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This lecture covers the hierarchy of simulation approaches in fluid dynamics, including Direct Numerical Simulation (DNS), Large-Eddy Simulation (LES), and Reynolds-Averaged Navier-Stokes equations (RANS). It explains the scale separation and the closure problem in Reynolds equations, highlighting the challenges in determining Reynolds stresses. The instructor discusses the limitations of DNS and the modeling assumptions in LES and RANS. The lecture emphasizes the importance of resolving all length- and timescales of turbulence for accurate simulations.