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The nonlinear Galerkin method: A multiscale method applied to the simulation of homogeneous turbulent flows. (English) Zbl 0838.76060
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.

MSC:
76M25 Other numerical methods (fluid mechanics) (MSC2010)
76F05 Isotropic turbulence; homogeneous turbulence
76D05 Navier-Stokes equations for incompressible viscous fluids
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
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