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Journal Articles Computer Methods in Applied Mechanics and Engineering Year : 2015

Efficient numerical computations of yield stress fluid flows using second-order cone programming

Abstract

This work addresses the numerical computation of the two-dimensional flow of yield stress fluids (with Bingham and Herschel-Bulkley models) based on a variational approach and a finite element discretization. The main goal of this paper is to propose an alternative op-timization method to existing procedures such as penalization and augmented Lagrangian techniques. It is shown that the minimum principle for Bingham and Herschel-Bulkley yield stress fluid steady flows can, indeed, be formulated as a second-order cone programming (SOCP) problem, for which very efficient primal-dual interior point solvers are available. In particular, the formulation does not require any regularization of the visco-plastic model as is usually the case for existing techniques, avoiding therefore the difficult choice of the regularization parameter. Besides, it is also unnecessary to adopt a mixed stress-velocity approach or discretize explicitly auxiliary variables as frequently proposed in existing meth-ods. Finally, the performance of dedicated SOCP solvers, like the Mosek software package, enables to solve large-scale problems on a personal computer within seconds only. The pro-posed method will be validated on classical benchmark examples and used to simulate the flow generated around a plate during its withdrawal from a bath of yield stress fluid.
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Dates and versions

hal-01081508 , version 1 (08-11-2014)

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Jeremy Bleyer, Mathilde Maillard, Patrick de Buhan, Philippe Coussot. Efficient numerical computations of yield stress fluid flows using second-order cone programming. Computer Methods in Applied Mechanics and Engineering, 2015, 283, pp.599 - 614. ⟨10.1016/j.cma.2014.10.008⟩. ⟨hal-01081508⟩
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