variavel0=<b>Milton Biage</b> - mbiage@mecanica.ufu.br Universidade Federal de Uberlândia
<b>Cassius Ricardo Nascimento Ferreira</b> - Cassius@mecanica.ufu.br Universidade Federal de Uberlândia
<b>Paulo Lopes Da Silva Junior</b> - plopes@mecanica.ufu.br Universidade Federal de Uberlândia
<b>Abstract.</b> This work is a study of development of the collocation spectral elements technique, in which intended to verify the efficiency of the technique to simulate compressible turbulent flow. For such, studies of simulation for both one-dimensional and two-dimensional flows were developed, involving the discontinuity propagations and the large scale fluctuations. In particular, the proposed studies allowed to verify the dissipation levels and of precision of the technique. It was chosen to simulate as onedimensional compressible flows the square wave’s propagation and shock tubes flow, as classically it is accomplished to gauge the dissipation level of numerical techniques. Also, it was chosen to simulate two-dimensional mixing layers developing either temporarily or spatially. These problems constitute flows with behaviors differentiated along the domain, characterized by multiple zones, which are dominated either by the hyperbolic effects or for elliptic effects, or for a mixture of these two effects. The monotonous convergence for a solution in the hyperbolic flow zone demands high levels of numerical dissipation, having the need to introduce an artificial numerical dissipation. In the case of the collocation spectral element technique, digital filter is used in the time or in frequency, with the advantage that the cutoff frequencies can be varied of elements for elements. The collocation spectral element technique used in that formulation considers that the surfaces among the elements are known. A completely original equation formulation was developed for mass conservation, momentum and energy for the interfaces among the elements that compose the domain. The importance of these formulations is in the fact of allowing obtaining solutions for problems with moving interfaces and in the fact that the conservation equations for the interface allow the propagation of discontinuity phenomena, such as shocks in compressible flow and ignitions in reacting flow. The obtained results showed that the technique of the collocation spectral elements was shown quite efficient to simulate complex flows, with presence of strong discontinuities and preserving the coherent structures of large scale, constituting a quite promising tool to simulate flows in fluid dynamics.
<b>Keywords.</b> Collocation spectral element method, shock tubes, propagation of waves, mixing layer developing temporarily.