Numerical solution of duct flows of multiple visco-plastic fluids

Numerical solution of duct flows of multiple visco-plastic fluids

M.A. Moyers-Gonzaleza∗, I.A. Frigaarda,b
a Department of Mathematics, University of British Columbia, 1984 Mathematics Road, Vancouver, BC, Canada V6T 1Z2
b Department of Mechanical Engineering, University of British Columbia, 2324 Main Mall, Vancouver, BC, Canada V6T 1Z4
Received 31 July 2003; received in revised form 13 November 2003; accepted 15 December 2003
This article is part of a Special Volume containing papers from the XIIIth International Workshop on Numerical Methods in Viscoelastic Flows
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Abstract

We consider numerical solution of duct flows of multiple visco-plastic fluids using both regularisation techniques and the augmented Lagrangian method. Using single fluid test problems, we demonstrate that there are certain classes of problems for which the augmented Lagrangian method is superior. These problems include those of determining the critical Bingham numbers and pressure gradients for which the flow stops, i.e. the yield limit.We then apply this method to two practical problems involving multiple fluids in ducts: multi-layer lubrication flows and counter-current exchange flows. Again we demonstrate the effectiveness of the augmented Lagrangian method for this type of problem.
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Keywords: Bingham fluid; Zero-flow limit; Multi-layer flow; Augmented lagrangian method