Optimization Techniques for the Numerical Simulation of Non-Newtonian Fluids

Sergio Gonzalez-Andrade^*

This talk is devoted to the discussion of several optimization techniques applied to the numerical simulation of non-Newtonian fluid flow. We focus on viscoplastic materials which are modeled by variational inequalities of the second kind. Particularly, we are concerned with Bingham, Casson and Herschel-Bulkley models. We propose a regularization approach for the numerical resolution of these models, based on local regularization procedures of Huber type. 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, we discuss several methods from semismooth Newton methods to trust regions methods. Further, we present several applications such as pipe flow, channel flow, convective flow and multiple fluids flow.

Mathematics Subject Classification: 76A05 65K10 47J20

Keywords: Bingham fluids, variational inequalities of second kind, path-following methods, optimization techniques

Minisymposion: Optimization of Mechanical Systems