Simulações de escoamentos de fluidos newtonianos usando o método do tubo de trajetórias nas variáveis vorticidade e função de corrente.

Abstract

Navier-Stokes equations are widely used in many areas of knowledge. However, one of its primary variables is not unique in determining what, sometimes, makes the analysis of physical phenomena unfeasible. This thesis aims, initially, to present a new lagrangian formulation for the Navier-Stokes equations by introducing the vorticity and stream functions as variables. In this way, the problem of uniqueness is eliminated. Then, we will address the flow of incompressible fluids in the plane and we will develop a new method for determining solutions of such equations. For this, we will describe the trajectory of each fluid particle, which gives rise to the name of Path Tube Method. Also, we will compare our method with tools previously used to solve the same problem. In addition, we will observe how the techniques derived from parallel computing can contribute to the reduction of the computational costs. To conclude, we will address the advantages of the new method and we will indicate perspectives for future research.