Simulação numérica das equações de Navier-Stokes pelo método de diferenças finitas para um escoamento incompressível

Abstract

The numeric simulation is used widely in the fluid dynamics area, because through the use of numeric methods the behavior of different types of fluid flows can be analyzed. In this work the numeric simulation of an incompressible flow was accomplished using Navier-Stokes equations applied for the fluid flow inside square cavity and also to a hydraulic jump. To solve these equations, we decided to apply the finite difference method, with a time-space discretization. In both cases, the square cavity and hydraulic jump, we used structured meshes with quadrangular elements in the discretization of the spatial domain. To couple the velocity and pressure in Navier-Stokes equations two methods were applied: the fractional-step projection method and the penalty method, facilitating the resolution of these equations. Through the code written in C++ language simulations of two-dimensional flow were accomplished for the Reynolds number 100, 400 and 1000 for the square cavity and Reynods 100 and 400 for the hydraulic jump. The numeric results obtained with the fractional-step projection method were satisfactory when compared with the results of the reference, different from the Penalty method that was less effective. For the case of the hydraulic jump decided to use the Projection method, because it was efficient in the previous case. The velocity fields were analyzed, in which some characteristics can be see, as vortexes in the lower corner, when the Reynolds number increases.