Statistical models (RANS)
Although much more expensive simulation methods (large eddy simulation, direct numerical simulation) are gaining importance, the standard in today’s industrial practice remains statistical (RANS) modeling and, even if the future is promised to the development of unsteady simulations, there will always be very important needs for statistical modeling.
A widespread practice consists in starting from models using too restrictive hypotheses and in making them more complex so that they are able to take into account the largest range of phenomena. A more productive approach is to start from models with much less restrictive assumptions, but impossible to use for industrial applications, and to reduce step by step their complexity and numerical instability while keeping as much physics as possible.
The Reynolds-averaged equations are closed at second order (7-equation model), to which are added the 6 elliptic relaxation equations to represent the wall effects (13-equation model), which in addition naturally include the additional physical phenomena (buoyancy effects, rotation effects, etc.). The aim is to simplify the models to make them more manageable for industrial applications, while trying to keep as much physics as possible: elliptic blending instead of elliptic relaxation; weak equilibrium assumptions to build algebraic models; reintroduction of the turbulent viscosity hypothesis. Many models of different levels of complexity can be built following this method, which meet different needs of industrial applications.
