Equações de Navier-Stokes Research Papers (original) (raw)
In parts 1 - 3 the method was described for solving cases of unidirectional flow. It was, obviously, an introduction to the concept of the method. In part 4 it is shown how this method can be used to solve an exemple of 2 dimensional... more
In parts 1 - 3 the method was described for solving cases of unidirectional flow. It was, obviously, an introduction to the concept of the method. In part 4 it is shown how this method can be used to solve an exemple of 2 dimensional flow. The square box problem with no convection is solved with this method in order to show its viability to be applied in cases of multidirectional fow
Stokes proposed a very ingenious method for describing 2-D flows, which uses one single equation that represents 3 different ones. However, this method is completelly useless to describe 3-D flows. Those have been a challenge to... more
Stokes proposed a very ingenious method for describing 2-D flows, which uses one single equation that represents 3 different ones. However, this method is completelly useless to describe 3-D flows. Those have been a challenge to mechanical engineers. So far there is no method described in the literature that allows analytical solution to 3-D flows. Numerical methods use routines that are extremely expensive, in terms of computer resources. This article proposes a method that allows analytical solution to 3-D flows - if the convective terms are not present - and present some advatages for using in numerical simulators. Because it is too long, it has been divided into parts. This is part one, an introduction and the description of its use only in the simplest situation of all: no convective terms and recttangular coordinates.
In parts 1 and 2 it has been shown how to use this method when the convective terms are not present. In those cases, if the boundaries are not much irregular, analytical solutions are possible. In this article it is shown how to use it... more
In parts 1 and 2 it has been shown how to use this method when the convective terms are not present. In those cases, if the boundaries are not much irregular, analytical solutions are possible. In this article it is shown how to use it when the convective terms ARE present. In those cases, only numerical methods can be applied to solve the equations. No example of numerical aplication of the method is presented.
The square box problem has no importance by itself. However it is a very usefull way to check de validity of certain numerical methods, due to its simplicity. Because this very simplicity, one should think that, if the non linear therms... more
The square box problem has no importance by itself. However it is a very usefull way to check de validity of certain numerical methods, due to its simplicity. Because this very simplicity, one should think that, if the non linear therms are present, an analytical solution would be easy to obtain. It is therefore surprising that, to the author's knowledge, there is still no analytical solution for this problem in the literature. This work shows an analytical solution for it, which shows that it is not so simple as the simplicity of the problem sugests. The importance or this solution is also discussed.