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Analysis of numerical errors in large eddy simulation. (English) Zbl 1026.76028

The numerical errors in large eddy simulation are studied analytically assming some time regularity of the solution of Navier-Stokes equations. First, a finite element formulation for LES method using Smagorinsky model is presented together with stability analysis. Then error equations are derived which suggest that uniformity in the Reynolds number can be accomplished by controlling subgrid scale effects and by using an adapted numerical method. Using a fractional step scheme with a finite element space discretization and a Smagorinsky sub-grid scale model, the authors present a numerical illustration for an academic two-dimensional flow with known exact solution, i.e. the decay of an array of opposite signed vortices. The maximum error as a function of the Reynolds number for two different space discretizations is studied, and its independence of the Reynolds number is shown which confirms the theoretical convergence analysis.

MSC:

76F65 Direct numerical and large eddy simulation of turbulence
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
76M10 Finite element methods applied to problems in fluid mechanics
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