Path following methods for steady laminar Bingham flow in cylindrical pipes
ESAIM: Modélisation mathématique et analyse numérique, Tome 43 (2009) no. 1, pp. 81-117.

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.

DOI : 10.1051/m2an/2008039
Classification : 47J20, 76A10, 65K10, 90C33, 90C46, 90C53
Mots clés : Bingham fluids, variational inequalities of second kind, path-following methods, semi-smooth Newton methods
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     author = {Juan Carlos De Los Reyes and Gonz\'alez, Sergio},
     title = {Path following methods for steady laminar {Bingham} flow in cylindrical pipes},
     journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
     pages = {81--117},
     publisher = {EDP-Sciences},
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}
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Juan Carlos De Los Reyes; González, Sergio. Path following methods for steady laminar Bingham flow in cylindrical pipes. ESAIM: Modélisation mathématique et analyse numérique, Tome 43 (2009) no. 1, pp. 81-117. doi : 10.1051/m2an/2008039. http://www.numdam.org/articles/10.1051/m2an/2008039/

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