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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.
Mots-clés : Bingham fluids, variational inequalities of second kind, path-following methods, semi-smooth Newton methods
@article{M2AN_2009__43_1_81_0,
author = {Juan Carlos De Los Reyes and Gonz\'alez, Sergio},
title = {Path following methods for steady laminar {Bingham} flow in cylindrical pipes},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {81--117},
publisher = {EDP-Sciences},
volume = {43},
number = {1},
year = {2009},
doi = {10.1051/m2an/2008039},
zbl = {1159.76033},
mrnumber = {2494795},
language = {en},
url = {https://geodesic-test.mathdoc.fr/articles/10.1051/m2an/2008039/}
}
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 PY - 2009 SP - 81 EP - 117 VL - 43 IS - 1 PB - EDP-Sciences UR - https://geodesic-test.mathdoc.fr/articles/10.1051/m2an/2008039/ DO - 10.1051/m2an/2008039 LA - en ID - M2AN_2009__43_1_81_0 ER -
%0 Journal Article %A Juan Carlos De Los Reyes %A González, Sergio %T Path following methods for steady laminar Bingham flow in cylindrical pipes %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2009 %P 81-117 %V 43 %N 1 %I EDP-Sciences %U https://geodesic-test.mathdoc.fr/articles/10.1051/m2an/2008039/ %R 10.1051/m2an/2008039 %G en %F M2AN_2009__43_1_81_0
Juan Carlos De Los Reyes; González, Sergio. Path following methods for steady laminar Bingham flow in cylindrical pipes. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 43 (2009) no. 1, pp. 81-117. doi : 10.1051/m2an/2008039. https://geodesic-test.mathdoc.fr/articles/10.1051/m2an/2008039/
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