Numerical simulations of cessation flows of a Bingham plastic with the augmented Lagrangian method

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...

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Bibliographic Details
Published in:Journal of non-Newtonian fluid mechanics 2010-05, Vol.165 (9), p.544-550
Main Authors: Muravleva, Larisa, Muravleva, Ekaterina, Georgiou, Georgios C., Mitsoulis, Evan
Format: Article
Language:English
Subjects:
Annular
Augmented Lagrangian method (ALM)
Bingham plastic
Cessation flows
Constitutive relationships
Couette flow
Finite stopping times
Iterative Uzawa algorithm
Laminar flow
Mathematical models
Planes
Poiseuille flows
Tubes
Variational inequalities
Walls
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Summary: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.
ISSN:0377-0257
1873-2631
DOI:10.1016/j.jnnfm.2010.02.002