7. Conclusion

The new concepts we have just presented are of two kinds: theoretical and numerical.

• New theories

  DNS (Direct Numerical Simulation). The unsteady Navier-Stokes equations for compressible fluids fully describe turbulent flows. Due to the technical limitations of computers, this resolution is currently impossible for complex flows. Hence the LES.

  LES (Large Eddy Simulation). Large structures are sensitive to flow geometry, whereas small structures have a more universal behavior that can be represented by a model. But this is still impossible for turbulent flows in large domains. Hence RANS.

  RANS (Reynolds Averaged Navier-Stokes ). This statistical approach to turbulence is the most widely used in industry. It gives a stationary solution of the flow, which may suffice...