Tese: Topology Optimization for non-Newtonian Fluid-Flow Problems using the Virtual Element Method
Aluno(a) : Miguel Ángel Ampuero SuárezOrientador(a): Ivan Menezes
Área de Concentração: Mecânica Aplicada
Data: 17/03/2020
Link para tese/dissertação: http://doi.org/10.17771/PUCRio.acad.49171
Resumo: This work presents selected applications of topology optimization for non-Newtonian fluid flow problems using the virtual element method (VEM) in arbitrary two-dimensional domains. The objective is to design an optimal layout into a fluid flow domain to minimize dissipative energy governed by the Navier–Stokes–Brinkman and non-Newtonian Carreau–Yasuda model equations. The porosity approach proposed by (Borrvall and Petersson, 2003) [1] is used in the topology optimization formulation. To solve this problem numerically, the recently proposed VEM method is used. The key feature that distinguishes VEM from the standard finite element method (FEM) is that the interpolation functions in the interior of the elements do not need to be computed explicitly. This is because the integration is on lower-order polynomial and basis functions, and there is great flexibility by using a nonconvex element. Therefore, the computation of the main element matrices and vectors are reduced to the evaluation of geometric quantities on the boundary of the elements. Finally, several numerical examples are provided to demonstrate the efficiency of the VEM compared to FEM and the applicability of the topology optimization to fluid flow problems.