The complex behavior of fluid ow, including turbulence, can be mathematically considered as the consequence of a fairly simple set of equations as those presented in Chapter 1. Unfortunately, analytical solutions to even the simplest turbulent ows have not been found so far or they simply do not exist. However, a complete turbulent ow where the ow variables are functions of space and time can be obtained numerically. is is known as the CFD approach. As advanced CFD techniques, DNS and LES have been evolving rapidly over the last few decades, mainly as tools for research. DNS has emerged as the most powerful numerical tool to understand the fundamentals of ow instabilities, transition to turbulence, and relatively low or moderate Reynolds number turbulent ows, but high Reynolds number ows and large-scale problems remain untouchable. In addition, complex geometry problems still represent a signicant diculty for DNS. In the meantime, LES has been gradually evolving from a research tool toward a useful tool for practical applications.