Debussche, A.; Dubois, T.; Temam, Roger The nonlinear Galerkin method: A multiscale method applied to the simulation of homogeneous turbulent flows. (English) Zbl 0838.76060 Theor. Comput. Fluid Dyn. 7, No. 4, 279-315 (1995). 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. Cited in 2 ReviewsCited in 23 Documents 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 Keywords:Kolmogorov-like flows; multilevel scheme; self-adaptative procedure PDFBibTeX XMLCite \textit{A. Debussche} et al., Theor. Comput. Fluid Dyn. 7, No. 4, 279--315 (1995; Zbl 0838.76060) Full Text: DOI References: [1] P. Moin and J. Kim, Numerical investigation of turbulent channel flow, J. Fluid Mech., 118 (1982), 341-377. · Zbl 0491.76058 [2] J. Kim, P. Moin, and R. Moser, Turbulence statistics in full developed channel flow at low Reynolds number, J. Fluid Mech., 177, (1987), 133-166. · Zbl 0616.76071 [3] G. Erlebacher, M.Y. Hussaini, C.G. Speziale, and T.A. Zang, Toward the large-eddy simulation of compressible turbulent flows, J. 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