THE NONLINEAR GALERKIN METHOD - A MULTISCALE METHOD APPLIED TO THE SIMULATION OF HOMOGENEOUS TURBULENT FLOWS

Using results of DNS in the case of two-dimensional homogeneous isotro pic flows, we first analyze in detail the behavior of the small and la rge scales of Kolmogorov-like flows at moderate Reynolds numbers. We d erive several estimates on the time variations of the small eddies and the nonlinear interaction terms; these terms play the role of the Rey nolds stress tenser in the case of LES. Since the time step of a numer ical scheme is determined as a function of the energy-containing eddie s of the flow, the variations of the small scales and of the nonlinear interaction terms over one iteration can become negligible by compari son with the accuracy of the computation. Based on this remark, we pro pose a multilevel scheme which treats the small and the large eddies d ifferently. Using mathematical developments, we derive estimates of al l the parameters involved in the algorithm, which then becomes a compl etely self-adaptative procedure. Finally, we perform realistic simulat ions of (Kolmogorov-like) flows over several eddy-turnover times. The results are analyzed in detail and a parametric study of the nonlinear Galerkin method is performed.