ALE finite element method for simulating flows with the streamfunction-vorticity formulation

• Ano de defesa: 2020
• Autor(a) principal: Cunha, Luís Henrique Carnevale da
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• Idioma: eng
• Instituição de defesa: Universidade do Estado do Rio de Janeiro; Centro de Tecnologia e Ciências::Faculdade de Engenharia; Brasil; UERJ; Programa de Pós-Graduação em Engenharia Mecânica
• Palavras-chave em Português: Mechanical engineering; Fluid dynamics; Finite element method; Algorithms; Engenharia mecânica; Dinâmica dos fluidos; Método dos elementos finitos; Algoritmos; ENGENHARIAS::ENGENHARIA MECANICA::FENOMENOS DE TRANSPORTE
• Link de acesso: http://www.bdtd.uerj.br/handle/1/17277

Fluid Dynamics is an important area of research in many fields of science and engineering. It is present in the study of aerodynamics, heat exchanges, meteorology and even in biological systems. Due to the complex behavior of flow in different circumstances, being able to accurately describe the fluid motion is a challenge. The purpose of this dissertation is to implement a Finite Element algorithm capable of simulating one phase two-dimensional flow using movable computational mesh grids. The mathematical model of fluid flow used is the stream function-vorticity formulation which is a substitute for the Navier-Stokes equation and is written for the Arbitrary Lagrangian-Eulerian referential to accommodate the mesh movement. A first order semi-Lagrangian method is used to approximate the advective term found in the formulation. This is an unconditionally stable method which allows the algorithm to take larger time steps. A third party open source software called GMSH is used to generate the computational mesh with linear triangular elements. To avoid large distortions, a Laplacian smoothing technique is implemented to help maintain the mesh quality during its movement. Code development is based on Python script language where highly demanding methods are implemented in its compiling version namely Cython. Several test cases were successfully used as benchmarks to verify and validate the proposed new methodology including the cavity driven and Poiseuille flows. Additionally, the flow past an object was chosen as study case for several interesting geometries including the classical cylinder.