Abstracts Mathematics

Soluções analíticas e numéricas para escoamentos incompressíveis Newtonianos e não-Newtonianos: Analytical and numerical solutions for Newtonian and non-Newtonian incompressible flows

by Isabella Lopes Corrêa

The present work presents a study about the analytical and numerical solutions for some classes of incompressible, isothermal and laminar flows of Newtonian fluids in the steady or transient state. Analytical solutions for steady state flows of non-Newtonian fluids will also be obtained, using the Power Law model. As a consequence of the difficulty in obtaining analytical solutions of a Partial Differential Equations system, the flows presented in this work belong to the class of unidirectional and rectilinear flows. In this way, the analytical problem is reduced to two primary unknown variables: the non-zero component of velocity and pressure, thus, a simple integration or consolidated techniques of mathematics, such as Solutions by Similarity and Separation of Variables, will be applied to obtain the analytical solutions. The numerical solutions are presented here in order to widen the studies in the area, which provides the possibility of solving the equations that model other classes of the flows. The method employed to obten the numerical solutions used will be the Projection Method, which consists on decoupling the velocity and pressure variables from the Navier-Stokes equations. The resulting equations will be approximated by the Finite Difference technique on a staggered grid. The analytical solutions obtained will be very useful for the process of verification of the numerical methodology, which is implemented in Python.