Turbulence modelling and numerical issues: from RANS to DNS and LES

The objective of this work is to show possibilities and limitations of different turbulence models from RANS to DNS and LES. Firstly, standard approaches based on time averaging the governing equations (the so called Reynolds Averaged Navier-Stokes equations or RANS models) are presented. Attention is focused on explicit algebraic and eddy-viscosity linear and non-linear two-equation models. Aspects related to forced and natural convection, low-Reynolds number approaches, numerical issues, etc. are shown. A different simulation level is then presented: the Direct Numerical Simulation or DNS approach. This kind of analysis describes the whole range of the turbulent motion scales, from the largest ones (similar to the domain size) to the smallest ones (also called dissipative or Kolmogorov scales), where the fluctuations are damped and turbulent energy is irreversibly converted into internal energy. Aspects related to the discretization of the governing equations and the necessity of preserving some properties of the Navier-Stokes equations are pointed out. Examples are shown with emphasis on the possibilities and limitations of this important approach where no empirical inputs are needed at all. The paper ends with promising turbulence models based on the full simulation of the largest scales of the turbulent flow, while the smaller ones are modelled. This is called Large Eddy Simulation or LES approach. Discussion starts with classical techniques based on modelling the non-linear interactions of the convective operator as a diffusion term. Afterwards, the use of regularization techniques as a large eddy simulation model is discussed. The formulation is based on symmetry-preserving discretization methodology on non-structured and collocated meshes. In this approach, the length of the filter is the only empirical parameter used by the model. Examples of both natural and forced convection in well-known benchmark cases, and also in industrial applications, are presented.