Les turbulence models. Relation with stabilized numerical methods

has turned into one of the most complex and important problems in science and engineering. It is accepted that Navier-Stokes equations, used to describe the behaviour of viscous incompressible fluids, describe properly turbulent phenomena. Consequently, considering the enormous capacity of actual computers, it is possible to consider that high precision numerical simulations of the Navier-Stokes equations can solve the problem of turbulence. Unfortunately, at current rhythm of growing of computing power, the attempts of direct numerical simulation of Navier-Stokes equations have been limited to low Reynolds numbers, Re . This type of direct simulations are usually known by its English acronym DNS. The reason for this limited success of the DNS is explained by means of the heuristic estimator of Kolmogorov, ( ) 9 O Re 4 , of the necessary degrees of freedom to simulate a flow to a certain Reynolds number. Considering the current advance of the computation technology, this estimator indicates that the possibility of using DNS for flows with high Reynolds numbers is still surely distant. From its beginnings the attempts of simulating turbulence have been focused on models based on the average in time or in space of magnitudes involved in the problem (velocity, pressure,…) originating the models of turbulence associated with the RANS equations (Reynolds Averaged Navier-Stokes) like k − ε , k − ω ,… These models have been widely used in engineering as an alternative to the impossibility to overcome the difficulties of DNS