Residual stress of approximate deconvolution models of turbulence
Résumé
We consider the case of a homogeneous, isotropic, fully developed, turbulent flow. We show analytically by using the -5/3 Kolmogorov's law that the time-averaged consistency error of the Nth approximate deconvolution LES (large eddy simulation) model converges to zero following a law as the cube root of the averaging radius, independently of the Reynolds number. The consistency error is measured by the residual stress. The filter under consideration is a second-order differential filter, but the 1/3 law is still valid in the case of the Gaussian filter and large class of filters used in LES. We also show how the 1/3 error law can be derived by a dimensional analysis.