Optimal Control problems applied to non-Newtonian Fluids

Orador: Telma Margarida Cotovio Guerra Santos (Escola Superior de Tecnologia do Barreiro do Instituto Politécnico de Setúbal e CEMAT). Data, hora e local: 22 de Abril de 2015, início às 16h na sala 6.16.

Resumo: Optimal control problems had a tremendous advance in the last few decades mainly motivated by several areas of engineering applications. In particular, applications of optimal control techniques to fluid flow has been a matter of great interest for researchers in the field.
This work is based on the study of control problems for a class of non-Newtonian fluids, with shear-dependent viscosity. Some theoretical results related to the steady, Navier-Stokes generalized state equations, and to the existence of solution for the control problem of a non-Newtonian, incompressible fluid governed by these equations are presented. On the other hand numerical simulations of Data Assimilation control problems applied to Hemodynamics with great interest in Biomedicine are presented considering two-dimensional and three-dimensional idealized geometries with physiological interest. A realistic cerebral artery with a saccular aneurysm is considered as well. The goal is to ​obtain numerical solutions to the proposed problems implementing Data Assimilation techniques in a variational approach prescribing a Dirichlet control at the inlet boundary. The results should coincide, whithin a certain error, to observed data measured at certain parts of the domain.
A discretize then optimize approach, together with a sequential quadratic programming algorithm, is applied to solve the nonlinear optimal control problem and we propose a weighted cost function that accurately recovers both the velocity and wall shear stress profiles. The results show that better accuracy is achieved, when compared with typical simulations based on flow rate measurements.

Funded by the Portuguese Government through the FCT – Fundação para a Ciência e a Tecnologia under the project UID/MAT/00212/2013


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