## 00-19

#### Analysis of Numerical Errors in Large Eddy Simulation

**Preprint series:** 00-19, Preprints

**MSC****:**- 65M60 Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods

**Abstract:** We consider the question of ``numerical errors\'\' in large eddy simulation. It is often claimed that straightforward discretization and solution using centered methods of models for large eddy motion can simulate the motion of turbulent flows with complexity independent of the Reynolds number and depending only on the resolution ``$\delta$\'\' of the eddies sought. This report considers precisely this question analytically: is it possible to prove error estimates for discretizations of {\it actually used} large eddy models whose error constants depend only on $\delta$ but not $Re$? We consider the most common, simplest and most mathematically tractable model and the most mathematically clear discretization. In two cases, we prove such an error estimate and carefully detail why our argument fails in the most general case. Our analysis aims to assume as little time regularity on the true solution as possible.

**Keywords:** large eddy simulation, Navier-Stokes equations, turbulence, finite element methods

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