# Path following methods for steady laminar Bingham flow in cylindrical pipes

Juan Carlos De Los Reyes; Sergio González

- Volume: 43, Issue: 1, page 81-117
- ISSN: 0764-583X

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topJuan Carlos De Los Reyes, and González, Sergio. "Path following methods for steady laminar Bingham flow in cylindrical pipes." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 43.1 (2009): 81-117. <http://eudml.org/doc/245853>.

@article{JuanCarlosDeLosReyes2009,

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.},

author = {Juan Carlos De Los Reyes, González, Sergio},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},

keywords = {Bingham fluids; variational inequalities of second kind; path-following methods; semi-smooth Newton methods; duality theory; regularization},

language = {eng},

number = {1},

pages = {81-117},

publisher = {EDP-Sciences},

title = {Path following methods for steady laminar Bingham flow in cylindrical pipes},

url = {http://eudml.org/doc/245853},

volume = {43},

year = {2009},

}

TY - JOUR

AU - Juan Carlos De Los Reyes

AU - González, Sergio

TI - Path following methods for steady laminar Bingham flow in cylindrical pipes

JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

PY - 2009

PB - EDP-Sciences

VL - 43

IS - 1

SP - 81

EP - 117

AB - 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.

LA - eng

KW - Bingham fluids; variational inequalities of second kind; path-following methods; semi-smooth Newton methods; duality theory; regularization

UR - http://eudml.org/doc/245853

ER -

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