Método de otimização topológica aplicado a escoamentos incompressíveis integrando o método de elementos finitos (MEF) multiescala estabilizado

Abstract

Flow machines, over the years, have played a significant role in industrial activity, contributing positively to the development of humanity. As a result, studies focused on the field of fluid mechanics have been increasingly explored in order to contribute to the development of new technologies in the field of engineering. The objective of this work is to employ topological optimization in incompressible flows, using as an aid the implementation of the multiscale variational method capable of providing a stabilized finite element formulation for the NavierStokes equation, to seek the best material distribution along the fixed domain of project. The initial step takes place through the calculation of all flow conditions from the equations of the Navier-Stokes equations, and then the finite element method performs the approximation of the differential equations. The interest in combining the stabilized multiscale variational finite element method with the topological optimization method is to be able to provide a stable finite element structure. Then, the topological optimization process is started, in this work, using as objective the minimization of head loss in a predefined domain in which a material model is used in a porous medium. In this process, a method based on the objective function gradient is used to define the sensitivity analysis. As a way of attesting the topological optimization, combined with the stabilized multiscale variational method proposed in this work, the application of topological optimization is performed in some geometries already known in the literature. The optimization results performed in this project presented results very close to those in the literature. In general, the device optimization project, by combining the MOT with the multiscale finite element method, proved to be usable in the proposed project.