Path following methods for steady laminar Bingham flow in cylindrical pipes

Juan Carlos De Los Reyes; Sergio González

ESAIM: Mathematical Modelling and Numerical Analysis (2008)

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

Abstract

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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.

How to cite

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De Los Reyes, Juan Carlos, and González, Sergio. "Path following methods for steady laminar Bingham flow in cylindrical pipes." ESAIM: Mathematical Modelling and Numerical Analysis 43.1 (2008): 81-117. <http://eudml.org/doc/194448>.

@article{DeLosReyes2008,
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 = {De Los Reyes, Juan Carlos, González, Sergio},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Bingham fluids; variational inequalities of second kind; path-following methods; semi-smooth Newton methods.; semi-smooth Newton methods; duality theory; regularization},
language = {eng},
month = {10},
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/194448},
volume = {43},
year = {2008},
}

TY - JOUR
AU - De Los Reyes, Juan Carlos
AU - González, Sergio
TI - Path following methods for steady laminar Bingham flow in cylindrical pipes
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2008/10//
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.; semi-smooth Newton methods; duality theory; regularization
UR - http://eudml.org/doc/194448
ER -

References

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