Direct and Large Eddy Simulations

This chapter presents Direct Numerical Simulation (DNS) and Large Eddy Simulation (LES) as two advanced techniques for resolving turbulent flows. The chapter outlines the turbulence energy spectrum, derives the Kolmogorov length scale, and details the spatial and temporal resolution requirements for DNS. LES filtering approaches explicit and implicit are examined using Gaussian, box, and spectral filters. The filtered Navier–Stokes equations are shown to yield subgrid stress terms, which are modeled. Subgrid scalar-flux modeling and near-wall treatments are also addressed. A case study on turbulent flow in a square duct demonstrates that LES can accurately capture secondary motions and wall shear stress distribution, consistent with DNS results. The chapter concludes with a discussion of enstrophy-preserving Arakawa scheme.