-NEWTONIAN FLUID MECHANICS
Volume 165, Issue 9-10, Pages 544-550Publisher
ELSEVIER
DOI: 10.1016/j.jnnfm.2010.02.002
Keywords
Bingham plastic; Poiseuille flows; Variational inequalities; Augmented Lagrangian method (ALM); Iterative Uzawa algorithm; Cessation flows; Finite stopping times
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Funding
- RFBR [08-01-00353a, 09-01-00565a]
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The augmented Lagrangian/Uzawa method has been used to study benchmark one-dimensional cessation flow problems of a Bingham fluid, such as the plane Couette flow, and the plane, round, and annular Poiseuille flows. The calculated stopping times agree well with available theoretical upper bounds for the whole range of Bingham numbers and with previous numerical results. The applied method allows for easy determination of the yielded and unyielded regions. The evolution of the rigid zones in these unsteady flows is presented. It is demonstrated that the appearance of an unyielded zone near the wall occurs for any non-zero Bingham number not only in the case of a round tube but also in the case of an annular tube of small radii ratio. The advantages of using the present method instead of regularizing the constitutive equation are also discussed. (c) 2010 Elsevier B.V. All rights reserved.
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