Stability of the dual Navier–Stokes equations and efficient computation of mean output in turbulent flow using adaptive DNS/LES

We discuss aspects of adaptive DNS/LES, where adaptive finite element methods are used to accurately compute chosen output from a turbulent flow with the computational power of a PC. The key to this break-through is: (i) application of the general approach to adaptive error control in Galerkin methods based on duality, coupled with (ii) crucial properties of turbulent flow allowing accurate computation of mean value quantities such as drag and lift without full resolution of all scales.