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.
@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 - Mod\'elisation Math\'ematique et Analyse Num\'erique},
volume = {43},
year = {2009},
pages = {81-117},
doi = {10.1051/m2an/2008039},
mrnumber = {2494795},
zbl = {1159.76033},
language = {en},
url = {http://dml.mathdoc.fr/item/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 - Modélisation Mathématique et Analyse Numérique, Tome 43 (2009) pp. 81-117. doi : 10.1051/m2an/2008039. http://gdmltest.u-ga.fr/item/M2AN_2009__43_1_81_0/
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