Path following methods for steady laminar Bingham flow in cylindrical pipes

Research Group on Optimization, Departmento de Matemática, EPN Quito, Ecuador. jcdelosreyes@math.epn.edu.ec; sgonzalez@math.epn.edu.ec

Received: 15 June 2007
Revised: 2 June 2008

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.