The nonlinear Galerkin method: A multiscale method applied to the simulation of homogeneous turbulent flows (Q1905654)

Using results of direct numerical simulations in the case of two-dimensional homogeneous isotropic flows, we first analyze in detail the behavior of the small and large scales of Kolmogorov-like flows at moderate Reynolds numbers. We propose a multilevel scheme which treats the small and the large eddies differently. We derive estimates of all the parameters involved in the algorithm, which then becomes a completely self-adaptative procedure. Finally, we perform realistic simulations 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.