Study of the Navier Stokes equations of an Airfoil via the FEM

The goal of the Master thesis is to understand though numerical experiments the following aspects: FEM methodology The Stokes problemThe Navier-Stokes problemThe present work is one of the five theses conforming the FEM-MAT-OO(finite element - Matlab - object oriented) project. The code has been de-veloped by five students and it can simulate several problem types: topologyoptimization, non-linear deformation, heat transfer and fluid flow problems.Finite element method (FEM) is a tool for solving engineering and physicalproblems. One of the main advantage of FEM is its capability to deal withcomplex geometry problems. In the past FEM was restricted to structuralanalysis, but since few decades ago its use in fluid problems has been increasing.The aim of this project to develop a finite element code for studying theLaplace’s problem, Stokes flow and Navier-Stokes flow. To this aim severalsteps have been followed. First, an introduction to finite element method in theelastic framework is done. Secondly, FEM is applied to a conduction problemgoverned by the Laplace’s equation. After that the study of the Stokes flow(either steady or transient), and the Navier-Stokes flow is performed (Onlytheoretical aspects are provided of the Navier-Stokes case, leaving the finalresults for the oral defense)