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Path following methods forsteady laminar Bingham flow in cylindrical pipes

Published online by Cambridge University Press:  16 October 2008

Juan Carlos De Los Reyes  and
Sergio González
Juan Carlos De Los Reyes
Affiliation:
Research Group on Optimization, Departmento de Matemática, EPN Quito, Ecuador. jcdelosreyes@math.epn.edu.ec; sgonzalez@math.epn.edu.ec
Sergio González
Affiliation:
Research Group on Optimization, Departmento de Matemática, EPN Quito, Ecuador. jcdelosreyes@math.epn.edu.ec; sgonzalez@math.epn.edu.ec
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Abstract

This paper is devoted to the numerical solution of stationary laminar Bingham fluids by path-following methods. By using duality theory, a system that characterizes the solution of the original problem is derived. Since this system is ill-posed, a family of regularized problems is obtained and the convergence of the regularized solutions to the original one is proved. For the update of the regularization parameter, a path-following method is investigated. Based on the differentiability properties of the path, a model of the value functional and a correspondent algorithm are constructed. For the solution of the systems obtained in each path-following iteration a semismooth Newton method is proposed. Numerical experiments are performed in order to investigate the behavior and efficiency of the method, and a comparison with a penalty-Newton-Uzawa-conjugate gradient method, proposed in [Dean et al., J. Non-Newtonian Fluid Mech.142 (2007) 36–62], is carried out.

Keywords

Bingham fluidsvariational inequalities of second kindpath-following methodssemi-smooth Newton methods.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 43 , Issue 1 , January 2009 , pp. 81 - 117
Copyright
© EDP Sciences, SMAI, 2008

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