Numerical simulations of cessation flows of a Bingham plastic with the augmented Lagrangian method |
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Authors: | Larisa Muravleva Ekaterina Muravleva Georgios C. Georgiou Evan Mitsoulis |
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Affiliation: | 1. College of Science and Engineering, Flinders University, GPO Box 2100, Adelaide SA 5001, Australia;2. Department of Mathematics and Statistics, University of Cyprus, PO Box 20537, 1678 Nicosia, Cyprus |
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Abstract: | 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. |
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